Subdynamics of fluctuations in a many-particle quantum system

Abstract

It is shown that the relevant part of an equilibrium two-time correlation function of operators related to a subsystem of S < N particles, selected from the whole system of N ≫ 1 quantum particles, obeys the exact completely closed (homogeneous) evolution equation. This equation differs from the conventional Nakajima–Zwanzig equation by the absence of the undesirable inhomogeneous term comprising all interparticle correlations at the initial time moment. The equation defines the subdynamics in a subspace of S selected particles and is obtained without any use of approximation like the Boltzmann ‘molecular chaos’, factorized initial state or Bogoliubov’s principle of weakening of initial correlations. In the second order in a small inter-particle interaction, this equation reduces to the Markovian evolution equation, which for a one-particle correlation function (S = 1) takes the form of the linear generalized quantum Boltzmann-like equation for a relevant part of a correlation function (one particle momentum distribution function) with the additional terms conditioned by initial correlations taken into account. This equation makes it possible to obtain the solution for the corresponding one-particle correlation function, which is valid for all timescales and reveals the influence of initial correlations on the evolution in time process. On a large timescale t ≫ t cor ∼ ℏ/k B T (decoherence time), the initial correlations cease to influence the damping process and the evolution enters a kinetic stage. However, the factor related to initial correlations survives on the large timescale, and can contribute to the kinetic coefficients.