Related papers: Classical and Quantum Brownian Motion
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
Building upon the work of Hu, Paz, and Zhang [1,2] on open quantum systems we consider the quantum Brownian motion (QBM) model with one oscillator (position variable $x$) as the system, {\it nonlinearly} coupled to an environment of $N$…
The quantum Langevin equation is derived from the Feynman-Veron forward--backward path integral representation for a density matrix of a quantum system in a thermal oscillator bath. We exhibit the mechanism by which the classical,…
Based on a coherent state representation of noise operator and an ensemble averaging procedure we have recently developed [Phys. Rev. E {\bf 65}, 021109 (2002); {\it ibid.} 051106 (2002)] a scheme for quantum Brownian motion to derive the…
Quantum Brownian motion in the strong friction limit is studied based on the exact path integral formulation of dissipative systems. In this limit the time-nonlocal reduced dynamics can be cast into an effective equation of motion, the…
In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its…
We solve the time-dependent Schr\"odinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under…
This work proposes an answer to a challenge posed by Bell on the lack of clarity in regards to the line between the quantum and classical regimes in a measurement problem. To this end, a generalized logarithmic nonlinear Schr\"odinger…
A de Broglie-Bohm like model of Klein-Gordon equation, that leads to the correct Schrodinger equation in the low-speed limit, is presented. Under this theoretical framework, that affords an interpretation of the quantum potential, the main…
The paper consists of two parts. In the first part Schroedinger's equation for a charged quantum particle in a Galilei-Newton curved space-time is derived in a fully geometrical way. Gravitational and electromagnetic fields are coded into…
The Newtonian motion of a macroscopic particle is derived from the linear Schr\"odinger equation with a Hamiltonian consisting of the free-particle term and a random Hamiltonian drawn from the Gaussian Unitary Ensemble. The random term…
The physical model of a nonrelativistic quantized Schrodinger's electron (SE) is offered. The behaviour of the SE well spread elementary electric charge had been understood by means of two independent and different in a frequency and size…
The Schrodinger equation based on the de Broglie wave is the most fundamental equation of the quantum mechanics. There can be no doubt about it's prediction validity. However, the probabilistic interpretation on the quantum mechanics has…
We show that the natural motion of particles in continuous space-time (CSTM) is not classical continuous motion (CCM), but one kind of essentially discontinuous motion, the wave function in quantum mechanics is the very mathematical complex…
Based on the dynamical quantization method we derive a quantum phase-space non-Markovian Smoluchowski equation describing the non-inertial Brownian motion of a harmonic oscillator immersed in a generic environment. In the long-time regime…
The central limit theorem has been found to apply to random vectors in complex Hilbert space. This amounts to sufficient reason to study the complex valued Gaussian, looking for relevance to quantum mechanics. Here we show that the…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
We construct a theory for the 1+1-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity, and (ii) reduces to the standard Brownian motion in the Newtonian limit case. In the…
An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical…