Justifying Born's rule $P_\alpha=|\Psi_\alpha|^2$ using deterministic chaos, decoherence, and the de Broglie-Bohm quantum theory

• URL: http://arxiv.org/abs/2109.09353v1
• Date: Mon, 20 Sep 2021 08:10:36 GMT
• Title: Justifying Born's rule $P_\alpha=|\Psi_\alpha|^2$ using deterministic chaos, decoherence, and the de Broglie-Bohm quantum theory
• Authors: Aur\'elien Drezet
• Abstract summary: We show that entanglement together with deterministic chaos lead to a fast relaxation from any statistitical distribution. Our model is discussed in the context of Boltzmann's kinetic theory.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work we derive Born's rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to a environement made of "qubits" (i.e., Bohmian pointers) we show that entanglement together with deterministic chaos lead to a fast relaxation from any statistitical distribution $\rho(x)$ (of finding a particle at point $x$) to the Born probability law $|\Psi(x)|^2$. Our model is discussed in the context of Boltzmann's kinetic theory and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.

Related papers

• Emptiness Instanton in Quantum Polytropic Gas [49.1574468325115]
  The problem involves determining the probability of the spontaneous formation of an empty interval in the ground state of the gas. By solving the hydrodynamic equations in imaginary time, we derive the analytic form of the emptiness instanton. This solution is expressed as an integral representation analogous to those used for correlation functions in Conformal Field Theory.
  arXiv  Detail & Related papers  (2024-12-16T11:58:51Z)
• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. We show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory [0.0]
  We show a new problem in nonlinear dispersive PDE with implications for quantum many-body chaos. Our finding spotlights a new problem in nonlinear dispersive PDE with implications for quantum many-body chaos.
  arXiv  Detail & Related papers  (2023-12-04T09:01:35Z)
• Quantum dissipation and the virial theorem [22.1682776279474]
  We study the celebrated virial theorem for dissipative systems, both classical and quantum. The non-Markovian nature of the quantum noise leads to novel bath-induced terms in the virial theorem. We also consider the case of an electrical circuit with thermal noise and analyze the role of non-Markovian noise in the context of the virial theorem.
  arXiv  Detail & Related papers  (2023-02-23T13:28:11Z)
• Quantum Heavy-tailed Bandits [36.458771174473924]
  We study multi-armed bandits (MAB) and linear bandits (SLB) with heavy-tailed rewards and quantum reward. We first propose a new quantum mean estimator for heavy-tailed distributions, which is based on the Quantum Monte Carlo Estimator. Based on our quantum mean estimator, we focus on quantum heavy-tailed MAB and SLB and propose quantum algorithms based on the Upper Confidence Bound (UCB) framework.
  arXiv  Detail & Related papers  (2023-01-23T19:23:10Z)
• An Introduction to Scattering Theory [0.0]
  Part A defines the theoretical playground, and develops basic concepts of scattering theory in the time domain. Part B is then to build up, in a step-by-step fashion, the time independent scattering theory in energy domain. Part C elaborates the nonhermitian scattering theory (Siegert pseudostate formalism)
  arXiv  Detail & Related papers  (2022-04-08T11:41:24Z)
• Bohmian mechanics is not deterministic [0.0]
  I argue that Bohmian mechanics cannot reasonably be claimed to be a deterministic theory. The advantages of Bohmian mechanics over other interpretations of quantum mechanics, if any, must lie at an ontological level.
  arXiv  Detail & Related papers  (2022-02-24T18:21:31Z)
• Sublinear quantum algorithms for estimating von Neumann entropy [18.30551855632791]
  We study the problem of obtaining estimates to within a multiplicative factor $gamma>1$ of the Shannon entropy of probability distributions and the von Neumann entropy of mixed quantum states. We work with the quantum purified query access model, which can handle both classical probability distributions and mixed quantum states, and is the most general input model considered in the literature.
  arXiv  Detail & Related papers  (2021-11-22T12:00:45Z)
• Chaos in Bohmian Quantum Mechanics: A short review [0.0]
  We develop a generic theoretical mechanism responsible for the generation of chaos in an arbitrary Bohmian system. We study the effect of chaos on Bohmian trajectories and study chaos and ergodicity in qubit systems. Our results shed light on a fundamental problem in Bohmian Mechanics, namely whether there is a dynamical approximation of Born's rule by an arbitrary initial distribution of Bohmian particles.
  arXiv  Detail & Related papers  (2020-09-12T21:01:21Z)
• Sub-bosonic (deformed) ladder operators [62.997667081978825]
  We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
  arXiv  Detail & Related papers  (2020-09-10T20:53:58Z)
• Existence of Schrodinger Evolution with Absorbing Boundary Condition [0.0]
  Consider a non-relativistic quantum particle with wave function inside a region $Omegasubset mathbbR3$. The question how to compute the probability distribution of the time at which the detector surface registers the particle boils down to finding a reasonable mathematical definition of an ideal detecting surface. A particularly convincing definition, called the absorbing boundary rule, involves a time evolution for the particle's wave function $psi$ expressed by a Schrodinger equation in $Omega$ together with an "absorbing" boundary condition on $partial Omega$ first considered by Werner in
  arXiv  Detail & Related papers  (2019-12-27T10:53:31Z)

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.