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An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schroedinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and…
The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average…
Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schr\"odinger equation with an…
Variational solutions of the Boltzmann equation usually rely on the concept of linear response. We extend the variational approach for tight-binding models at high entropies to a regime far beyond linear response. We analyze both weakly…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
In highly conducting astrophysical plasmas, charged particles are generically accelerated through Fermi-type processes involving repeated interactions with moving magnetized scattering centers. The present paper proposes a generalized…
The action reaction principle is violated by the projection of state in some simple quantum measurements. A formulation of Quantum Mechanics in an extended phase space is proposed in order to restore the action reaction principle. All…
A fundamental idea in wave mechanics is that propagation in a periodic medium can be described by Bloch waves whose conserved crystal momenta define their transformations when displaced by the set of discrete lattice translations. In…
Bloch oscillations are a hallmark of coherent wave dynamics in periodic potentials. They occur as the response of quantum mechanical particles in a lattice if a weak force is applied. In optical lattices with their perfect periodic…
We consider spatially coupled systems governed by a set of scalar density evolution equations. Such equations track the behavior of message-passing algorithms used, for example, in coding, sparse sensing, or constraint-satisfaction…
Recently, the spectral manipulation of single photons has been achieved through spatial-temporal modulation of the optical refractive index. Here, we generalize this mechanism to massive particles, i.e. realizing the acceleration or…
We develop a theoretical framework for the diffusion of a single unconstrained species of atoms on a crystal lattice that provides a generalization of the classical theories of atomic diffusion and diffusion-induced phase separation to…
We report the direct observation and characterization of position-space Bloch oscillations using an ultracold gas in a tilted optical lattice. While Bloch oscillations in momentum space are a common feature of optical lattice experiments,…
Universality class of wave chaos emerges in many areas of science, such as molecular dynamics, optics, and network theory. In this work, we generalize the wave chaos theory to cavity lattice systems by discovering the intrinsic coupling of…
We study waves governed by the planar Helmholtz equation, propagating in an infinite lattice of subwavelength Dirichlet scatterers, the periodicity being comparable to the wavelength. Applying the method of matched asymptotic expansions,…
Several applications exist in which lattice Boltzmann methods (LBM) are used to compute stationary states of fluid motions, particularly those driven or modulated by external forces. Standard LBM, being explicit time-marching in nature,…
This paper presents a formalism describing the dynamics of a quantum particle in a one-dimensional, time-dependent, tilted lattice. The formalism uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a…
The Lorentz covariant theory of propagation of light in the (weak) gravitational fields of N-body systems consisting of arbitrarily moving point-like bodies with constant masses is constructed. The theory is based on the Lienard-Wiechert…
In this study, we use the concept of Bohmian trajectories to present a dynamical and deterministic interpretation for the gravity induced wave function reduction. We shall classify all possible regimes for the motion of a particle, based on…
A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a…