Related papers: Dirac Particle with Memory: Proper Time Non-Locali…
Our main interest in this paper is the study of homogenised limit of a parabolic equation with a nonlinear dynamic boundary condition of the micro-scale model set on a domain with periodically place particles. We focus on the case of…
Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the…
In this paper we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the…
In 1932, Dirac proposed a formulation in terms of multi-time wave functions as candidate for relativistic many-particle quantum mechanics. A well-known consistency condition that is necessary for existence of solutions strongly restricts…
Generalized solutions of the standard gauge transformation equations are presented and discussed in physical terms. They go beyond the usual Dirac phase factors and they exhibit nonlocal quantal behavior, with the well-known Relativistic…
Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. The vast majority of them are for highly symmetric stationary systems. Moreover, only a handful of solutions for time dependent dynamics…
Quantum reservoir computing (QRC) harnesses driven quantum dynamics for time-series processing, yet the mechanisms behind the differing performance levels across its many implementations remain unclear. We show that apparently unrelated…
Pump-probe techniques with high temporal resolution allow one to drive a system of interest out of equilibrium and at the same time, probe its properties. Recent advances in these techniques open the door to studying new, non-equilibrium…
Dirac structures are geometric objects that generalize Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems and play an essential role in structuring a…
Recently a new type of Kramers-Fokker-Planck Equation has been proposed [R. Friedrich et al. Phys. Rev. Lett. {\bf 96}, 230601 (2006)] describing anomalous diffusion in external potentials. In the present paper the explicit cases of a…
Dirac, Fock, and Podolsky [Ref. 1] devised a relativistic model in 1932 in which a fixed number of $N$ Dirac electrons interact through a second-quantized electromagnetic field. It is formulated with the help of a multi-time wave function…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body…
We consider two models of deterministic active particles in an external potential. In the limit where the speed of a particle is fixed, both models coincide and can be formulated as a Hamiltonian system, but only if the potential is…
In a previous work we have described the classical structure and analyzed the interaction of the classical Dirac particle with uniform and oscillating electric and magnetic fields. In the present paper we consider the interaction of the…
We consider the Dirac equation coupled to an external electromagnetic field in curved four-dimensional spacetime with a given timelike worldline $\gamma$ representing a classical clock. We use generalised Fermi normal coordinates in a…
A generalization of the pseudoclassical action of a spinning particle in the presence of an anomalous magnetic moment is given. The leading considerations, to write the action, are gotten from the path integral representation for the causal…
We consider kinetic models for Fermi-Dirac-like particles obeying the exclusion principle. A generalized notion of Fisher information, tailored to kinetic equations of Fermi-Dirac-Fokker-Planck type, is introduced via the associated entropy…
Lack of memory (locality in time) is a major limitation of almost all present time-dependent density functional approximations. By using semiclassical dynamics to compute correlation effects within a density-matrix functional approach, we…
The formalism of Operational Dynamical Modeling [Phys. Rev. Lett. {\bf 109}, 190403 (2012)] is employed to analyze dynamics of spin half relativistic particles. We arrive at the Dirac equation from specially constructed relativistic…