Dissipation and Diffusion of Quantum Light Field

H. C. Fan, Liyun Hu

Zahid Zakir

The theory of non-dissipative diffusion is constructed on an example of diffusion of a light particle in a dilute medium of heavy particles and it is shown that in low dissipative systems there are specific effects of non-dissipativity similar to quantum effects.In a non-dissipativity region mean energy of the light particle is conserved and processes are described by two non-linear diffusion equations with forward and backward time derivatives.Then these two diffusion equations are linearized and give one linear Schrödinger equation for complex amplitudes of probability.As a result, in the non-dissipative classical diffusion should be added probability amplitudes and there holds the superposition principle for these amplitudes.A mean square length of free passage and a mean square momentum define an elementary phase volume and a diffusion constant and they obey the uncertainty relations.It is shown that the formalism of quantum mechanics describes the classical non-dissipative diffusion with a homogeneous diffusion constant and that quantum mechanics is only a particular case when the elementary phase volume of free passage is universal and equal to the Planck constant.

Прудников Олег Николаевич, А. В. Тайченачев, Valeriy I. Yudin

The kinetics of atoms in a bichromatic field formed by waves with an arbitrary elliptical polarisation is considered. Analytical expressions are derived for the force and the friction and diffusion coefficients within the model of an atom with the j g = 1/2 → j e = 3/2 optical transition. These expressions are presented in the general form as an expansion in gradients of light field parameters. Some specific features of the kinetics of atoms are found, which are due to the interference contributions to the friction and diffusion coefficients. The kinetics of atoms in the field of an optical lattice formed as a result of the interference of a wave with a uniform elliptical polarisation and a nonuniformly polarised dissipative field is analysed.

Sam Tarzi

P. A. Nosov, D. S. Shapiro, Moshe Goldstein +1 more

The use of dissipation for the controlled creation of nontrivial quantum many-body correlated states is of much fundamental and practical interest. What is the result of imposing number conservation, which, in closed system, gives rise to diffusive spreading? We investigate this question for a paradigmatic model of a two-band system, with dissipative dynamics aiming to empty one band and to populate the other, which had been introduced before for the dissipative stabilization of topological states. Going beyond the mean-field treatment of the dissipative dynamics, we demonstrate the emergence of a diffusive regime for the particle and hole density modes at intermediate length- and timescales, which, interestingly, can only be excited in nonlinear response to external fields. We also identify processes that limit the diffusive behavior of this mode at the longest length- and timescales. Strikingly, we find that these processes lead to a reaction-diffusion dynamics governed by the Fisher-Kolmogorov-Petrovsky-Piskunov equation, making the designed dark state unstable towards a state with a finite particle and hole density.

R. Loudon