# Schedule for: 19w5016 - Charge and Energy Transfer Processes: Open Problems in Open Quantum Systems

Beginning on Sunday, August 18 and ending Friday August 23, 2019

All times in Banff, Alberta time, MDT (UTC-6).

Sunday, August 18 | |
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16:00 - 17:30 | Check-in begins at 16:00 on Sunday and is open 24 hours (Front Desk - Professional Development Centre) |

17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |

20:00 - 22:00 | Informal gathering (Corbett Hall Lounge (CH 2110)) |

Monday, August 19 | |
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07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |

08:45 - 09:00 |
Introduction and Welcome by BIRS Staff ↓ A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions. (TCPL 201) |

09:00 - 09:30 |
Marco Merkli: Quantum resonance theory of open system dynamics ↓ We present a mathematical method allowing to prove the validity of the Markovian approximation for an $N$-level quantum system in contact with thermal reservoirs. The true system dynamics is approximated by a completely positive, trace preserving dynamical group $f\!or\ all\ times\ t\ge0$, provided the system-reservoir coupling $\lambda$ is small but fixed. No weak coupling condition $\lambda^2 t\lesssim {\rm const.}$ is imposed. (TCPL 201) |

09:30 - 10:00 |
Francesco Petruccione: Open Quantum Walks: a short review and some recent results ↓ After a brief review of the theory of open quantum walks, we present some recent results, some potential applications, and some open problems. (TCPL 201) |

10:00 - 10:30 | Coffee Break (TCPL Foyer) |

10:30 - 11:00 |
Christiane Koch: Fast and accurate qubit reset via optimal control - where quantum information meets open quantum systems ↓ The ability to quickly and reliably reset qubits is a basic prerequisite in quantum information science. The key question is: How fast can we export entropy in order to purify a qubit and erase its correlations with the environment? We address this question for a qubit which interacts with a structured environment, using a combination of geometric and numerical optimal control theory. Starting from the scenario of quantum reservoir engineering where the coupling between qubit and environment is tunable, we find the optimized reset strategy to consist in maximizing the decay rate from one state and driving non-adiabatic population transfer into the strongly decaying state. We then consider the simplest paradigm of non-Markovian dynamics where the qubit is coupled to the environment via an ancilla. We derive time-optimal reset protocols and find, for factorizing initial states, a lower limit for the entropy reduction as well as a speed limit. Initial correlations, remarkably, allow for faster reset and smaller errors. Use of the Cartan decomposition of su(4) allows us to generalize our findings to all conceivable qubit drives and qubit-ancilla interactions. (TCPL 201) |

11:30 - 13:00 |
Lunch ↓ Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |

13:00 - 14:00 |
Guided Tour of The Banff Centre ↓ Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus. (Corbett Hall Lounge (CH 2110)) |

14:00 - 14:20 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL 201) |

14:20 - 14:50 |
Martin B Plenio: Efficient Numerical Methods for Extended System in Contact with non-Markovian Environments ↓ In this lecture I will present the time evolving density operator method with orthogonal polynomials [1-3] and the most recent developments of this method to spatially extended systems [4] as well as arbitrary temperatures [5, 6] and fermionic environments [7].
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[1] J. Prior, A.W. Chin, S.F. Huelga and M.B. Plenio. Efficient simulation of strong system-environment interactions. Phys. Rev. Lett. 105, 050404 (2010)
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[2] A.W. Chin, A. Rivas, S.F. Huelga and M.B. Plenio. Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials. J. Math. Phys. 51, 092109 (2010)
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[3] A.W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S.F. Huelga and M.B. Plenio. The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes. Nature Physics 9, 113 - 118 (2013)
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[4] A. Somoza-Marquez, O. Marty, J. Lim, S.F. Huelga, and M.B. Plenio. Dissipation assisted matrix product factorization. To appear in Phys. Rev. Lett. (2019) and E-print arXiv:1903.05443
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[5] D. Tamascelli, A. Smirne, S.F. Huelga and M.B. Plenio. Non-perturbative treatment of non-Markovian dynamics of open quantum systems. Phys. Rev. Lett. 120, 030402 (2018)
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[6] D. Tamascelli, A. Smirne, S.F. Huelga and M.B. Plenio, Efficient simulation of finite-temperature open quantum systems. To appear in Phys. Rev. Lett. (2019) and E-print arXiv:1811.12418
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[7] A. Nüßeler, I. Dhand, S.F. Huelga and M.B. Plenio. Fermionic TEDOPA. In preparation (TCPL 201) |

15:00 - 15:30 | Coffee Break (TCPL Foyer) |

15:30 - 16:00 |
Jonathan Keeling: Efficient non-Markovian quantum dynamics using time-evolving matrix product operators ↓ In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. I will describe our novel approach to this problem, a general and yet exact numerical approach that efficiently describes the time evolution of a quantum system coupled to a non-Markovian harmonic environment [1]. Our method relies on expressing the system state and its propagator as a matrix product state and operator, respectively, and using a singular value decomposition to compress the description of the state as time evolves. This is based on an approach developed by Makri and Makaraov [2], but re-expressed in the language of tensor networks, providing several orders of magnitude improvement in the size of problem that can be addressed. I will present a number of examples using this method which demonstrate the power and flexibility of our approach, including the localization transition of the Ohmic spin-boson model, and applications to time-dependent problems.
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[1] A. Strathearn, P. Kirton, D. Kilda, J. Keeling & B. W. Lovett. Nat. Comm. 9, 3322 (2018)
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[2] N. Makri & D. E. Makarov. J. Chem. Phys. 102, 4600 (1995); ibid 4611 (1995). (TCPL 201) |

16:00 - 16:30 |
David Limmer: Unravelled master equations for the study of photoisomerization pathways in the condensed phase ↓ In this talk, I will present our recent work developing hybrid master equations to study the relaxation dynamics through conical intersections. These approaches leverage a separation of time an energy scales to treat different degrees of freedom at applicable levels of approximation. The quantum master equation approaches can be further unravelled into stochastic wavefunction methods, defining a trajectory space that can be conditioned on various outcomes. This enables the extension of transition path theory into the realm of quantum dynamics. (TCPL 201) |

16:30 - 17:00 |
Dominique Spehner: Adiabatic transitions of a two-level system coupled to a free Boson reservoir ↓ We consider a slowly varying time-dependent two-level open quantum
system coupled to a free boson reservoir.
The coupling to the reservoir is energy conserving and also depends
slowly on time, with the same adiabatic parameter $\epsilon$ as for the
system Hamiltonian.
Assuming that the reservoir is initially decoupled from the system and
in the vacuum state,
we compute the transition probability from one eigenstate of the
two-level system to the other eigenstate at some later time in the limit
of small
$\epsilon$ and small coupling constant $\lambda$, and analyse the
deviations from the adiabatic transition probability obtained in absence
of the reservoir.
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This is joint work with A. Joye and M. Merkli (TCPL 201) |

17:00 - 17:30 |
Alain Joye: Nonlinear Quantum Adiabatic Approximation ↓ We consider the adiabatic limit of a nonlinear Schrödinger equation in which the Hamiltonian depends on time and on a finite number of components of the wave function. We show the existence of instantaneous nonlinear eigenvectors and of solutions which remain close those, up to a rapidly oscillating phase in the adiabatic regime. Consequences on the energy content of the solutions are spelled out.
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This is joint work with Clotilde Fermanian (TCPL 201) |

17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |

Tuesday, August 20 | |
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07:00 - 09:00 | Breakfast (Vistas Dining Room) |

09:00 - 09:30 |
Janet Anders: Energetic footprints of coherence and irreversibility in the quantum regime ↓ In this quantum thermodynamics [1] talk, I will discuss work extraction in the quantum regime. We set up an optimal quantum thermodynamic process that removes quantum information in analogy to Landauer’s erasure of classical information. The thermodynamic analysis of this optimal process uncovers that work can be extracted from quantum coherences in addition to the work that can be extracted from classical non-equilibrium states [2].
In the second part of the talk I will discuss how the unavoidable presence of irreversibility affects entropic and energetic exchanges during a non-optimal protocol. I will show that the heat footprint of quantum irreversibility differs markedly from the classical case [3]. The analysis is made possible by employing quantum trajectories that allow to construct distributions for classical heat and quantum heat exchanges. We also quantify how the occurrence of quantum irreversibility reduces the amount of work that can be extracted from a state with coherences. Our results show that decoherence leads to both entropic and energetic footprints which play an important role in the optimization of controlled quantum operations at low temperature, including quantum processors.
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[1] Quantum thermodynamics, S. Vinjanampathy, J. Anders, Contemporary Physics 57, 545 (2016).
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[2] Coherence and measurement in quantum thermodynamics, P. Kammerlander, J. Anders, Scientific Reports 6, 22174 (2016).
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[3] Energetic footprints of irreversibility in the quantum regime, H. Mohammady, A. Auffeves, J. Anders, arXiv:1907.06559 (TCPL 201) |

09:55 - 10:25 |
Luis A. Correa: Classical emulation of quantum-coherent thermal machines ↓ The performance enhancements observed in various models of continuous quantum thermal machines have been linked to the buildup of coherences in a preferred basis. But, is this connection always an evidence of 'quantum-thermodynamic supremacy'? By force of example, we show that this is not the case. In particular, we compare a power-driven three-level continuous quantum refrigerator with a four-level combined cycle, partly driven by power and partly by heat. We focus on the weak driving regime and find the four-level model to be superior since it can operate in parameter regimes in which the three-level model cannot, it may exhibit a larger cooling rate, and, simultaneously, a better coefficient of performance. Furthermore, we find that the improvement in the cooling rate matches the increase in the stationary quantum coherences exactly. Crucially, though, we also show that the thermodynamic variables for both models follow from a classical representation based on graph theory. This implies that we can build incoherent stochastic-thermodynamic models with the same steady-state operation or, equivalently, that both coherent refrigerators can be emulated classically. More generally, we prove this for any $N$-level weakly driven device with a 'cyclic' pattern of transitions. Therefore, even if coherence is present in a specific quantum thermal machine, it is often not essential to replicate the underlying energy conversion process. (TCPL 201) |

10:00 - 10:30 | Coffee Break (TCPL Foyer) |

10:55 - 11:25 |
Ronnie Kosloff: The quantum Carnot engine and its quantum signature ↓ Quantum thermodynamics follows the tradition of learning by example. The Carnot cycle would
be a primary candidate. The attempts to model the four stroke quantum Carnot cycle failed due
to the diculty to model the isothermal branches, where the working medium is driven while in
contact to the thermal bath. Motivated by this issue we derived a time dependent Non Adiabatic
Master Equation (NAME) [1] with a xed driving protocol. This master equation is consistent with
thermodynamic principles. We then were able to generalise to protocols with small acceleration
with respect to the xed fast protocols. This approach was conrmed experimentally in a driven
Ytterbium ion in a Paul trap[2]. Using this construction we are able to nd shortcuts to an isothermal
transformation [3]. Unlike unitary transformations the map changes entropy. After this journey, we
are able close a Carnot like cycle in nite time and explore its performance. We are also able to
identify the quantum signature of the cycle at very short cycle times [4].
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[1] R. Dann, A. Levy, and R. Kosloff, Physical Review A 98, 052129 (2018).
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[2] C.-K. Hu, R. Dann, J.-M. Cui, Y.-F. Huang, C.-F. Li, G.-C. Guo, A. C. Santos, and R. Koslo, arXiv preprint
arXiv:1903.00404 (2019).
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[3] R. Dann, A. Tobalina, and R. Kosloff, Physical Review Letters 122, 250402 (2019).
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[4] R. Dann and R. Kosloff, arXiv preprint arXiv:1906.06946 (2019). (TCPL 201) |

11:30 - 13:30 | Lunch (Vistas Dining Room) |

13:30 - 14:00 |
Jianshu Cao: Quantum Coherence in Light-harvesting Energy Transfer ↓ Quantum coherence in light-harvesting complexes is explored in a minimal model of V-shape
three-level system. We systematically solve the model to predict both its transient and steadystate
coherences and demonstrate the interplay of exciton trapping at the reaction center and
the non-canonical distribution due to the system-bath coupling [1,2]. Further, we analyze the
efficiency and energy flux of the three-level model and show the optimal performance in the
intermediate range of temperature and coupling strength, consistent with our understanding of
quantum heat engines. [3] Finally, if time allows, we will explain how to generalize the above
analysis to complex light-harvesting networks using the waiting time distribution function [4].
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[1] Can natural sunlight induce coherent exciton dynamics? Olsina, Dijkstra, Wang, Cao,
arXiv:1408.5385 (2014/2019)
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[2] Non-canonical distribution and non-equilibrium transport beyond weak system-bath
coupling regime: A polaron transformation approach. D. Xu and J. Cao, Front. Phys. 11, 1
(2016)
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[3] Polaron effects on the performance of light-harvesting systems: A quantum heat engine
perspective. D. Xu, C. Wang, Y. Zhao, and J. Cao, New J. Phys. 18, 023003 (2016)
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[4] Correlations in single molecule photon statistics: Renewal indicator. J. Cao, J. Phys.
Chem. B, 110, 19040 (2006) (TCPL 201) |

14:00 - 14:30 |
Javier Cerrillo: Transfer tensor method: efficient simulation of open quantum systems ↓ The transfer tensor method [1] is a compact and intuitive tool for the analysis and simulation of general open quantum systems. By extracting the information contained in short samples of the initial dynamics, it has the ability to extend the simulation power of existing exact approaches, like the chain-mapping DMRG-based simulation method TEDOPA [2] or stochastic methods [3]. Crucially, it can treat problems with initial system-environment correlations, such as emission and absorption spectra of multichromophoric molecules [3]. In combination with the hierarchy of equations of motion, transfer tensors that contain information about energetic and particle currents of the environment may be derived, facilitating quantum transport studies in the strong-coupling and non-Markovian regimes.
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[1] J. Cerrillo, J. Cao, Phys Rev. Lett. 112, 110401 (2014).
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[2] R. Rosenbach, J. Cerrillo, S.F. Huelga, J. Cao, M.B. Plenio, New J. Phys. 18, 023035 (2016).
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[3] M. Buser, J. Cerrillo, G. Schaller, and J. Cao, Phys. Rev. A 96, 062122 (2017). (TCPL 201) |

14:30 - 15:00 |
Philipp Strasberg: Quantum non-Markovianity: A physicist's perspective ↓ The rigorous detection and quantification of non-Markovianity in open quantum systems has recently gained a lot of attention. Despite generating many insights on the mathematical side, the proposed quantifiers of non-Markovianity are very hard to compute in practice and the relation to more traditional quantities of physical interest is not clear. In the first part of my talk I will present a very simple, yet rigorous way to witness non-Markovianty, which is based on linear response theory. In the second part of my talk I will discuss when (and when not) temporal negativities of the entropy production rate imply non-Markovianity. This creates an important link between the mathematical concept of non-Markovianity and a physical observable, which quantifies the overall irreversibility of the open system dynamics. (TCPL 201) |

15:00 - 15:30 | Coffee Break (TCPL Foyer) |

15:30 - 16:00 |
Erik Gauger: Microscopically-derived modelling of quantum networks subject to multiple environments ↓ The interplay between coherent and dissipative processes that governs both bio-inspired as well as engineered quantum networks supports a rich tapestry of non-equilibrium phenomena. These hold promise for enabling quantum-enhanced light harvesting, molecular electronics, generation of thermopower, and nanoscale sensing. A theoretical challenge consists of developing well-founded and tractable models for exploring the dynamics of systems that are simultaneously strongly coupled to more than one environment, for instance through interactions with surrounding electromagnetic and vibrational modes — typical for many networks comprised of condensed matter nanostructures. In this talk, I will cover our recent work in this area, with a particular focus on master equation approaches. (TCPL 201) |

16:00 - 16:30 |
Ahsan Nazir: Environmental non-additivity and strong-coupling in non-equilibrium quantum systems ↓ We consider quantum systems coupled simultaneously to multiple environments. Examples include solid-state photon emitters, with coupling both to vibrations and the electromagnetic field, and molecular nanojunctions, with coupling both to vibrations and electronic leads. We show that enforcing additivity of such combined influences results in non-equilibrium dynamics that does not respect the Franck-Condon principle in the former case, and can lead to unphysical electronic current under equilibrium conditions in the latter. We overcome these shortcomings by employing a collective coordinate representation of the vibrational environment, which permits the derivation of a non-additive master equation. When applied to a two-level emitter our treatment predicts decreasing photon emission rates with increasing vibrational coupling, consistent with Franck-Condon physics. Applied to a molecular nanojunction we employ counting statistics techniques to track electron flow between the system and the electronic leads, revealing both strong-coupling and non-additive effects in the electron current, noise and Fano factor. (TCPL 201) |

16:30 - 17:00 |
Yuta Fujihashi: Intramolecular vibrations complement the robustness of primary charge separation in the photosystem II reaction center ↓ The energy conversion of oxygenic photosynthesis is triggered by primary charge separation in
proteins at the photosystem II reaction center. In this talk, I will discuss the impacts of the protein
environment and intramolecular vibrations on primary charge separation at the photosystem II reaction
center [1]. We report that individual vibrational modes play a minor role in promoting charge
separation, contrary to the discussion in recent publications. Nevertheless, these small contributions
accumulate to considerably influence the charge separation rate, resulting in subpicosecond charge
separation almost independent of the driving force and temperature. We suggest that the intramolecular
vibrations complement the robustness of the charge separation in the photosystem II reaction center
against the inherently large static disorder of the involved electronic energies.
Finally, if time allows, I will talk about our recent work on electronic excitation dynamics triggered
by the interaction with quantum entangled light [2].
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[1] Y. Fujihashi, M. Higashi and A. Ishizaki, J. Phys. Chem. Lett. 9, 4921 (2018).
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[2] Y. Fujihashi, R. Shimizu and A. Ishizaki, arXiv: 1904.11669 (2019). (TCPL 201) |

17:00 - 17:30 |
Gabriel Hanna: Mixed quantum-classical simulations of nonequilibrium heat transport in molecular junctions ↓ The study of nonequilibrium heat transport in molecular junctions (MJs) has gathered much attention in recent years due to its crucial role in the field of molecular electronics. To gain insight into the factors determining the heat currents in MJs, reduced models of MJs have been studied using both approximate and exact quantum dynamical methods. One such model, known as the nonequilibrium spin-boson (NESB) model, consists of a two-level system in contact with two harmonic oscillator baths at different temperatures. Recently, we developed a mixed quantum-classical framework for studying heat transport in MJs, which could enable the simulation of heat transport in more realistic models of MJs with many degrees of freedom [1]. In this talk, I will give an overview of this framework and discuss the ability of a novel mixed quantum-classical dynamics method, known as Deterministic Evolution of Coordinates with Initial Decoupled Equations (DECIDE) [2], for calculating the steady-state heat current in the NESB model in a variety of parameter regimes [3].
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[1] Liu, J., Hsieh, C-Y., Segal, D., Hanna, G., J. Chem. Phys, 149, 224104 (2018).
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[2] Liu, J., Hanna, G., J. Phys. Chem. Lett., 9, 3928 (2018).
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[3] Carpio-Martinez, P., Hanna, G., J. Chem. Phys, in press. (TCPL 201) |

17:30 - 19:30 | Dinner (Vistas Dining Room) |

Wednesday, August 21 | |
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07:00 - 09:00 | Breakfast (Vistas Dining Room) |

09:00 - 09:30 |
Takaaki Aoki: Quantum time-dependent temperature ↓ We consider one harmonic oscillator attached to a bath of many harmonic oscillators. We define a time-dependent temperature of the oscillator and show that the temperature
relaxes to that of the bath. (TCPL 201) |

09:30 - 10:00 |
Naomichi Hatano: Exceptional points of the Lindblad operator of a two-level system ↓ The Lindblad equation for a two-level system under an electric field is analyzed by mapping it to a linear equation with a non-Hermitian matrix. Exceptional points of the matrix are found to be extensive; the second-order ones are located on lines in a two-dimensional parameter space, while the third-order one is at a point. (TCPL 201) |

10:00 - 10:30 | Coffee Break (TCPL Foyer) |

10:30 - 11:00 |
Abraham Nitzan: Quantum thermodynamics of strongly coupled driven resonant level models ↓ The driven resonance level model (a driven molecular level coupled to one or more fermionic baths) has been recently used to study thermodynamic aspects of energy conversion in simple mechanically driven strongly coupled quantum systems. Our original treatment of this problem was based on the non-equilibrium Green function (NEGF) approach[1]. In this talk I will discuss this model using other methodologies that reveal different physical aspects of this problem. First, I will describe an approach[2] based on an expansion of the full system-bath density matrix as a series in powers of the modulation rate, from which the functional form of work, heat, and entropy production rates can be obtained. This approach allows for the inclusion of electron-electron interaction in an approximate way. Second, I repeat the derivation by expressing the density matrix in terms of the asymptotic eigenstates of the system by employing Moller transition operators [3]. The resulting expression, which coincides with results from the steady-state theories of McLean – Zubarev and Hershfield, can reproduce the standard NEGF results for the dot population and the current and, when extended to include driving of the dot energy level and/or the dot-leads coupling, yields the non-adiabatic (second order to the driving speed) corrections to the power, energy and heat production obtained from the NEGF formalism. Using this approach we can easily go beyond the wide band approximation and consider models where the dot is coupled to many leads held at different temperatures and under different chemical potentials. Finally, we employ a numerical solution based on the driven-Liouville-von Neumann approach, which can be used to investigate systems subjected to high driving speeds.
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[1] A. Bruch, M. Thomas, S. V. Kusminsky, F. von Oppen and A. Nitzan, Phys. Rev. B, 93, 115318 (2016); M A. Ochoa, A. Bruchand A. Nitzan, Phys. Rev. B 94, 035420 (2016)
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[2] W. Dou, M. A. Ochoa,A. Nitzan and J. E. Subotnik, Phys. Rev. B 98, 134306 (2018)
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[3] A. Semenov and A. Nitzan, to be published
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[4] I. Oz, O. Hod and A. Nitzan, Molecular Physics, in press, and to be published. (TCPL 201) |

11:00 - 11:30 |
Roman Krems: Bayesian optimization for inverse problems in quantum dynamics ↓ Machine learning models are usually trained by a large number of observations
(big data) to make predictions through the evaluation of complex mathematical
objects. However, in many applications in science, particularly in quantum
dynamics, obtaining observables is expensive so information is limited. In the
present work, we consider the limit of ‘small data’. Usually, ‘big data’ are
for machines and ‘small data’ are for humans, i.e. humans can infer physical
laws given a few isolated observations, while machines require a huge array of
information for accurate predictions. Here, we explore the possibility of
machine learning that could build physical models based on very restricted
information.
In this talk, I will show how to build such models using Bayesian machine
learning and how to apply such models to inverse problems aiming to infer the
Hamiltonians from the dynamical observables. I will illustrate the methods by
two applications: (1) the inverse problem in quantum reaction dynamics aiming
to construct accurate potential energy surfaces based on reaction dynamics
observables; (2) the model selection problem aiming to derive the particular
lattice model Hamiltonian that gives to rise to specific quantum transport
properties for particles in a phonon field. (TCPL 201) |

11:30 - 13:30 | Lunch (Vistas Dining Room) |

13:30 - 17:30 | Free Afternoon (Banff National Park) |

17:30 - 19:30 | Dinner (Vistas Dining Room) |

Thursday, August 22 | |
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07:00 - 09:00 | Breakfast (Vistas Dining Room) |

09:00 - 09:30 |
Giuseppe Luca Celardo: Macroscopic coherence as an emergent property in molecular nanotubes ↓ Nanotubular molecular self-aggregates are characterized by a high degree of symmetry and they are fundamental systems for light-harvesting and energy transport.
While coherent effects are thought to be at the basis of their high efficiency, the relationship between structure, coherence and functionality is still an open problem.
We analyze natural nanotubes present in Green Sulfur Bacteria. We show that they have the ability to support macroscopic coherent states,
i.e. delocalized excitonic states coherently spread over many molecules, even at room temperature.
Specifically, assuming a canonical thermal state we find, in natural structures, a large thermal coherence length, of the order of 1000 molecules.
By comparing natural structures with other mathematical models, we show that
this macroscopic coherence cannot be explained either by the magnitude of the nearest-neighbour coupling between the molecules, which would
induce a thermal coherence length of the order of 10 molecules, or by the presence of long-range interactions between the molecules.
Indeed we prove that the existence of macroscopic coherent states is an emergent property of such structures due to the interplay between geometry and cooperativity (superradiance and super-transfer).
In order to prove that, we give evidence that the lowest part of the spectrum of natural systems is determined by a cooperatively enhanced coupling (super-transfer) between the eigenstates of modular sub-units of the whole structure.
Due to this enhanced coupling strength, the density of states is lowered close to the ground state, thus boosting the thermal coherence length.
As a striking consequence of the lower density of states, an energy gap between the excitonic ground state and the first excited state emerges. Such energy gap increases with the length of the nanotube (instead of decreasing as one would expect), up to a critical system size which is close to the length of the natural complexes considered.
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VIDEO-ABSTRACT: https://vimeo.com/313618747
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REFERENCES:
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1) Macroscopic coherence as an emergent property in molecular nanotubes, M. Gull; A. Valzelli; F. Mattiotti; M. Angeli; F. Borgonovi and G. L. Celardo; New J. Phys. 21 013019 (2019).
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2) On the existence of superradiant excitonic states in microtubules G. L. Celardo; M. Angeli; T. J. A. Craddock and P. Kurian New J. Phys. 21 023005 (2019). (TCPL 201) |

09:30 - 10:00 |
Géraldine Haack: Autonomous entanglement engines: open questions raised by the use of the reset master equation ↓ Entanglement is a key phenomenon distinguishing quantum from classical physics, and is a paradigmatic resource enabling many applications of quantum information science. Generating and maintaining entanglement is therefore a central challenge.
In the past years, with my colleagues in Geneva and Vienna, we have proposed a series of autonomous thermal machines that allow to generate in the steady-state regime quantum correlations between two or more quantum systems (that can be of arbitrary dimension) [1-3]. In contrast to other proposals towards nanoscale thermal machines, these ones have a genuine quantum output and do not have a classical counterpart. They are now often referred to as entanglement engines.
In this talk, I will present the general functioning of those entanglement engines. In particular, their dynamics and the steady-state regime were investigated using a reset evolution equation which describes in a probabilistic and phenomenological way the interaction of a quantum system with an environment. The use and validity of this reset equation with respect to the laws of thermodynamics open new questions and will be discussed, in particular with respect to local detailed balance condition and the entropy balance [4].
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[1] J. Bohr Brask, G. Haack, N. Brunner, M. Huber, NJP 17 (2015)
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[2] A. Tavakoli, G. Haack, M. Huber, N. Brunner, J. Bohr Brask, Quantum 2 (2018)
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[3] A. Tavakoli, G. Haack, N. Brunner, J. Bohr Brask, arXiv:1906.00022 (2019)
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[4] G. Haack et al., on going work. (TCPL 201) |

10:00 - 10:30 | Coffee Break (TCPL Foyer) |

10:30 - 11:00 |
Andrew Kent Harter: Floquet edge state protection in non-Hermitian topological systems ↓ In previous works [1], we have considered a two-level system with time periodic (Floquet), PT-symmetric [2] gain and loss. Although this system is generically non-Hermitian, at any instant, the system may be in a broken or unbroken PT-symmetric phase, and its long-term behavior is governed by an effective Floquet Hamiltonian. Interestingly, the PT phase diagram for this system features a re-entrant PT unbroken phase, in which, as the driving frequency is swept from zero (static) to near the natural resonance frequency, the system enters the PT-broken phase; however, if the driving frequency is sufficiently increased, the system will re-enter the PT-unbroken phase again. By extension, one can apply a PT-symmetric, Floquet driving to the one-dimensional Su-Schrieffer-Heeger (SSH) model, which exhibits a topologically nontrivial phase. In the static case [3], the edge states are pushed into far ends of the energy spectrum in the imaginary plane [4]; however, in the time-periodic case, the Floquet energy spectrum provides a stabilizing, periodically-repeating structure in the frequency domain. At high enough driving frequencies, the non-Hermitian dynamics can stabilize, leading to a completely real spectrum [5]. Specifically, in our study, we used a simplified, pulsed time dependence allowing us to analyze the viability of the topologically relevant states for a broad range of driving frequencies which can be below the critical high-frequency threshold.
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[1] Li, J., Harter, A., Liu, J., de Melo, L., Joglekar, Y. and Luo, L. Nat. Comms. 10, 855, (2019)
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[2] Bender, C. and Boettcher, S. Phys. Rev. Lett. 80, 5243 (1998)
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[3] Rudner, M. S. and Levitov, L. S. Phys. Rev. Lett. 102, 065703 (2009)
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[4] Hu, Y. C. and Hughes, T. L. Phys. Rev. B 84, 153101 (2011)
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[5] C. Yuce, Eur. Phys. J. D 69, 184 (2015) (TCPL 201) |

11:00 - 11:30 | Jean-Bernard Bru: Macroscopic Long-Range Dynamics of Fermions and Quantum Spins on the Lattice (TCPL 201) |

11:30 - 13:30 | Lunch (Vistas Dining Room) |

13:30 - 14:00 | Michael Thorwart: Is the dynamics of biomolecular excitons quantum coherent? (TCPL 201) |

14:00 - 14:30 |
David Coker: First Principles Model Hamiltonian Ensembles for Light Harvesting: Modeling Dissipative Down Conversion - Signatures of Vibronic Energy Transfer in Nonlinear 2DES Signals - CSDM+PLDM ↓ Accurate model Hamiltonians for excitation energy transfer, including vibronic transitions, in a variety of down-conversion pigment-protein complexes are parameterized, using Molecular Dynamics and first principles calculations. Semi-classical methods based on a new hybrid partial linearized and coherent state density matrix dynamics approach are outlined and used to compute non-linear 2D electronic spectra for these models elucidating the signatures of excitonic and vibronic energy transfer in these systems. Results are analyzed in terms of simple models for dissipative electronic and vibronic dynamics. (TCPL 201) |

14:30 - 15:00 |
Aaron Kelly: Approximate quantum dynamics simulation methods for charge and energy transport ↓ A selection of recently developed approaches for simulating nonequilibrium quantum dynamics will be discussed. The unifying feature that these methods share is an ensemble of trajectories that is employed in order to construct observables and transport properties. We will explore the performance of selected techniques of this type in a variety of nonadiabatic charge and energy transfer processes, including cavity-bound spontaneous emission, charge separation and polaron formation donor-acceptor interfaces, and heat transport through molecular junctions. (TCPL 201) |

15:00 - 15:30 | Coffee Break (TCPL Foyer) |

15:30 - 16:00 |
Paul Brumer: The Steady State Induced by Natural Incoherent Light: Rates, Dynamics and Coherences ↓ Processes induced by natural light (e.g. photosynthesis, vision) display
properties distinct from those often studied in the laboratory using
pulsed laser irradiation. The natural processes display complexities
associated with systems operating in steady state and coupled to both
an irradiative bath as well as a thermal protein environment.
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We have examined assorted problems associated with such systems, such
as the presence or absence of stationary coherences, tests for the range of
validity of secular vs nonsecular treatments, the generation of coherences
under naturally slow turn-on of the radiation, rates of radiationless
process under solar radiation, etc. Several of these will be described
in this talk, with the remainder left for discussion during the meeting. (TCPL 201) |

16:00 - 16:30 |
Qiang Shi: Charge and energy transfer dynamics in condensed phase using the non-perturbative hierarchical equations of motion approach ↓ Charge transfer dynamics play an important role in organic semiconductor materials and devices. I will present some recent progresses in theoretical studies of charge transfer dynamics in different systems: (1) Real time charge separation dynamics at the donor/acceptor interface in organic photovoltaic (OPV) devices. Charge separation dynamics with multiple timescales are indentified, including an ultrafast component within hundreds of femtoseconds, an intermediate component related to the relaxation of the hot charge transfer (CT) state, and a slow component on the timescale of tens of picoseconds from the thermally equilibrated CT state. Effects of hot exciton dissociation, as well as its dependence on the energy offset between the Frenkel exciton and the CT state are also analyzed.（2）Non-pertubative memory kernels and generating functions to study the charge transfer dynamics. By using the hierarchical equation of motion (HEOM) and extended HEOM methods, we present a new approach to calculate the exact time non-local and time-local memory kernels and their high order perturbative expansions. The new approach is applied to the spin-boson model with different sets of parameters, a model of excitation energy transfer in the Fenna-Matthews-Olson complex, and a model of electron transport in molecular junctions. (TCPL 201) |

16:30 - 17:00 |
Dvira Segal: Full counting statistics of charge and energy transport: Methods and applications ↓ Methods developed to study the dynamics of open quantum systems can be generalized to hand over
the probability distribution function of integrated currents. Considering steady state transport of
particles and energy, I will describe benefits of the full counting statistics (FCS) approach:
(i) It may be easier in fact to evaluate the cumulant generating function - than study directly-individually
the averaged current and its noise.
(ii) By verifying the steady state fluctuation symmetry we can validate the thermodynamics consistency our approximations.
(iii) We automatically generate high order cumulants beyond the averaged current.
I will describe our studies of FCS in charge and energy transport problems, and portray several applications including derivation of the delta-T electronic shot noise, analysis of the anomalous electronic noise, and studies of fluctuations - entropy production trade-off relations. (TCPL 201) |

17:30 - 19:30 | Dinner (Vistas Dining Room) |

Friday, August 23 | |
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07:00 - 09:00 | Breakfast (Vistas Dining Room) |

09:00 - 09:30 |
Naomichi Hatano: A non-Markovian Analysis of Quantum Otto Engine ↓ We consider a quantum version of the Otto engine, in which we use a non-Markovian time-evolution equation
for the contact of the system with heat baths. We show that the engine can have a high heat efficiency
when the contact with the hot bath is short by taking advantage of an energy backflow that temporarily
breaks the second law of thermodynamics. (TCPL 201) |

09:30 - 10:00 |
Jianshu Cao: Stochastic Formalism and Simulation of Quantum Dissipative Dynamics ↓ Our starting point is a stochastic decomposition scheme to study dissipative
dynamics of an open system. In this scheme, any two-body interactions between
constituents of the quantum system can be decoupled with a common white
noise that acts on the two individual subsystems.
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(I) Using the decomposition scheme, we obtain a stochastic–differential
equation, which reduces to generalized hierarchical equations of
motion (GHEOM) and thus represents a unified treatment of boson,
fermion, and spin baths.[1] Applications of GHEOM to spin baths
confirm the scaling relation that maps spin baths to boson baths and
characterizes anharmonic effects often associated with low-frequency
or strong coupling spin modes. [2]
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(II) The decomposition scheme also leads to the stochastic path integral
approach, which directly simulates quantum dissipation with complex
noise. The approach is applied successfully to obtain the equilibrium
density matrix, multichomophoric spectra, and Forster energy transfer
rate. [3] For real time propagation, we demonstrate the advantages of
combining stochastic path integrals, deterministic quantum master
equations [4], and possibly the transfer tensor method [5].
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[1] A unified stochastic formalism of quantum dissipation: I. Generalized
Hierarchical equation, Hsien and Cao, JCP 148, p014103 (2018)
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[2] A unified stochastic formalism of quantum dissipation: II. Beyond linear
response of spin baths. Hsien and Cao, JCP 148, p014104 (2018)
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[3] Equilibrium-reduced density matrix formulation: Influence of noise, disorder,
and temperature on localization in excitonic systems. J. Moix, Y. Zhao, and J.
Cao, Phys. Rev. B 85, 115412 (2012)
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[4] A hybrid stochastic hierarchy equations of motion approach to treat the low
temperature dynamics of non-Markovian open quantum systems. J. M. Moix and
J. Cao, J. Chem. Phys. 139, 134106 (2013)
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[5] Non-Markovian dynamical maps: Numerical processing of open quantum
trajectories. J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014) (TCPL 201) |

10:00 - 10:30 | Coffee Break (TCPL Foyer) |

10:30 - 11:30 | Discussion (TCPL 201) |

11:30 - 12:00 |
Checkout by Noon ↓ 5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon. (Front Desk - Professional Development Centre) |

12:00 - 13:30 | Lunch from 11:30 to 13:30 (Vistas Dining Room) |