Related papers: Manifestly covariant classical correlation dynamic…
Many-body quantum systems typically display fast dynamics and ballistic spreading of information. Here we address the open problem of how slow the dynamics can be after a generic breaking of integrability by local interactions. We develop a…
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of…
General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…
In this study the notion of particular integrability in Classical Mechanics, introduced in [J. Phys. A: Math. Theor. 46 025203, 2013], is revisited within the formalism of symplectic geometry. A particular integral $\cal I$ is a function…
At high temperature, generic strongly interacting spin systems are expected to display hydrodynamics: local transport of conserved quantities, governed by classical partial differential equations like the diffusion equation. I argue that…
The system is described by three mass-shell constraints. After a nonlinear transformation of the momenta, the analytic form taken by admissible interactions (allowing compatibility) is characterized in terms of the new variables. These…
We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational…
(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…
We provide a detailed discussion about the unitary and reduced evolution induced by family of Hamiltonian models describing a multilevel system, with a ground state and a possibly multilevel excited sector, coupled to a multimode boson…
Master equations are commonly used to describe time evolution of open systems. We introduce a general method for calculating a Markovian solution of the Nakajima-Zwanzig generalized master equation. We do so for a time dependent transport…
The probabilistic description of finite classical systems often leads to linear kinetic equations. A set of physically motivated mathematical requirements is accordingly formulated. We show that it necessarily implies that solutions of such…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
It is well known that Einstein's equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that {\em time} evolution of the…
We consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on…
The theory of real-time quantum many-body dynamics as put forward in Ref. [arXiv:0710.4627] is evaluated in detail. The formulation is based on a generating functional of correlation functions where the Keldysh contour is closed at a given…
The dynamical equation of hybrid systems, being the combination of Schr\"odinger and Liouville equations, produces noncausal evolution when the initial state of interacting quantum and classical mechanical systems is as it is demanded in…
The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum…