Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical and Quantum Brownian Motion   In the frames of classical mechanics the generalized Langevin equation is
derived for an arbitrary mechanical subsystem coupled to the harmonic bath of a
solid. A time-acting temperature operator is introduced for the quantum
Klein-Kramers and Smoluchowski equations, accounting for the effect of the
quantum thermal bath oscillators. The model of Brownian emitters is
theoretically studied and the relevant evolutionary equations for the
probability density are derived. The Schrodinger equation is explained via
collisions of the target point particles with the quantum force carriers,
transmitting the fundamental interactions between the point particles. Thus,
electrons and other point particles are no waves and the wavy chapter of
quantum mechanics originated for the force carriers. A stochastic
Lorentz-Langevin equation is proposed to describe the underlaying Brownian-like
motion of the point particles in quantum mechanics. Considering the Brownian
dynamics in the frames of the Bohmian mechanics, the density functional
Bohm-Langevin equation is proposed, and the relevant Smoluchowski-Bohm equation
is derived. A nonlinear master equation is proposed by proper quantization of
the classical Klein-Kramers equation. Its equilibrium solution in the exact
canonical Gibbs density operator, while the well-known Caldeira-Leggett
equation is simply a linearization at high temperature. In the case of a free
quantum Brownian particles, a new law for the spreading of the wave packet it
discovered, which represents the quantum generalization of the classical
Einstein law of Brownian motion. A new projector operator is proposed for the
collapse of the wave function of a quantum particle moving in a classical
environment. Its application results in dissipative Schrodinger equations, as
well as in a new form of dissipative Liouville equation in classical mechanics.

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The categories of this paper are: econ
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph