The Wigner-Vlasov formalism for time-dependent quantum oscillator
- URL: http://arxiv.org/abs/2305.06069v3
- Date: Sat, 13 May 2023 08:49:41 GMT
- Title: The Wigner-Vlasov formalism for time-dependent quantum oscillator
- Authors: E.E. Perepelkin, B.I. Sadovnikov, N.G. Inozemtseva, A.A. Korepanova
- Abstract summary: A new method is proposed to find an exact solution of this problem using a relation of the Vlasov equation chain with the Schr"odinger equation and with the Moyal equation for the Wigner function.
An analysis of the dynamics of an unstable quantum system shows that the phase space square bounded with the Wigner function level line conserves in time, but the phase space square bounded with the energy function line increases.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This paper presents a comprehensive investigation of the problem of a
harmonic oscillator with time-depending frequencies in the framework of the
Vlasov theory and the Wigner function apparatus for quantum systems in the
phase space. A new method is proposed to find an exact solution of this problem
using a relation of the Vlasov equation chain with the Schr\"odinger equation
and with the Moyal equation for the Wigner function. A method of averaging the
energy function over the Wigner function in the phase space can be used to
obtain time-dependent energy spectrum for a quantum system. The Vlasov equation
solution can be represented in the form of characteristics satisfying the Hill
equation. A particular case of the Hill equation, namely the Mathieu equation
with unstable solutions, has been considered in details. An analysis of the
dynamics of an unstable quantum system shows that the phase space square
bounded with the Wigner function level line conserves in time, but the phase
space square bounded with the energy function line increases. In this case the
Vlasov equation characteristic is situated on the crosspoint of the Wigner
function level line and the energy function line. This crosspoint moves in time
with a trajectory that represents the unstable system dynamics. Each such
trajectory has its own energy, and averaging these energies over the Wigner
function results in time-dependent discreet energy spectrum for the whole
system. An explicit expression has been obtained for the Wigner function of the
4th rank in the generalized phase space $\left\{ x,p,\dot{p},\ddot{p}
\right\}.$
Related papers
- Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay.
We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
arXiv Detail & Related papers (2024-05-27T16:11:39Z) - Denoising and Extension of Response Functions in the Time Domain [48.52478746418526]
Response functions of quantum systems describe the response of a system to an external perturbation.
In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain.
arXiv Detail & Related papers (2023-09-05T20:26:03Z) - Wigner function properties for electromagnetic systems [0.0]
An exact 3D solution of the Schr"odinger equation for a scalar particle in an electromagnetic field is constructed.
The search for two types of the Wigner functions is conducted.
Knowing the Wigner functions allows one to find the distribution of the mean momentum vector field and the energy spectrum of the quantum system.
arXiv Detail & Related papers (2023-08-24T07:23:23Z) - Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods.
We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians.
For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z) - Dispersion chain of quantum mechanics equations [0.0]
The paper considers the construction of a new chain of equations of quantum mechanics of high kinematical values.
The proposed approach can be applied to consideration of classical and quantum systems with radiation.
arXiv Detail & Related papers (2022-09-28T12:58:19Z) - Real-Space, Real-Time Approach to Quantum-Electrodynamical
Time-Dependent Density Functional Theory [55.41644538483948]
The equations are solved by time propagating the wave function on a tensor product of a Fock-space and real-space grid.
Examples include the coupling strength and light frequency dependence of the energies, wave functions, optical absorption spectra, and Rabi splitting magnitudes in cavities.
arXiv Detail & Related papers (2022-09-01T18:49:51Z) - Exact Floquet solutions of quantum driven systems [1.0152838128195467]
We give out the exact Floquet solutions of wave function for three physical models.
The idea presented in this paper can be used in mathematics to solve partial differential equations.
arXiv Detail & Related papers (2022-02-02T15:15:05Z) - 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) - New approach to describe two coupled spins in a variable magnetic field [55.41644538483948]
We describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field.
We modify the time-dependent Schr"odinger equation through a change of representation.
The solution is highly simplified when an adiabatically varying magnetic field perturbs the system.
arXiv Detail & Related papers (2020-11-23T17:29:31Z) - Extended Wigner function for the harmonic oscillator in the phase space [0.0]
The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane.
The Wigner function is equal to the deviation values of the points on the surface of the membrane from the equilibrium state.
As an example, a time dependent Wigner function corresponding to the standing wave of quasi-probability density arising in the phase plane is considered.
arXiv Detail & Related papers (2020-03-26T04:18:41Z) - A high-order integral equation-based solver for the time-dependent
Schrodinger equation [0.0]
We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential.
A spatially uniform electric field may be included, making the solver applicable to simulations of light-matter interaction.
arXiv Detail & Related papers (2020-01-16T23:50:26Z)
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.