Canonically consistent quantum master equation
- URL: http://arxiv.org/abs/2205.12848v2
- Date: Mon, 1 Aug 2022 15:51:48 GMT
- Title: Canonically consistent quantum master equation
- Authors: Tobias Becker, Alexander Schnell, Juzar Thingna
- Abstract summary: 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.
- Score: 68.8204255655161
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We put forth a new class of quantum master equations that correctly reproduce
the asymptotic 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. The correction not only steers
the reduced system towards a correct steady state but also improves the
accuracy of the dynamics, thereby refining the archetypal Born-Markov
weak-coupling second-order master equations. In case of equilibrium, since a
closed form for the steady state exists in terms of a mean force Gibbs state,
we utilize this form to correct the Redfield quantum master equation. Using an
exactly solvable harmonic oscillator system we benchmark our approach with the
exact solution showing that our method also helps correcting the long-standing
issue of positivity violation, albeit without complete positivity. Our method
of a canonically consistent quantum master equation, opens a new perspective in
the theory of open quantum systems leading to a reduced density matrix accurate
beyond the commonly used Redfield and Lindblad equations, while retaining the
same conceptual and numerical complexity.
Related papers
- A Realist Interpretation of Unitarity in Quantum Gravity [0.0]
Unitarity is a difficult concept to implement in canonical quantum gravity because of state non-normalizability and the problem of time.
We use the postulate of a definite configuration in the theory to define a global time for the gravitational-fermionic system.
We find unitary states in mini-superspace by finding an approximate solution to the Hamiltonian constraint.
arXiv Detail & Related papers (2023-10-23T17:56:28Z) - 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) - Quantum trajectories for time-local non-Lindblad master equations [0.0]
In the Markovian regime, when the dynamics is described by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, this procedure is known as Monte-Carlo wavefunction (MCWF) approach.
We propose a pseudo-Lindblad quantum trajectory (PLQT) unraveling.
It does not require an effective extension of the state space, like other approaches, except for the addition of a single classical bit.
arXiv Detail & Related papers (2023-06-26T17:45:36Z) - Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent
and Incoherent Photons Found with Gradient Search [77.34726150561087]
We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control.
We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
arXiv Detail & Related papers (2023-02-28T07:36:02Z) - On optimization of coherent and incoherent controls for two-level
quantum systems [77.34726150561087]
This article considers some control problems for closed and open two-level quantum systems.
The closed system's dynamics is governed by the Schr"odinger equation with coherent control.
The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
arXiv Detail & Related papers (2022-05-05T09:08:03Z) - Minimum-Time Quantum Control and the Quantum Brachistochrone Equation [3.0616044531734192]
We present the general solution to the full quantum brachistochrone equation.
We prove that the speed of evolution under constraints is reduced with respect to the unrestricted case.
We find that solving the quantum brachistochrone equation is closely connected to solving the dynamics of the Lagrange multipliers.
arXiv Detail & Related papers (2022-04-27T09:26:59Z) - Renormalization in the Theory of Open Quantum Systems via the
Self-Consistency Condition [0.0]
We investigate the topic of renormalization in the theory of weakly interacting open quantum systems.
Our starting point is an open quantum system interacting with a single heat bath.
arXiv Detail & Related papers (2021-12-22T15:34:14Z) - 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) - A Nonlinear Master Equation for Open Quantum Systems [0.0]
A nonlinear master equation is derived, reflecting properly the entropy of open quantum systems.
The corresponding nonlinear equation for the Wigner function accounts rigorously for the thermo-quantum entropy.
arXiv Detail & Related papers (2020-10-12T12:19:29Z)
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.