Related papers: On the time evolution of fermionic occupation numb…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time ). The…
New spherical scalar modes on the expanding part of Sitter spacetime, eigenfunctions of a conserved Hamiltonian-like operator are found by solving the Klein-Gordon equation in the appropriate coordinate chart, with the help of a time…
The Feynman parametrization of the Dirac equation is considered in order to obtain an indefinite mass formulation of relativistic quantum mechanics. It is shown that the parameter that labels the evolution is related to the proper time. The…
We present a stochastic method for the simulation of the time evolution in systems which obey generalized statistics, namely fractional exclusion statistics and Gentile's statistics. The transition rates are derived in the framework of…
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…
We start from a Hamiltonian describing non-interacting fermions and add bosons to the model, with a Jaynes-Cummings-like interaction between the bosons and fermions. Because of the specific form of the interaction the model can be solved…
We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…
The evolution equations mentioned in the title of this paper read as follows: x~n = P(n)(x1; x2) , n = 1, 2 , where l is the "discrete-time" independent variable taking integer values (l =0, 1, 2, ...), xn = xn (l) are the 2 dependent…
It is shown, under weak conditions, that the dynamical evolution of an important class of large systems of globally coupled, heterogeneous frequency, phase oscillators is, in an appropriate physical sense, time-asymptotically attracted…
Usually, in supersymmetric theories, it is assumed that the time-evolution of states is determined by the Hamiltonian, through the Schr\"odinger equation. Here we explore the superevolution of states in superspace, in which the supercharges…
We show that a 2-dimensional system of N fermions interacting through a pairwise electric and magnetic singular interactions with Slater initial data preserves its Slater structure over time when N gets large. In other words, the wave…
The purpose of the present paper is to discuss the time dependent Schr\"odinger equation on a metric graph with time-dependent edge lengths, and the proper way to pose the problem so that the corresponding time evolution is unitary. We show…
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…
We provide a new perspective on non-Hermitian evolution in quantum mechanics by emphasizing the same method as in the Hermitian quantum evolution. We first give a precise description of the non unitary evolution, and collecting the basic…
The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics…
Dynamics of classical scattering in the system of fermions is studied. The model is based on the coherent state representation and the equations of motion for fermions are derived from the time-dependent variational principle. It is found…
We outline an extension of the classical Langevin equation to a quantum formulation of the treatment of dissipation and fluctuations of all collective degrees of freedom with unitary evolution of a many-fermion system within an extension of…
Given a self-adjoint operator $H\geq 0$ and (appropriate) densely defined and closed operators $P_{1},\dots, P_{n}$ in a Hilbert space $\mathscr{H}$, we provide a systematic study of bounded operators given by iterated integrals…
There is a widespread belief in the quantum physical community, and in textbooks used to teach Quantum Mechanics, that it is a difficult task to apply the time evolution operator Exp{-itH/h} on an initial wave function. That is to say,…