Related papers: Kinetic Equations for Quantum Many-Particle System…
The article provides an overview of some advances in the mathematical understanding of the nature of the kinetic equations of quantum systems of many particles. The fundamental equations of modern mathematical physics are studied, in…
This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to construct the kinetic equations in scaling limits in the presence…
In these lecture notes we discuss recent progress in the rigorous derivation of effective evolution equations for the description of the dynamics of quantum mechanical many-body systems.
We present a new way of quantum kinetic equation derivation. This method appears as a natural generalization of the many-particle quantum hydrodynamic method. Kinetic equations are derived for different system of particles. First of all we…
In the paper we discuss possible approaches to the problem of the rigorous derivation of quantum kinetic equations from underlying many-particle dynamics. For the description of a many-particle evolution we construct solutions of the Cauchy…
Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions…
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful…
In the paper we review some recent results of the theory of hierarchies of quantum evolution equations.
We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of a one-particle density operator…
Difference Kinetic Equations are derived quantum mechanically in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors…
The principle of energy conservation leads to a generalized choice of transition probability in a piecewise adiabatic representation of quantum(-classical) dynamics. Significant improvement (almost an order of magnitude, depending on the…
We discuss functional-integral approaches to far-from-equilibrium quantum many-body dynamics. Specific techniques considered include the two-particle-irreducible effective action and the real-time flow-equation approach. Different…
In this Ph.D. thesis dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. The research is neither restricted to static properties or long-term relaxation evolutions nor does it…
We discuss three different aspects of the quantum dynamics of bio-molecular systems and more generally complex networks in the presence of strongly coupled environments. Firstly, we make a case for the systematic study of fundamental…
From the analysis of the quantum and relativistic properties of the particles it results the unified quantum-relativistic dynamics of the physical reality (Universe).
We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems.
Generally, multi-particle spring system is an important and widely used physical model. However, with the increase of the number of particles, the difficulty of solving the kinematic trajectory of the particles becomes more and more…
We discuss the possibility to modify many-body Hilbert quantum formalism that is necessary for the representation of quantum systems dynamics. The notion of effective classical algorithm and visualization of quantum dynamics play the key…
In this paper, we deal with fluid motion in terms of quantum mechanics. Mechanism accounting for the appearance of quantum behavior is discussed.