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For a scattering problem of tight-binding Bloch electrons by a weak random surface potential, a generalized Levinson theorem is put forward showing the equality of the total density of surface states and the density of the total time delay.…
The role of acceleration in particle physics can provide an alternative method for probing the properties of quantum gravity. To analyze acceleration-induced processes one utilizes the formalism of quantum field theory in curved spacetime.…
We introduce and study a generalized energy conservation relation for scattering of time-modulated waves, where conventional energy conservation does not hold. Based on this relation, we derive an optical theorem and compute the active…
Acoustic fields effect steady transport of suspended particles by rectifying the inertia of primary oscillations. We develop a fully analytic theory that relates this steady particle motion to incident oscillatory (acoustic) flow and the…
We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in $\R^n$, $n \in \{1, 2, 3\}$. Standard homogenization theory provides, for the limit of a small periodicity length…
The classical motion of a one-dimensional chain of atoms coupled through a specific force function that depends on position shows features very similar to the Wannier-Stark problem of a quantum particle under the combined effects of a…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We show that the lattice Boltzmann formalism can be used to describe wave propagation in a heterogeneous media, as well as solid-body-like systems and fracture propagation. Several fundamental properties of real fractures (such as…
We investigate the scattering of scalar plane waves in two dimensions by a heterogeneous layer that is periodic in the direction parallel to its boundary. On describing the layer as a union of periodic laminae, we develop a solution of the…
We develop a theory of Brownian motion of a massive particle, including the effects of inertia (Kramers' problem), in spaces with curvature and torsion. This is done by invoking the recently discovered generalized equivalence principle,…
We present a compact and general derivation of the generalized Bloch-Wangsness-Redfield kinetic equations for systems with the static spin Hamiltonian utilizing the concept of the Liouville space. We show that the assumptions of short…
We consider a quantum particle, moving on a lattice with a tight-binding Hamiltonian, which is subjected to measurements to detect it's arrival at a particular chosen set of sites. The projective measurements are made at regular time…
We propose a scheme to realize lattice potentials of sub-wavelength spacing for ultracold atoms. It is based on spin-dependent optical lattices with a time-periodic modulation. We show that the atomic motion is well described by the…
We consider a classical test particle subject to electromagnetic and gravitational fields, described by a Lagrangian depending on the acceleration and on a fundamental length. We associate to the particle a moving local reference frame and…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
We show that under certain circumstances an atom can follow an oscillatory motion in a periodic laser profile with a Gaussian envelope. These oscillations can be well explained by using a model of energetically forbidden spatial regions.…
We analyze Bohm's potential effects both in the realms of Quantum Mechanics and Optics, as well as in the study of other physical phenomena described in terms of classical and quantum wave equations. We approach this subject by using…
We present theoretical and numerical results on the dynamics of ultracold atoms in an accelerated single- and double-periodic optical lattice. In the single-periodic potential Bloch oscillations can be used to generate fast directed…
We present a generalization of Bloch's theorem to finite-range lattice systems of independent fermions, in which translation symmetry is broken only by arbitrary boundary conditions, by providing exact, analytic expressions for all energy…
Wavefunction effects in uncorrelated systems are characterized by the Berry curvature and quantum metric. Beyond those, we propose gauge-independent tensors describing Bloch wavefunction effects on local interaction between correlated…