Related papers: Commutator expansions in NMR diffusometry
The paper presents solution of quantum problem of neutron propagation in the magnetic field with multipole field expansion. Rigorous solution of the Pauli equation for neutron reveals existence of two solutions, finite and infinite, for any…
We explore particle accelerator electrodynamics in the magnetosphere of a rapidly rotating neutron star (NS). We address the importance of a self-consistent treatment of pair production, solving the Poisson equation describing the…
This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\"uller equation to composite structures through the global multi-trace…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…
New solvable one-dimensional quantum mechanical scattering problems are presented. They are obtained from known solvable potentials by multiple Darboux transformations in terms of virtual and pseudo virtual wavefunctions. The same method…
We present an approach to spin dynamics by extending the optical Bloch equations for the driven two-level system to derive microscopic expressions for the transverse and longitudinal spin relaxation times. This is done for the 6-level…
A pseudo-spectral method with an absorbing outer boundary is used to solve a set of the time-dependent force-free equations. In the method, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH)…
We develop a general framework for response theory in diffusion processes governed by Fokker-Planck equations, based on the notion of the Dissipation Function. Using the analytically solvable Brownian oscillator model, we derive exact…
Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the…
We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by…
We study the relaxation of a test particle immersed in a bath of field particles interacting via weak long-range forces. To order 1/N in the $N\to +\infty$ limit, the velocity distribution of the test particle satisfies a Fokker-Planck…
We analyze the many-particle Schrodinger equation for fermions in a thermal ensemble by introducing an exponential operator expansion, defined in the context of thermofield dynamics. The expansion is optimized variationally at each time…
The paper starts by giving a motivation for this research and justifying the considered stochastic diffusion models for cosmic microwave background radiation studies. Then it derives the exact solution in terms of a series expansion to a…
The double series approximation method of Bonnor is a means for examining the gravitational radiation from an axisymmetric isolated source that undergoes a finite period of oscillation. It involves an expansion of the metric as a double…
We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential…
The aim of this paper is the rigorous derivation of a stochastic non-linear diffusion equation from a radiative transfer equation perturbed with a random noise. The proof of the convergence relies on a formal Hilbert expansion and the…
Maxwell-Bloch system describing the resonant propagation of electromagnetic pulses in both two-level media with degeneracy in angle moment projection and three-level media with equal oscillator forces is considered. The inhomogeneous…
The Bloch equation is the fundamental dynamical model applicable to arbitrary two-level systems. Analytical solutions to date are incomplete for a number of reasons that motivate further investigation. The solution obtained here for the…
We give a self-contained exposition of the combinatorial solution of quantum mechanical systems of coupled spins on a one-dimensional lattice. Using Trotter formula, we write the partition function as a generating function of a spanning…
We prove existence of propagators for a time dependent Schr\"odinger equation with a new class of softened Coulomb potentials, which we allow to be time dependent, in the context of time dependent density functional theory. We compute…