Related papers: Anomalous Threshold Laws in Quantum Sticking
A spinless nonrelativistic quantum particle on the curved surface of a homogeneous spherocylindrical capsule is considered. We apply Costa's formalism to solve the Schr\"{o}dinger equation with only a confined potential forcing the particle…
The power-law disks are a family of infinitesimally thin, axisymmetric stellar disks of infinite extent. The rotation curve can be rising, falling or flat. The self-consistent power-law disks are scale-free, so that all physical quantities…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each…
Anomalous tunneling refers to the phenomenon in which the transmission coefficient through a potential barrier approaches unity as the energy of an incident particle or quasiparticle tends to zero. This counterintuitive effect has been…
We present a general virial theorem for quantum particles with arbitrary zero-range or finite-range interactions in an arbitrary external potential. We deduce virial theorems for several situations relevant to trapped cold atoms: zero-range…
Particles of low velocity, travelling without dissipation in a superfluid, can interact and emit sound when they collide. We propose a minimal model in which the equations of motion of the particles, including a short-range repulsive force,…
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body…
We study charged particles in three dimensions interacting via a short-range potential in addition to the Coulomb potential. When the Bohr radius and the scattering length are much larger than the potential range, low-energy physics of the…
We start with a rather detailed, general discussion of recent results of the replica approach to statistical mechanics of a single classical particle placed in a random $N (\gg 1)$-dimensional Gaussian landscape and confined by a…
Particle-antiparticle pairs are predicted by quantum field theory to appear as vacuum fluctuations. The model of the vacuum used here is postulated to have the following properties: To minimize the violation of conservation energy allowed…
Quantum gravitational effects become significant at a cut-off species scale that can be much lower than the Planck scale whenever we get a parametrically large number of fields becoming light. This is expected to occur at any perturbative…
In this work, we study the analytic properties of S-matrix for unstable particles, which is defined as the residues on the unphysical sheets where unstable poles reside. We demonstrate that anomalous thresholds associated with UV physics…
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model…
The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a…
The probability amplitude for $N$ particles in a quantum gas with negligible range of interparticle interaction potentials to come to a small region of size $r$ scales like $r^\gamma$. It is shown that $\gamma$ is quantitatively related to…
We show analytically and numerically that, the velocity $v_\pm$ of a particle near the turning points $x_0$ vanishes, i. e. $v_\pm\rightarrow 0$ as $x\rightarrow x_0$, according to the power law scaling $\left|v_\pm\right| \propto…
It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization…
The small energy anomaly in the single particle density of states of disordered interacting systems is studied for the zero dimensional case. This anomaly interpolates between the non--perturbative Coulomb blockade and the perturbative…
In the present paper, first the mathematical basic properties of the exceptional points are discussed. Then, their role in the description of real physical quantum systems is considered. Most interesting value is the phase rigidity of the…