Related papers: Manifestly covariant classical correlation dynamic…
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved…
The quantum-classical Liouville equation describes the dynamics of a quantum subsystem coupled to a classical environment. It has been simulated using various methods, notably, surface-hopping schemes. A representation of this equation in…
The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability…
Liouville theorems for scaling invariant nonlinear elliptic systems (saying that the system does not possess nontrivial entire solutions) guarantee a priori estimates of solutions of related, more general systems. Assume that $p=2q+3>1$ is…
We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our projection operator based theory yields a highly efficient…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
We propose a simple method that allows, in one dimension, to solve exactly a wide class of classical stochastic many-body systems far from equilibrium. For the sake of illustration and without loss of generality, we focus on a model that…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic…
Full information about a many-body quantum system is usually out-of-reach due to the exponential growth -- with the size of the system -- of the number of parameters needed to encode its state. Nonetheless, in order to understand the…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
We study the 1D quantum many-body dynamics with a screened Coulomb potential in the mean-field setting. Combining the quantum mean-field, semiclassical, and Debye length limits, we prove the global derivation of the 1D Vlasov-Poisson…
We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics, including variations of the Bolker-Pacala-Dieckmann-Law model. Under the…
Dynamics in correlated quantum matter is a hard problem, as its exact solution generally involves a computational effort that grows exponentially with the number of constituents. While a remarkable progress has been witnessed in recent…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…
The problem of the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on phase space. The original work of Zaslovskii {\it et al} showed that the resulting evolution contains a…
We review the recently proposed unreduced, complex-dynamical solution to the many-body problem with arbitrary interaction and its application to the unified solution of fundamental problems, including dynamic foundations of causally…