Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation

• URL: http://arxiv.org/abs/2103.12042v3
• Date: Sun, 25 Jul 2021 20:13:22 GMT
• Title: Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation
• Authors: Anton Trushechkin
• Abstract summary: Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account nonsecular effects. We provide a fully rigorous derivation of such equation based on a formalization of the weak-coupling limit for the general case.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account nonsecular effects, but nevertheless has the mathematically correct Gorini-Kossakowski-Lindblad-Sudarshan form (in particular, it preserves positivity of the density operator) and also satisfies the standard thermodynamic properties is a known long-standing problem in theory of open quantum systems. The nonsecular terms are important when some energy levels of the system or their differences (Bohr frequencies) are nearly degenerate. We provide a fully rigorous derivation of such equation based on a formalization of the weak-coupling limit for the general case.

Related papers

• Quantum Circuits for the heat equation with physical boundary conditions via Schrodingerisation [33.76659022113328]
  This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension.
  arXiv  Detail & Related papers  (2024-07-22T03:52:14Z)
• Dirac Brackets $\leftrightarrow$ Lindblad Equation: A Correspondence [0.0]
  We study the time evolution of an open quantum system governed by the Gorini-Kossakowski-Sudarshan-Lindlad equation. In a similar fashion, the time evolution of a physical observable in a classically constrained dynamical system is governed by a generalization of the Liouville equation. We derive an intriguing, but precise classical-quantum correspondence between the aforementioned situations which connects the Lindblad operators to the constraints.
  arXiv  Detail & Related papers  (2024-05-04T04:42:15Z)
• Quantum Instability [30.674987397533997]
  We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system. An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
  arXiv  Detail & Related papers  (2022-08-05T19:53:46Z)
• Canonically consistent quantum master equation [68.8204255655161]
  We put forth a new class of quantum master equations that correctly reproduce the state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics.
  arXiv  Detail & Related papers  (2022-05-25T15:22:52Z)
• Nonperturbative renormalization of quantum thermodynamics from weak to strong couplings [2.542198147027801]
  By solving the exact master equation of open quantum systems, we formulate the quantum thermodynamics from weak to strong couplings. We find that the exact solution of the reduced density matrix of these systems approaches a Gibbs-type state in the steady-state limit for both the weak and strong system-reservoir coupling strengths.
  arXiv  Detail & Related papers  (2022-05-17T06:25:03Z)
• Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
  Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Our results explain finite-time thermalization in chaotic open quantum systems.
  arXiv  Detail & Related papers  (2021-12-14T18:48:31Z)
• Open-system approach to nonequilibrium quantum thermodynamics at arbitrary coupling [77.34726150561087]
  We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths. Our approach is based on the exact time-local quantum master equation for the reduced open system states.
  arXiv  Detail & Related papers  (2021-09-24T11:19:22Z)
• Quantum master equations and steady states for the ultrastrong-coupling limit and the strong-decoherence limit [0.0]
  We derive quantum master equations for the ultrastrong system-bath coupling regime. In this regime, the strong decoherence is complemented by slow relaxation processes.
  arXiv  Detail & Related papers  (2021-09-04T15:28:08Z)
• 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)
• Sufficient conditions for adiabaticity in open quantum systems [0.0]
  We introduce sufficient conditions for the adiabatic approximation in open quantum systems. We first illustrate our results by showing that the adiabatic approximation for open systems is compatible with the description of quantum thermodynamics at thermal equilibrium. We also apply our sufficient conditions as a tool in quantum control, evaluating the adiabatic behavior for the Hamiltonians of both the Deutsch algorithm and the Landau-Zener model under decoherence.
  arXiv  Detail & Related papers  (2020-07-29T22:19:42Z)
• From Thermodynamic Sufficiency to Information Causality [0.0]
  We derive information causality from monotonicity of divergence. We conjecture that under very weak regularity conditions it can be used to deduce the complex Hilbert space formalism of quantum theory.
  arXiv  Detail & Related papers  (2020-02-07T16:53:12Z)

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.