Can Schrodingerist Wavefunction Physics Explain Brownian Motion? II. The Diffusion Coefficient

• URL: http://arxiv.org/abs/2308.01437v1
• Date: Wed, 2 Aug 2023 21:20:02 GMT
• Title: Can Schrodingerist Wavefunction Physics Explain Brownian Motion? II. The Diffusion Coefficient
• Authors: W. David Wick
• Abstract summary: In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories. I concluded that it was possible, but left unsettled the second claim in Einstein's classical program: diffusive motion. In this paper, I derive a criterion for diffusive motion, as well as an expression for the diffusion coefficient.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories of the heavy particle. I concluded that it was possible, but left unsettled the second claim in Einstein's classical program: diffusive motion, proportional to the square-root of time, as opposed to ballistic motion, proportional to the time. In this paper, I derive a criterion for diffusive motion, as well as an expression for the diffusion coefficient. Unfortunately, as in paper I, no exact solutions are available for the models, making checking the criterion difficult. But a virtue of the method employed here is that, given adequate information about model eigenvalues and eigenfunctions, diffusion can be definitively ruled in or out.

Related papers

• Analogue black string in a quantum harmonic oscillator [49.1574468325115]
  We write the exact solution of the Klein-Gordon equation in the background of a chargeless, static black string. The eigenvalue problem provides complex energy values for the particle, which may indicate the presence of quasinormal modes. We show a simple quantum system that can imitate the particle in the black string background, whose solutions are also applications of the biconfluent Heun function.
  arXiv  Detail & Related papers  (2024-12-31T15:03:57Z)
• Can Schroedingerist Wavefunction Physics Explain Brownian Motion? III: A One-Dimensional Heavy and Light Particles Model Exhibiting Brownian-Motion-Like Trajectories and Diffusion [0.0]
  We introduce a one-space-dimensional perturbation model which, granted a finite series, fulfills the criteria for BML trajectories and diffusion. We note that Planck's constant makes an appearance in the diffusion coefficient, which further differentiates the present theory from the work of Poincare and Einstein in the previous century.
  arXiv  Detail & Related papers  (2024-12-11T20:30:47Z)
• Brownian Particles and Matter Waves [0.0]
  We examine whether Brownian particles can manifest a particle-wave duality without employing a priori arguments from quantum decoherence. Our one-dimensional calculations show that for this to happen, the trapping needs to be very strong so that a Brownian nanoparticles needs to be embedded in an extremely stiff solid.
  arXiv  Detail & Related papers  (2024-04-02T15:01:14Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Can Schroedingerist Wavefunction Physics Explain Brownian Motion? [0.0]
  Einstein's 1905 analysis of the Brownian Motion of a pollen grain in a water droplet provided one of the most convincing demonstrations of the reality of atoms. In 1926 Schroedinger replaced classical particles by wavefunctions, which cannot undergo collisions. Can a Schroedingerist wavefunction physics account for Perrin's observations?
  arXiv  Detail & Related papers  (2023-05-19T19:50:00Z)
• The nonlocal advection diffusion equation and the two-slit experiment in quantum mechanics [0.0]
  The state variable of the equation is the probability density function of particle positions. The model is compared to the Schr"odinger equation model of the experiment.
  arXiv  Detail & Related papers  (2023-03-17T15:44:10Z)
• Classical Elastic Two-Particle Collision Energy Conservation using Edward Nelson's Energy, Double Diffusion and Special Relativity [0.2741266294612775]
  Properties of the classical elastic momentum collision expression determine the full Edward Nelson energy collision energy for both particles. Quantum mechanics can be obtained by modelling the incident particle as a non-random potential. Under suitable conditions it will be shown that the colliding particles satisfy Minkowski metric in special relativity.
  arXiv  Detail & Related papers  (2022-12-05T22:44:23Z)
• Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery [17.736465741047315]
  We introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term.
  arXiv  Detail & Related papers  (2022-11-20T00:46:33Z)
• Partition of kinetic energy and magnetic moment in dissipative diamagnetism [20.218184785285132]
  We analyze dissipative diamagnetism, arising due to dissipative cyclotron motion in two dimensions, in the light of the quantum counterpart of energy equipartition theorem. The expressions for kinetic energy and magnetic moment are reformulated in the context of superstatistics.
  arXiv  Detail & Related papers  (2022-07-30T08:07:28Z)
• Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-Informed Deep Generative Models [27.623119767592385]
  We propose a new method for inferring the governing ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants. Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots. By training a physics-informed generative model that generates "fake" sample paths, we aim to fit the observed particle ensemble distributions with a curve in the probability measure space.
  arXiv  Detail & Related papers  (2020-08-05T03:06:40Z)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)

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.