Related papers: Universality in scattering by large-scale potentia…
This paper blends two techniques recently developed in [2] and [3] to prove the presence of absolutely continuous spectrum for the multidimensional Schrodinger operator provided that the potential is summable over trajectory with positive…
The electron-electron scattering increases the resistance of ballistic many-mode channels whose width is smaller than their length. We show that this increase saturates in the limit of infinitely long channels. Because the mechanisms of…
Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement $\overline{\delta^2}$ of individual particles remains a random variable while indicating that the particle…
A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be…
Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…
We prove that, in (2+1) dimensions, the S-wave phase shift, $ \delta_0(k)$, k being the c.m. momentum, vanishes as either $\delta_0 \to {c\over \ln (k/m)} or \delta_0 \to O(k^2)$ as $k\to 0$. The constant $c$ is universal and $c=\pi/2$.…
We study the statistical properties of wave scattering in a disordered waveguide. The statistical properties of a "building block" of length (delta)L are derived from a potential model and used to find the evolution with length of the…
We derive constraints on the statistics of the charge transfer between two conductors in the model of arbitrary time-dependent instant scattering of non-interacting fermions at zero temperature. The constraints are formulated in terms of…
We analyze electron transport through relatively short coherent conductors in the presence of Coulomb interaction. We evaluate the current-voltage characteristics of such conductors taking into account the effect of an external environment.…
Anomalous dynamics in which local perturbations spread faster than diffusion are ubiquitously observed in the long-time behavior of a wide variety of systems. Here, the manner by which such systems evolve towards their asymptotic…
In this letter, we present the unified paradigm on entropy-ruled Einstein diffusion-mobility relation ({\mu}/D ratio) for all dimensional systems (1D, 2D and 3D) of molecules and materials. The different dimension-associated fractional…
Theory of electron-acoustic single phonon scattering has been reconsidered. It is assumed that the non-degenerate semiconductor has a spherical parabolic band structure. In the basis of the reconsideration there is a phenomenon of the…
The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…
It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…
We consider the scattering theory for the Schrodinger equation with $-\Delta -|x|^{\alpha}$ as a reference Hamiltonian, for $0< \alpha \leq 2$, in any space dimension. We prove that when this Hamiltonian is perturbed by a potential, the…
A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
The universal form for the average scattering intensity from systems undergoing order-disorder transitions is found by numerical integration of the Langevin dynamics. The result is nearly identical for simulations involving two different…
Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal…
The scattering of free particles constrained to move on a cylindrically symmetric curved surface is studied. The nontrivial geometry of the space contributes to the scattering cross section through the kinetic as well as a possible scalar…