相关论文: Time Evolution of Two-Level Systems Driven by Peri…
Unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point. We find that for initial conditions with isolated particles, each hierarchy level exhibits an…
We investigate theoretically the dynamics of the system that consists of a cascade three-level emitter interacting with a single-mode resonator in the deep-strong-coupling regime. We show that the dynamical evolution of the system can only…
Periodically driven systems provide a novel route to control the topology of quantum materials. In particular, Floquet theory allows an effective band description of periodically-driven systems through the Floquet Hamiltonian. Here, we…
We study the convergence of stochastic time-discretization schemes for evolution equations driven by random velocity fields, including examples like stochastic gradient descent and interacting particle systems. Using a unified framework…
Complex Earth System Models are widely utilised to make conditional statements about the future climate under some assumptions about changes in future atmospheric greenhouse gas concentrations; these statements are often referred to as…
Simulation of population dynamics is a central research theme in computational biology, which contributes to understanding the interactions between predators and preys. Conventional mathematical tools of this theme, however, are incapable…
In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…
We consider the problem of two-level system dynamics induced by the time-dependent field B={a(t)cos\omega t,a(t)sin\omega t,\omega_0}, with a(t) \sim cn(\nu t,k). The problem is exactly analytically solvable and we propose the scheme for…
We study the dissipative dynamics of a two-level system under ultrastrong driving when the frequency and strength of the exciting field exceed significantly the transition frequency. We find three qualitatively different regimes of such…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve $\cC$…
We have obtained propagators in the position space as an expansion over Landau levels for the charged scalar particle, fermion, and massive vector boson in a constant external magnetic field. The summation terms in the resulting expressions…
In the evolutionary Prisoner's Dilemma (PD) game, agents play with each other and update their strategies in every generation according to some microscopic dynamical rule. In its spatial version, agents do not play with every other but,…
Evolutionary games on graphs play an important role in the study of evolution of cooperation in applied biology. Using rigorous mathematical concepts from a dynamical systems and graph theoretical point of view, we formalize the notions of…
Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an {\it arrow of time} that follows from the fact that…
We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme which treat the nonlinear term explicitly (backward differentiation formula with a one-leg method). Uniform bounds on…
Multiple time correlation functions are found in the dynamical description of different phenomena. They encode and describe the fluctuations of the dynamical variables of a system. In this paper we formulate a theory of non-Markovian…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…
The dynamical systems methods are used to study evolution of the polymerised scalar field cosmologies with the cosmological constant. We have found all evolutional paths admissible for all initial conditions on the two-dimensional phase…
We study the evolution of an oscillator interacting via the most general bilinear coupling (with time-independent coefficients) with an ``environment'' consisting of a set of other harmonic oscillators. We are mainly interested in a…