Strong coupling effects in quantum thermal transport with the reaction coordinate method

Anto-Sztrikacs, Nicholas; Segal, Dvira

doi:10.1088/1367-2630/ac02df

Cited by 31 publications

(21 citation statements)

References 62 publications

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“…The reaction coordinate approach is a non-perturbative approach to dealing with intermediate and strongly coupled systems. It was originally developed quite some time ago 246,247 but has recently been much extended to various applications in the quantum thermodynamic context 21,24,25,[248][249][250][251][252][253][254][255] . The basic idea is to redefine that part of the bath B that contributes most strongly to the system-bath coupling into a collective single degree of freedom, the reaction coordinate (RC).…”

Section: Reaction Coordinate Approachmentioning

confidence: 99%

Open quantum system dynamics and the mean force Gibbs state

Trushechkin,

Merkli,

Cresser

et al. 2021

Preprint

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The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a standard assumption across all of the physical sciences. The Gibbs state is determined just by temperature and the system's energies alone. But at decreasing system sizes, i.e. for nanoscale and quantum systems, the interaction with their environments is not negligible. The question then arises: Is the system's steady state still the Gibbs state? And if not, how may the steady state depend on the interaction details? Here we provide an overview of recent progress on answering these questions. We expand on the state-of-the-art along two general avenues: First we take the static point-of-view which postulates the so-called mean force Gibbs state. This view is commonly adopted in the field of strong coupling thermodynamics, where modified laws of thermodynamics and non-equilibrium fluctuation relations are established on the basis of this modified state. Second, we take the dynamical point-of-view, originating from the field of open quantum systems, which examines the time-asymptotic steady state within two paradigms. We describe the mathematical paradigm which proves return to equilibrium, i.e. convergence to the mean force Gibbs state, and then discuss a number of microscopic physical methods, particularly master equations. We conclude with a summary of established links between statics and equilibration dynamics, and provide an extensive list of open problems. This comprehensive overview will be of interest to researchers in the wider fields of quantum thermodynamics, open quantum systems, mesoscopic physics, statistical physics and quantum optics, and will find applications whenever energy is exchanged on the nanoscale, from quantum chemistry and biology, to magnetism and nanoscale heat management.

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Section: Reaction Coordinate Approachmentioning

confidence: 99%

Open quantum system dynamics and the mean force Gibbs state

Trushechkin,

Merkli,

Cresser

et al. 2021

Preprint

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“…A recent alternative numerical method, TEMPO, is based on time-evolving matrix product operators [68], and can efficiently describe the time evolution of quantum systems coupled to a non-Markovian harmonic environment. Furthermore, analytical approaches to solve the dynamics when the coupling is no longer weak could be based on reaction coordinate methods [15,16,39,40,[69][70][71][72][73][74][75].…”

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confidence: 99%

Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State

Cresser

Anders

2021

Phys. Rev. Lett.

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The Gibbs state is widely taken to be the equilibrium state of a system in contact with an environment at temperature T. However, non-negligible interactions between system and environment can give rise to an altered state. Here, we derive general expressions for this mean force Gibbs state, valid for any system that interacts with a bosonic reservoir. First, we derive the state in the weak coupling limit and find that, in general, it maintains coherences with respect to the bare system Hamiltonian. Second, we develop a new expansion method suited to investigate the ultrastrong coupling regime. This allows us to derive the explicit form for the mean force Gibbs state, and we find that it becomes diagonal in the basis set by the systemreservoir interaction instead of the system Hamiltonian. Several examples are discussed including a single qubit, a three-level V-system, and two coupled qubits all interacting with bosonic reservoirs. The results shed light on the presence of coherences in the strong coupling regime, and provide key tools for nanoscale thermodynamics investigations.

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“…Since the method enables cheap computations, it has been used in studies involving strongly-coupled system-reservoirs. For example, it was utilized for studying quantum dynamics and steady state behavior of impurity models [16][17][18] , thermal transport in nanojunctions 19,20 , the operation of quantum thermal machines [21][22][23][24] , transport in electronic systems [25][26][27] . Besides capturing system-bath coupling to high orders, the RC-QME method reports on non-Markovian effects 28 .…”

Section: Introductionmentioning

confidence: 99%

“…The RC method was recently implemented for studying the nonequilibrium spin-boson model (NESB) at strong coupling 20 , a quintessential model in the quantum thermodynamics field. The model includes an impurity two-level system (spin) interacting with two thermal harmonic-oscillator environments held at different temperatures, allowing for a steady state heat current to flow from one reservoir to the other.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Thermal Transport Beyond Second Order with the Reaction Coordinate Mapping

Anto-Sztrikacs,

Ivander,

Segal

2022

Preprint

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Standard quantum master equation techniques such as the Redfield or Lindblad equations are perturbative to second order in the microscopic system-reservoir coupling parameter λ . As a result, characteristics of dissipative systems, which are beyond second order in λ , are not captured by such tools. Moreover, if the leading order in the studied effect is higher-than-quadratic in λ , a second-order description fundamentally fails even at weak coupling. Here, using the reaction coordinate (RC) quantum master equation framework, we are able to investigate and classify higherthan-second order transport mechanisms. This technique, which relies on the redefinition of the system-environment boundary, allows for the effects of system-bath coupling to be included to high orders. We study steady-state heat current beyond second-order in two models: The generalized spin-boson model with non-commuting system-bath operators and a three-level ladder system. In the latter model heat enters in one transition and it is extracted from a different one. Crucially, we identify two transport pathways: (i) System's current, where heat conduction is mediated by transitions in the system, with the heat current scaling as j q ∝ λ 2 to lowest order in λ . (ii) Inter-bath current, with the thermal baths directly exchanging energy between them, facilitated by the bridging quantum system. To the lowest order in λ , this current scales as j q ∝ λ 4 . These mechanisms are uncovered and examined using numerical and analytical tools. We contend that the RC mapping brings already at the level of the mapped Hamiltonian much insights on transport characteristics.

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Strong coupling effects in quantum thermal transport with the reaction coordinate method

Cited by 31 publications

References 62 publications

Open quantum system dynamics and the mean force Gibbs state

Open quantum system dynamics and the mean force Gibbs state

Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State

Quantum Thermal Transport Beyond Second Order with the Reaction Coordinate Mapping

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