相关论文: BBGKY Hierarchy Underlying Many Particle Quantum M…

In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…

Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…

Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which…

We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…

This paper is devoted to the problem of the description of nonequilibrium correlations in quantum many-particle systems. The nonlinear quantum BBGKY hierarchy for marginal correlation operators is rigorously derived from the von Neumann…

A generalization of the Gibbs-von Neumann relative entropy is proposed based on the quantum BBGKY [Bogolyubov-Born-Green-Kirkwood-Yvon] hierarchy as the nonequilibrium entropy for an N-body system. By using a generalization of the…

We use the Feynman path integral approach to nonrelativistic quantum mechanics twofold. First, we derive the lagrangian for a spinless particle moving in a uniformly but not necessarily constantly accelerated reference frame; then, applying…

The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…

The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…

We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…

The issue of non-locality in quantum mechanics can potentially be resolved by considering relativistically covariant diffusion in four-dimensional spacetime. Stochastic particles described by the Klein-Gordon equation are shown to undergo a…

The Poincar\'e-Snyder relativity was introduced in an earlier paper of ours as an extended form of Einstein relativity obtained by appropriate limiting setting of the full Quantum Relativity. The latter, with fundamental constants $\hbar$…

We introduce into classical mechanics the concept of non-discerned particles for particles that are identical, non-interacting and prepared in the same way. The non-discerned particles correspond to an action and a density which satisfy the…

Quantum simulations on current NISQ hardware are limited by its noisy nature, making efficient quantum error mitigation methods highly demanded. In this paper we introduce a novel mitigation scheme, applicable to arbitrary quantum…

The Schr\"odinger's wave function can naturally be realized as an 'instantaneous resonant spatial mode' in which quantum particle moves and hence the Born's rule is derived after identifying its origin. This realization facilitates the…

The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses because its discussion usually requires wavepackets built on the Airy functions -- a difficult computation. Here, on the…

We present an old and regretfully forgotten method by Jacobi which allows one to find many Lagrangians of simple classical models and also of nonconservative systems. We underline that the knowledge of Lie symmetries generates Jacobi last…

A fundamental belief is that the formulism of relativistic quantum mechanics equations (RQMEs) should remain in low momentum motion. However, it is found that some formulas from RQMEs were lost in Schr\"odinger equation. For example, a free…

Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…

All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…