Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations

• URL: http://arxiv.org/abs/2109.03854v2
• Date: Wed, 13 Mar 2024 19:03:43 GMT
• Title: Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations
• Authors: Choon-Lin Ho,
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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. The formalism of supersymmetric quantum mechanics is extended by applying the Darboux transformation directly to the non-stationary Schr\"odinger equation. From a solution of a Fokker-Planck equation a solution of the Darboux partner is obtained. For drift coefficients satisfying the condition of shape invariance, a supersymmetric hierarchy of Fokker-Planck equations with solutions related by the Darboux transformation is obtained.

Related papers

• Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian [55.2480439325792]
  We rigorously derive a leading correction in the weak-field approximation to the known relativistic Foldy-Wouthuysen Hamiltonian. For Dirac particles, the relativistic wave equation of the second order is obtained with the correction similar to that to the Foldy-Wouthuysen Hamiltonian.
  arXiv  Detail & Related papers  (2024-08-03T12:53:41Z)
• Quantum simulation of the Fokker-Planck equation via Schrodingerization [33.76659022113328]
  This paper studies a quantum simulation technique for solving the Fokker-Planck equation. We employ the Schrodingerization method-it converts any linear partial and ordinary differential equation with non-Hermitian dynamics into systems of Schrodinger-type equations.
  arXiv  Detail & Related papers  (2024-04-21T08:53:27Z)
• Interpolating supersymmetric pair of Fokker-Planck equations [0.0]
  We consider Fokker-Planck equations that interpolate a pair of supersymmetrically related Fokker-Planck equations with constant coefficients.
  arXiv  Detail & Related papers  (2024-04-15T08:16:43Z)
• Radiative transport in a periodic structure with band crossings [52.24960876753079]
  We derive the semi-classical model for the Schr"odinger equation in arbitrary spatial dimensions. We consider both deterministic and random scenarios. As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness.
  arXiv  Detail & Related papers  (2024-02-09T23:34:32Z)
• 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)
• Calculation of the wave functions of a quantum asymmetric top using the noncommutative integration method [0.0]
  We obtain a complete set of solutions to the Schrodinger equation for a quantum asymmetric top in Euler angles. The spectrum of an asymmetric top is obtained from the condition that the solutions are in with respect to a special irreducible $lambda$-representation of the rotation group.
  arXiv  Detail & Related papers  (2022-11-27T12:38:22Z)
• Self-Consistency of the Fokker-Planck Equation [117.17004717792344]
  The Fokker-Planck equation governs the density evolution of the Ito process. Ground-truth velocity field can be shown to be the solution of a fixed-point equation. In this paper, we exploit this concept to design a potential function of the hypothesis velocity fields.
  arXiv  Detail & Related papers  (2022-06-02T03:44:23Z)
• Lindblad master equations for quantum systems coupled to dissipative bosonic modes [0.0]
  We derive Lindblad master equations for a subsystem whose dynamics is coupled to bosonic modes. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins. This master equation accurately predicts the Dicke phase transition and gives the correct steady state.
  arXiv  Detail & Related papers  (2022-03-07T11:21:48Z)
• Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schr\"odinger Equation [77.34726150561087]
  We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts. We discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor.
  arXiv  Detail & Related papers  (2021-06-25T17:25:38Z)
• 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)
• Generalization of SUSY Intertwining Relations: New Exact Solutions of Fokker-Planck Equation [0.0]
  A new class of analytically solvable models is presented for Fokker-Planck equation. What is important, this approach allows us to deal with the drift coefficients depending on both variables.
  arXiv  Detail & Related papers  (2020-04-08T12:56:36Z)

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.