Stability of the Grabert master equation

• URL: http://arxiv.org/abs/2103.08982v1
• Date: Tue, 16 Mar 2021 11:19:41 GMT
• Title: Stability of the Grabert master equation
• Authors: Eyal Buks and Dvir Schwartz
• Abstract summary: We study the dynamics of a quantum system having Hilbert space of finite dimension $d_mathrmH$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the dynamics of a quantum system having Hilbert space of finite dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the nonlinear master equation derived by Grabert. The dynamics near a fixed point is analyzed by using the method of linearization, and by evaluating the eigenvalues of the Jacobian matrix. We find that all these eigenvalues are non-negative, and conclude that the fixed point is stable. This finding raises the question: under what conditions instability is possible in a quantum system having finite $d_{\mathrm{H}}$?

Related papers

• Linear quantum systems: poles, zeros, invertibility and sensitivity [2.7694956548319762]
  The noncommutative nature of quantum mechanics imposes fundamental constraints on system dynamics. This paper investigates the zeros and poles of linear quantum systems. Two types of stable input observers are constructed for unstable linear quantum systems.
  arXiv  Detail & Related papers  (2024-09-14T14:03:48Z)
• A non-hermitean momentum operator for the particle in a box [49.1574468325115]
  We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example. The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
  arXiv  Detail & Related papers  (2024-03-20T12:51:58Z)
• Small-time controllability for the nonlinear Schr\"odinger equation on $\mathbb{R}^N$ via bilinear electromagnetic fields [55.2480439325792]
  We address the small-time controllability problem for a nonlinear Schr"odinger equation (NLS) on $mathbbRN$ in the presence of magnetic and electric external fields. In detail, we study when it is possible to control the dynamics of (NLS) as fast as desired via sufficiently large control signals.
  arXiv  Detail & Related papers  (2023-07-28T21:30:44Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Dynamical chaos in nonlinear Schr\"odinger models with subquadratic power nonlinearity [137.6408511310322]
  We deal with a class of nonlinear Schr"odinger lattices with random potential and subquadratic power nonlinearity. We show that the spreading process is subdiffusive and has complex microscopic organization. The limit of quadratic power nonlinearity is also discussed and shown to result in a delocalization border.
  arXiv  Detail & Related papers  (2023-01-20T16:45:36Z)
• Perturbation theory for nonlinear Schrodinger equations [0.0]
  This power series is proved to be convergent when the parameter representing the intensity of the nonlinear term is less in absolute value than a threshold value. It gives a stationary solution to the nonlinear Schrodinger equation.
  arXiv  Detail & Related papers  (2022-06-20T14:58:33Z)
• A unified approach to the nonlinear Rabi models [0.0]
  An analytical approach is proposed and applied to study the two-photon, two-mode and intensity-dependent Rabi models. This work paves a way for the analysis of the novel physics in nonlinear quantum optics.
  arXiv  Detail & Related papers  (2022-06-20T14:29:14Z)
• 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)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• The Eigenvalue Problem of Nonlinear Schr\"odinger Equation at Dirac Points of Honeycomb Lattice [4.549831511476248]
  We give a rigorous deduction of the eigenvalue problem of the nonlinear Schr"odinger equation (NLS) at Dirac Points for potential of honeycomb lattice symmetry. We observe the bifurcation of the eigenfunctions into eight distinct modes from the two-dimensional degenerated eigenspace of the regressive linear Schr"odinger equation.
  arXiv  Detail & Related papers  (2022-02-12T16:46:52Z)
• 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.