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We study the real-time dynamics of quantum models with long-range interactions coupled to a heat-bath within the closed-time path-integral formalism. We show that quantum fluctuations depress the transition temperature. In the subcritical…
For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…
The processes of ecological interactions, dispersal and mutations shape the dynamics of biological communities, and analogous eco-evolutionary processes acting upon economic entities have been proposed to explain economic change. This…
The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches…
A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last…
The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this work, we show that, remarkably,…
The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman and von Neumann and was developed in later decades by many…
Dynamics of many-body Hamiltonian systems with long range interactions is studied, in the context of the so called $\alpha-$HMF model. Building on the analogy with the related mean field model, we construct stationary states of the…
Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental…
Classical cosmology exhibits a particular kind of scaling symmetry. The dynamics of the invariants of this symmetry forms a system that exhibits many of the features of open systems such as the non-conservation of mechanical energy and the…
The paper deals with the problem of the rigorous description of the evolution of states of large particle quantum systems by means of correlation operators. A nonperturbative solution of the Cauchy problem of the hierarchy of nonlinear…
In many physical situations the behavior of a quantum system is affected by interaction with a larger environment. We develop, using the method of influence functional, how to deduce the density matrix of the quantum system incorporating…
The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation of its reduced density. The influence of the environment is incorporated through a mean-field which is both stochastic…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We…
We introduce a framework that represents a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based only on order-theoretic assumptions and show how applications across almost all…
This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three…
In this work, we present a quantization scheme for the damped harmonic oscillator (QDHO) using a framework known as momentous quantum mechanics. Our method relies on a semiclassical dynamical system derived from an extended classical…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…