English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the process of diffusion scattering of a wave function given onthe phase space. In this process the heat diffusion is considered only alongmomenta. We write down the modified Kramers equation describing this situation.In this model, the usual quantum description arises as asymptotics of thisprocess for large values of resistance of the medium per unit of mass ofparticle. It is shown that in this case the process passes several stages.During the first short stage, the wave function goes to one of "stationary"values. At the second long stage, the wave function varies in the subspace of"stationary" states according to the Schrodinger equation. Further, dissipationof the process leads to decoherence, and any superposition of states goes toone of eigenstates of the Hamilton operator. At the last stage, the mixed stateof heat equilibrium (the Gibbs state) arises due to the heat influence of themedium and the random transitions among the eigenstates of the Hamiltonoperator.  Besides that, it is shown that, on the contrary, if the resistance of themedium per unit of mass of particle is small, then in the considered model, thedensity of distribution of probability $\rho =|\phi |^2$ satisfies the standardLiouville equation, as in classical statistical mechanics.

Quantum Mechanics as Asymptotics of Solutions of Generalized Kramers Equation