Related papers: Statistical Field Theory of Interacting Nambu Dyna…
In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we…
There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter…
The dynamics of quasi-stationary states of long-range interacting systems with $N$ particles can be described by kinetic equations such as the Balescu-Lenard and Landau equations. In the case of one-dimensional homogeneous systems, two-body…
We review recent developments in the theory of interacting quantum many-particle systems that are not in equilibrium. We focus mainly on the nonequilibrium generalizations of the flow equation approach and of dynamical mean-field theory…
A recently proposed statistical theory of the mean fields associated with the ground and excited collective states of a generic many-body system is extended by increasing the dimensions of the P-space. In applying the new framework to…
Concepts of quantum open systems and ideas of correlation dynamics in nonequilibrium statistical mechanics, as well as methods of closed-time-path effective action and influence functional in quantum field theory can be usefully applied for…
Nonequilibrium states of closed quantum many-body systems defy a thermodynamic description. As a consequence, constraints such as the principle of equal a priori probabilities in the microcanonical ensemble can be relaxed, which can lead to…
Advances in controlling and measuring systems of ultra-cold atoms provided strong motivation to theoretical investigations of quantum dynamics in closed many-body systems. Fundamental questions on quantum dynamics and statistical mechanics…
As the quantification of metabolism, nonequilibrium steady states play a central role in living matter, but are beyond the purview of equilibrium statistical mechanics. Here we develop a fermionic theory of nonequilibrium steady states in…
We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…
We here discuss the emergence of Quasi Stationary States (QSS), a universal feature of systems with long-range interactions. With reference to the Hamiltonian Mean Field (HMF) model, numerical simulations are performed based on both the…
A statistical approach to a self-consistent description of kinetic and hydrodynamic processes in systems of interacting particles is formulated on the basis of the nonequilibrium statistical operator method by D.N.Zubarev. It is shown how…
This contribution presents a derivation of the steady-state distribution of velocities and distances of driven particles on a onedimensional periodic ring. We will compare two different situations: (i) symmetrical interaction forces…
The Hamiltonian Mean Field model describes a system of N fully-coupled particles showing a second-order phase transition as a function of the energy. The dynamics of the model presents interesting features in a small energy region below the…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
The new scheme employed (throughout the thermodynamic phase space), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions are formulated…
The present paper gives a new method of attack on the Nambu-Goldstone dynamics in spontaneously broken theories. Since the target space of the Nambu-Goldstone fields is a group coset space, their effective quantum dynamics can be naturally…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…
The relationship between the mean-field approximations in various interacting models of statistical physics and measures of classical and quantum correlations is explored. We present a method that allows us to bound the total amount of…