In this paper a new approach to investigation of Quantum and Statistical Mechanics of the Early Universe (Planck scale)-density matrix deformation-is proposed. The deformation is understood as an extension of a particular theory by inclusion of one or several additional parameters in such a way that the initial theory appears in the limiting transition. In the first part of this chapter Quantum...

there are many claims that quantum mechanics plays a key role in the origin and/or operation of biological organisms. the mechanism of the meiosis, mitosis and gametes life cycle from the view-point of quantum for human has been represented. the quantum gates have been used to simulate these processes for the first time. the reason of several hundred sperms has been explained in the male too

A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of probability distributions into the space of all square-integrable functions. More precisely, by consideration of the square-root density function we can regard M as a ...

If a many-body quantum system approaches thermal equilibrium from a generic initial state, then the expectation value 〈ψ(t)|Ai|ψ(t)〉, where |ψ(t)〉 is the system’s state vector and Ai is an experimentally accessible observable, should approach a constant value which is independent of the initial state, and equal to a thermal average of Ai at an appropriate temperature. We show that this is the c...

We study the statistical mechanics and dynamical relaxation process of modulationally unstable one-dimensional quantum droplets described by a modified Gross-Pitaevskii equation. To determine classical partition function thereof, we leverage semi-analytical transfer integral operator (TIO) technique. The latter predicts distribution observed wave amplitudes yields two-point correlation function...