Exact finite-time correlation functions for multi-terminal setups: Connecting theoretical frameworks for quantum transport and thermodynamics

• URL: http://arxiv.org/abs/2312.15065v3
• Date: Wed, 29 May 2024 12:32:54 GMT
• Title: Exact finite-time correlation functions for multi-terminal setups: Connecting theoretical frameworks for quantum transport and thermodynamics
• Authors: Gianmichele Blasi, Shishir Khandelwal, Géraldine Haack,
• Abstract summary: Transport in open quantum systems can be explored through various theoretical frameworks, including the quantum master equation, scattering matrix, and Heisenberg equation of motion. Existing literature treats these approaches independently, lacking a unified perspective. Our work addresses this gap by clarifying the role and status of these approaches using a minimal single-level quantum dot model in a two-terminal setup.
• Score: 11.061707876645764
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Transport in open quantum systems can be explored through various theoretical frameworks, including the quantum master equation, scattering matrix, and Heisenberg equation of motion. The choice of framework depends on factors such as the presence of interactions, the coupling strength between the system and environment, and whether the focus is on steady-state or transient regimes. Existing literature treats these frameworks independently, lacking a unified perspective. Our work addresses this gap by clarifying the role and status of these approaches using a minimal single-level quantum dot model in a two-terminal setup under voltage and temperature biases. We derive analytical expressions for particle and energy currents and their fluctuations in both steady-state and transient regimes. Exact results from the Heisenberg equation are shown to align with scattering matrix and master equation approaches within their respective validity regimes. Crucially, we establish a protocol for the weak-coupling limit, bridging the applicability of master equations at weak-coupling with Heisenberg or scattering matrix approaches at arbitrary coupling strength.

Related papers

• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Markovian dynamics for a quantum/classical system and quantum trajectories [0.0]
  We develop a general approach to the dynamics of quantum/classical systems. An important feature is that, if the interaction allows for a flow of information from the quantum component to the classical one, necessarily the dynamics is dissipative.
  arXiv  Detail & Related papers  (2024-03-24T08:26:54Z)
• Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories [0.0]
  We show a new method to treat open quantum-spin lattices, based on the solution of the open-system dynamics. We validate this approach in the paradigmatic case of the phase transitions of the dissipative 2D XYZ lattice, subject to spontaneous decay.
  arXiv  Detail & Related papers  (2022-09-27T13:23:38Z)
• Open quantum dynamics of strongly coupled oscillators with multi-configuration time-dependent Hartree propagation and Markovian quantum jumps [0.0]
  We implement a quantum state trajectory scheme for solving Lindblad quantum master equations. We show the potential for solving the dissipative dynamics of finite size arrays of strongly interacting quantized oscillators with high excitation densities.
  arXiv  Detail & Related papers  (2022-08-02T03:01:14Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Steering Interchange of Polariton Branches via Coherent and Incoherent Dynamics [1.9573380763700712]
  We propose the control of single- and two-body Jaynes-Cummings systems in a non-equilibrium scenario. Our findings provide a systematic approach to manipulate polaritons interchange, that we apply to reveal new insights in the transition between Mott Insulator- and Super-like states.
  arXiv  Detail & Related papers  (2020-10-07T16:31:03Z)
• Phase space theory for open quantum systems with local and collective dissipative processes [0.0]
  We investigate driven dissipative quantum dynamics of an ensemble of two-level systems given by a Markovian master equation with collective and noncollective dissipators. Our results expose, utilize and promote pioneered techniques in the context of laser theory.
  arXiv  Detail & Related papers  (2020-06-05T07:22:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.