Related papers: The Linear Dynamics of Wave Functions in Causal Fe…
A first-order relativistic wave equation is constructed in five dimensions. Its solutions are eight-component spinors, which are interpreted as single-particle fermion wave functions in four-dimensional spacetime. Use of a ``cylinder…
A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics that can be described by the Lindblad master equation in Liouville density operator space. The method extends the Hilbert space…
We investigate fermion production in the background of Minkowski space solutions to the equations of motion of $SU(2)$ gauge theory spontaneously broken via the Higgs mechanism. First, we attempt to evaluate the topological charge $Q$ of…
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…
It is shown that one can obtain canonically-defined dynamical equations for non-conservative mechanical systems by starting with a first variation functional, instead of an action functional, and finding their zeroes. The kernel of the…
We derive a model Hamiltonian whose ground state expectation value of any two-body operator coincides with that obtained with the Jastrow correlated wave function of the many-body Fermi system. Using this Hamiltonian we show that the…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential…
General formula for causal Green's function of linear differential operator of given degree in one variable is given according to coefficient functions of differential operator as a series of integrals. The solution also provides analytic…
Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin-1/2 fermions (typically, electrons) including the Zeeman effect and the spin-orbit coupling. This Wigner…
An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on…
The periodic standing wave approach to binary inspiral assumes rigid rotation of gravitational fields and hence helically symmetric solutions. To exploit the symmetry, numerical computations must solve for ``helical scalars,'' fields that…
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
It is expected that the quantum nature of spacetime leaves its imprint in all semiclassical gravitational systems, at least in certain regimes, including gravitational waves. In this paper we investigate such imprints on gravitational waves…
We introduce and analyze a system of relativistic fermions in a space-time continuum, which interact via an action principle as previously considered in a discrete space-time. The model is defined by specifying the vacuum as a sum of Dirac…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a…
Within the f-deformed oscillator formalism, we derive a Markovian master equation for the description of the damped dynamics of nonlinear systems that interact with their environment. The applicability of this treatment to the particular…
We formulate the dynamical mean field theory directly in the continuum. For a given definition of the local Green's function, we show the existence of a unique functional, whose stationary point gives the physical local Green's function of…
The multivariate analogue of Dalamber's equation in the space of generalized functions is considered. The method of generalized functions for the building of solutions of nonstationary boundary value problems for wave equations in spaces of…