Wigner current in multidimensional quantum billiards

• URL: http://arxiv.org/abs/2408.14164v1
• Date: Mon, 26 Aug 2024 10:17:43 GMT
• Title: Wigner current in multidimensional quantum billiards
• Authors: S. S. Seidov, D. G. Bezymiannykh,
• Abstract summary: We derive Wigner current of the particle in a multidimensional billiard. The calculation is based on proposed by us previously method of imposing boundary conditions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the present paper we derive the Wigner current of the particle in a multidimensional billiard - the compact region of space in which the particle moves freely. The calculation is based on proposed by us previously method of imposing boundary conditions by convolution of the free particle Wigner function with some time independent function, defined by the shape of the billiard. This method allowed to greatly simplify the general expression for the Wigner current, representing its $\mathbf{p}$-component as a surface integral of the product of the shifted free particle wave functions (the inverse Fourier transform of the free particle Wigner function). The results are also connect to an alternative approach, which takes into account the boundary conditions by adding the $\propto \delta'(x)$ term to the Hamiltonian. The latter is also generalized to the multidimensional case.

Related papers

• JKO for Landau: a variational particle method for homogeneous Landau equation [7.600098227248821]
  We develop a novel implicit particle method for the Landau equation in the framework of the JKO scheme. A key observation is that while the flow map evolves according to a rather complicated integral equation, the unknown component is merely a score function of the corresponding density.
  arXiv  Detail & Related papers  (2024-09-18T20:08:19Z)
• Closed-form solutions for the Salpeter equation [41.94295877935867]
  We study the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. The analytical extension of the Hamiltonian in the complex plane allows us to formulate the equivalent problem, namely the B"aumer equation. This B"aumera corresponds to the Green function of a relativistic diffusion process that interpolates between Cauchy for small times and Gaussian diffusion for large times.
  arXiv  Detail & Related papers  (2024-06-26T15:52:39Z)
• Particle-based Variational Inference with Generalized Wasserstein Gradient Flow [32.37056212527921]
  We propose a ParVI framework, called generalized Wasserstein gradient descent (GWG) We show that GWG exhibits strong convergence guarantees. We also provide an adaptive version that automatically chooses Wasserstein metric to accelerate convergence.
  arXiv  Detail & Related papers  (2023-10-25T10:05:42Z)
• Wigner function dynamics with boundaries expressed as convolution [0.0]
  A method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. The solution is brought to a form of convolution of the free particle solution with some function, defined by the shape of the well.
  arXiv  Detail & Related papers  (2023-04-28T15:39:44Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Efficient displacement convex optimization with particle gradient descent [57.88860627977882]
  Particle gradient descent is widely used to optimize functions of probability measures. This paper considers particle gradient descent with a finite number of particles and establishes its theoretical guarantees to optimize functions that are emphdisplacement convex in measures.
  arXiv  Detail & Related papers  (2023-02-09T16:35:59Z)
• Continuous-time Particle Filtering for Latent Stochastic Differential Equations [37.51802583388233]
  We propose continuous latent particle filters, an approach that extends particle filtering to the continuous-time domain. We demonstrate how continuous latent particle filters can be used as a generic plug-in replacement for inference techniques relying on a learned variational posterior.
  arXiv  Detail & Related papers  (2022-09-01T01:05:31Z)
• DPVI: A Dynamic-Weight Particle-Based Variational Inference Framework [20.9197547258307]
  We develop a Dynamic-weight Particle-based Variational Inference (DPVI) framework according to a novel continuous composite flow. By using different finite-particle approximations in our general framework, we derive several efficient DPVI algorithms.
  arXiv  Detail & Related papers  (2021-12-02T02:50:05Z)
• Exact transparent boundary condition for the multidimensional Schr\"odinger equation in hyperrectangular computational domain [0.0]
  An exact transparent boundary condition is proposed for the multidimensional Schr"odinger equation. The proposed boundary condition is simple, robust and can be useful in the field of computational quantum mechanics.
  arXiv  Detail & Related papers  (2021-05-22T18:24:23Z)
• Variational Transport: A Convergent Particle-BasedAlgorithm for Distributional Optimization [106.70006655990176]
  A distributional optimization problem arises widely in machine learning and statistics. We propose a novel particle-based algorithm, dubbed as variational transport, which approximately performs Wasserstein gradient descent. We prove that when the objective function satisfies a functional version of the Polyak-Lojasiewicz (PL) (Polyak, 1963) and smoothness conditions, variational transport converges linearly.
  arXiv  Detail & Related papers  (2020-12-21T18:33:13Z)
• Weak asymptotics of wave function for N-particle system and asymptotic filtering [0.0]
  The phenomenon of scattering is discovered, which consists in the fact that only scattering processes contribute to the leading terms of such a representation. The obtained representations are used to construct the corrects of the partial components of the wave function of $N$ particles in the hyperspherical representation.
  arXiv  Detail & Related papers  (2020-10-11T18:59:30Z)

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.