The Generalized Fokker-Planck Equation in terms of Dunkl-type
Derivatives
- URL: http://arxiv.org/abs/2310.05017v4
- Date: Thu, 18 Jan 2024 00:40:01 GMT
- Title: The Generalized Fokker-Planck Equation in terms of Dunkl-type
Derivatives
- Authors: R. D. Mota, D. Ojeda-Guill\'en and M. A. Xicot\'encatl
- Abstract summary: We introduce two different generalizations of the Fokker-Planck equation in (1+1) dimensions.
We solve exactly the generalized Fokker-Planck equations for the harmonic oscillator and the centrifugal-type potentials.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this work we introduce two different generalizations of the Fokker-Planck
equation in (1+1) dimensions by replacing the spatial derivatives in terms of
generalized Dunkl-type derivatives involving reflection operators. As
applications of these results, we solve exactly the generalized Fokker-Planck
equations for the harmonic oscillator and the centrifugal-type potentials.
Related papers
- Novel approach of exploring ASEP-like models through the Yang Baxter
Equation [49.1574468325115]
Ansatz of Yang Baxter Equation inspired by Bethe Ansatz treatment of ASEP spin-model.
Various classes of Hamiltonian density arriving from two types of R-Matrices are found which also appear as solutions of constant YBE.
A summary of finalised results reveals general non-hermitian spin-1/2 chain models.
arXiv Detail & Related papers (2024-03-05T17:52:20Z) - The Dunkl-Fokker-Planck Equation in $1+1$ Dimensions [0.0]
We obtain the Dunkl-Fokker-Planck eigenvalues equation and solve it for the harmonic oscillator plus a centrifugal-type potential.
We reduce our results to those of the recently developed Wigner-Dunkl supersymmetry.
arXiv Detail & Related papers (2023-10-08T05:19:47Z) - Moving mirror-field dynamics under intrinsic decoherence [77.34726150561087]
We study the decaying dynamics in the mirror-field interaction by means of the intrinsic decoherence scheme.
We show expectation values, correlations, and Husimi functions for the solutions obtained.
arXiv Detail & Related papers (2023-05-06T03:41:45Z) - Relativistic Solutions of Generalized-Dunkl Harmonic and Anharmonic
Oscillators [0.0]
Dunkl derivative enriches solutions by discussing parity due to its reflection operator.
We show that degenerate states can occur according to the Wigner parameter values.
arXiv Detail & Related papers (2022-08-22T17:47:08Z) - Effect of the two-parameter generalized Dunkl derivative on the
two-dimensional Schr\"odinger equation [0.0]
We introduce a generalization of the Dunkl-derivative with two parameters to study the Schr"odinger equation in Cartesian and polar coordinates in two dimensions.
arXiv Detail & Related papers (2022-07-20T17:27:08Z) - Intrinsic decoherence for the displaced harmonic oscillator [77.34726150561087]
We use the complete solution of the Milburn equation that describes intrinsic decoherence.
We calculate the expectation values of position quadrature, and the number operator in initial coherent and squeezed states.
arXiv Detail & Related papers (2021-12-06T03:15:43Z) - Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations [0.0]
A procedure is presented for solving the Fokker-Planck equation with constant diffusion but non-stationary drift.
It is based on the correspondence between the Fokker-Planck equation and the non-stationary Schr"odinger equation.
arXiv Detail & Related papers (2021-09-08T18:09:03Z) - Intrinsic decoherence dynamics in the three-coupled harmonic oscillators
interaction [77.34726150561087]
We give an explicit solution for the complete equation, i.e., beyond the usual second order approximation used to arrive to the Lindblad form.
arXiv Detail & Related papers (2021-08-01T02:36:23Z) - Exact solutions of the Schr\"odinger Equation with Dunkl Derivative for
the Free-Particle Spherical Waves, the Pseudo-Harmonic Oscillator and the
Mie-type Potential [0.0]
The equations for the radial and angular parts are obtained by using spherical coordinates and separation of variables.
It is shown that our results are adequately reduced to those previously reported when we remove the Dunkl derivative parameters.
arXiv Detail & Related papers (2021-03-07T21:34:20Z) - Feynman Functional Integral in the Fokker Theory [62.997667081978825]
equivalence of two formulations of Fokker's quantum theory is proved.
The common basis for the two approaches is the generalized canonical form of Fokker's action.
arXiv Detail & Related papers (2020-11-11T12:10:01Z) - Dissipative flow equations [62.997667081978825]
We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations.
We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode.
arXiv Detail & Related papers (2020-07-23T14:47:17Z)
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.