The BBGKY hierarchy in quantum statistical mechanics

M. Yu. Rasulova

Abstract In this paper, a new encryption method based on statistical mechanics is proposed, which enables transmitting information without transmitting the encryption key after sending the information, and also makes it possible to determine its own transformation for each information cell. For these purposes, solutions of the Schrödinger equation (Lieb–Liniger model) and a hierarchy of quantum kinetic BBGKY equations with the delta-function potential are used.

Ola Bratteli, Derek W. Robinson

Masakazu Ichiyanagi

By means of the time-smoothing method developed in the previous papers of this series, the quantum kinetic equation is derived from the principles of statistical mechanics. In this paper, we avoid the BBGKY hierarchy; instead we use the Liouville-von Neumann equation for the time-smoothed density matrix. The Boltzmann distribution function is defined in terms of this time-smoothed density matrix. The present scheme may be applied to strong-coupling systems even if they are not in near equilibrium.

Carl S. Helrich

Mukhayo Yunusovna Rasulova

In this paper, a new encryption method based on statistical mechanics is proposed, which enables transmitting information without transmitting the encryption key after sending the information, and also makes it possible to determine its own transformation for each information cell.For these purposes, solutions of the Schrödinger equation (Lieb -Liniger Model) and a hierarchy of quantum kinetic BBGKY equations with the delta function potential are used.

Ivo Sachs, Siddhartha Sen, James Sexton