Kinetic Equation for Elementary Excitations in Quantum Systems

V. G. Bar’yakhtar, Vladimir N. Kostur, Serhii E. Shafranjuk

Alexander I. Akhiezer, S. V. Peletminskiǐ

Isaak M. Khalatnikov

The distribution function of the elementary excitations satisfies the kinetic equation ( 18-1 ) ∂ n ∂ t + ∂ n ∂ r ⋅ ∂ H ∂ p − ∂ n ∂ p ⋅ ∂ H ∂ r = ℐ ( n ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429502897/20d72e0b-9d39-4175-acc6-a943547edf8a/content/eq539.tif"/>

José Tito Mendonça

We discuss the Schrödinger–Newton (SN) equation in the context of cold atom physics. For that purpose, we establish the wave-kinetic equation equivalent to the SN equation, which stays valid in different physical scenarios relevant to cold atoms. They include: (1) the usual scenario of matter confined in a self-gravitating field, (2) atomic molasses, confined and cooled by laser beams in a magneto-optical trap (MOT), (3) Bose–Einstein condensates, with or without long range dipolar interactions, and (4) electron states in a quantum plasma. We show that these different systems can be described by a formally identical equation, and they also manifest similar elementary excitations. The wave-kinetic equation is obtained by following the well-known Wigner–Moyal procedure, allowing the representation of quantum states in a classical phase-space. It is particularly well suited to discuss kinetic properties associated with Landau damping, as shown. We also consider generalisation of the SN equation onto the relativistic domain, and its impact on the proposed wave-kinetic description.

G. O. Balabanyan