Related papers: Dynamique des nombres et physique des oscillateurs
The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose…
I present a theory of electron dynamics in semiconductors with slowly varying composition. I show that the frequency-dependent conductivity, required for the description of transport and optical properties, can be obtained from a knowledge…
Different types of nonstandard homology groups based on the various subcomplexes of differential forms are considered as a continuation of the recent authors works. Some of them reflect interesting properties of dynamical systems on the…
We study a quantum theory with complex time parameter and non-Hermitian Hamiltonian structure. In this theory, the real part of the complex time is equal to `usual' physical time, whereas the imaginary one is proportional to inverse…
The Jacobi theta-functions admit a definition through the autonomous differential equations (dynamical system); not only through the famous Fourier theta-series. We study this system in the framework of Hamiltonian dynamics and find…
This paper is a continuation of our study of the dynamics of contact Hamiltonian systems in \cite{JY}, but without monotonicity assumption. Due to the complexity of general cases, we focus on the behavior of action minimizing orbits. We…
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed…
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the…
Physical and chemical systems can be characterized by their natural frequency and energy scales. It is hardly an exaggeration that most of what we know about such systems, from the acoustics of a violin to the energy levels of atoms, comes…
We develop a thermodynamic framework for modeling innovation adoption and abandonment dynamics using statistical mechanics. Starting from a mathematical model for an adoption distribution that fits empirically obtained date, we construct a…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
The notion of spectrum of first-order properties introduced by J. Spencer for Erdos-Renyi random graph is considered in relation to random uniform hypergraphs. We study properties of spectrum for first-order formulae with bounded quantifier…
We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system has a dissipative structure, we proved that a random…
We introduce an extension of hamiltonian dynamics, defined on hyperkahler manifolds, which we call ``hyperhamiltonian dynamics''. We show that this has many of the attractive features of standard hamiltonian dynamics. We also discuss the…
The model of the physical system with discrete interactions is based on the postulates that (i) parameters of the physical system are defined in process of its interaction; (ii) the process of interaction is discrete. Consequently ordering…
We study stochastic dynamics of an inverted pendulum subject to a random force in the horizontal direction (Whitney's problem). Considered on the entire time axis, the problem admits a unique solution that always remains in the upper half…
The manipulation of mechanical waves is a long-standing challenge for scientists and engineers, as numerous devices require their control. The current forefront of research in the control of classical waves has emerged from a seemingly…
In the present contribution we investigate some features of dynamical lattice systems near periodic traveling waves. First, following the formal averaging method of Whitham, we derive modulation systems expected to drive at main order the…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…