Complete Positivity and Thermal Relaxation in Quadratic Quantum Master Equations

• URL: http://arxiv.org/abs/2406.10477v2
• Date: Thu, 14 Nov 2024 16:46:20 GMT
• Title: Complete Positivity and Thermal Relaxation in Quadratic Quantum Master Equations
• Authors: F. Nicacio, T. Koide,
• Abstract summary: The ultimate goal of this paper is to develop a systematic method for deriving quantum master equations. We establish a CPTP criterion for our quantum master equation.
• Score: 0.0
• License:
• Abstract: The ultimate goal of this paper is to develop a systematic method for deriving quantum master equations that satisfy the requirements of a completely positive and trace-preserving (CPTP) map, further describing thermal relaxation processes. In this paper, we assume that the quantum master equation is obtained through the canonical quantization of the generalized Brownian motion proposed in our recent paper [T. Koide and F. Nicacio, Phys. Lett. A 494, 129277 (2024)]. At least classically, this dynamics describes the thermal relaxation process regardless of the choice of the system Hamiltonian. The remaining task is to identify the parameters ensuring that the quantum master equation meets complete positivity. We limit our discussion to many-body quadratic Hamiltonians and establish a CPTP criterion for our quantum master equation. This criterion is useful for applying our quantum master equation to models with interaction such as a network model, which has been used to investigate how quantum effects modify heat conduction.

Related papers

• Does canonical quantization lead to GKSL dynamics? [0.0]
  We introduce a generalized classical model of Brownian motion for describing thermal relaxation processes. We reproduce a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation satisfying the detailed balance condition.
  arXiv  Detail & Related papers  (2023-10-25T23:48:20Z)
• Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr\"odinger Equation [56.9919517199927]
  "Wasserstein Quantum Monte Carlo" (WQMC) uses the gradient flow induced by the Wasserstein metric, rather than Fisher-Rao metric, and corresponds to transporting the probability mass, rather than teleporting it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.
  arXiv  Detail & Related papers  (2023-07-06T17:54:08Z)
• 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)
• Lyapunov equation in open quantum systems and non-Hermitian physics [0.0]
  The continuous-time differential Lyapunov equation is widely used in linear optimal control theory. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic Hamiltonian, linear equations of motion) open quantum systems. We establish the Lyapunov equation as a fundamental and efficient formalism for linear open quantum systems.
  arXiv  Detail & Related papers  (2022-01-03T14:40:07Z)
• 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)
• Eigenvalues and Eigenstates of Quantum Rabi Model [0.0]
  We present an approach to the exact diagonalization of the quantum Rabi Hamiltonian. It is shown that the obtained eigenstates can be represented in the basis of the eigenstates of the Jaynes-Cummings Hamiltonian.
  arXiv  Detail & Related papers  (2021-04-26T17:45:41Z)
• 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)
• Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks [48.7576911714538]
  Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
  arXiv  Detail & Related papers  (2020-12-11T12:55:17Z)
• Hybrid Quantum-Classical Eigensolver Without Variation or Parametric Gates [0.0]
  We present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space. A process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given.
  arXiv  Detail & Related papers  (2020-08-26T02:31:24Z)
• Variational Quantum Eigensolver for Frustrated Quantum Systems [0.0]
  A variational quantum eigensolver, or VQE, is designed to determine a global minimum in an energy landscape specified by a quantum Hamiltonian. Here we consider the performance of the VQE technique for a Hubbard-like model describing a one-dimensional chain of fermions. We also study the barren plateau phenomenon for the Hamiltonian in question and find that the severity of this effect depends on the encoding of fermions to qubits.
  arXiv  Detail & Related papers  (2020-05-01T18:00:01Z)
• Simulation of Thermal Relaxation in Spin Chemistry Systems on a Quantum Computer Using Inherent Qubit Decoherence [53.20999552522241]
  We seek to take advantage of qubit decoherence as a resource in simulating the behavior of real world quantum systems. We present three methods for implementing the thermal relaxation. We find excellent agreement between our results, experimental data, and the theoretical prediction.
  arXiv  Detail & Related papers  (2020-01-03T11:48:11Z)

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.