Related papers: Application of the Trace Formula in Pseudointegrab…
Recently, we have demonstrated that the problems finding a suitable adiabatic approximation in time-dependent one-body reduced density matrix functional theory can be remedied by introducing an additional degree of freedom to describe the…
We demonstrate how an effective density of states can be derived from the S-matrix describing a coupled-channel system. Besides the locations of poles, the phase of the determinant of the S-matrix encodes essential details in characterizing…
Recently, new quantum effects have been studied in thin nano-grating layers. Nano-grating on the surface imposes additional boundary conditions on the electron wave function and reduces the density of states (DOS). When the nano-grating…
We compute the orbital magnetization in real materials by evaluating a recently discovered formula for periodic systems, within density functional theory. We obtain improved values of the orbital magnetization in the ferromagnetic metals…
The paper is devoted to the derivation of random unitary matrices whose spectral statistics is the same as statistics of quantum eigenvalues of certain deterministic two-dimensional barrier billiards. These random matrices are extracted…
We study the semiclassical quantization of an ensemble of billiards with a small random shape deformation. We derive a trace formula averaged over shape disorder. The results are illustrated by the study of supershells in rough metal…
We study diffractive effects in two dimensional polygonal billiards. We derive an analytical trace formula accounting for the role of non-classical diffractive orbits in the quantum spectrum. As an illustration the method is applied to a…
The dynamics of a test particle in a non-spinning binary black hole system of equal masses is numerically investigated. The binary system is modeled in the context of the pseudo-Newtonian circular restricted three-body problem, such that…
A scattering process can be described by suitably closing the system and considering the first return map from the entrance onto itself. This scattering map may be singular and discontinuous, but it will be measure preserving as a…
We consider classical billiards in plane, connected, but not necessarily bounded domains. The charged billiard ball is immersed in a homogeneous, stationary magnetic field perpendicular to the plane. The part of dynamics which is not…
We have extended the spectral dynamics formalism introduced by Binney & Spergel, and have implemented a semi-analytic method to represent regular orbits in any potential, making full use of their regularity. We use the spectral analysis…
Given a finitely generated amenable group we consider ergodic random Schr\"odinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normalised eigenvalue counting functions of finite volume…
Under conditions of clean flow we compute the leading term in the STF when the set of periods of the energy surface is discrete. Comparing to the case of non-degenerate periodic orbits, we obtain a supplementary term which is given in terms…
Spectral properties of random Schr\"odinger operators are encoded in the average of products of Greens functions. For probability distributions with enough finite moments, the supersymmetric approach offers a useful dual representation.…
The modern theory of orbital magnetization addresses crystalline materials at the noninteracting level: therein the observable is the k-space integral of a geometrical integrand. Alternatively, magnetization admits a local representation in…
A periodic trajectory on a polygonal billiard table is stable if it persists under any sufficiently small perturbation of the table. It is a standard result that a periodic trajectory on an $n$-gon gives rise in a natural way to a closed…
The energy spectrum and the eigenstates of a rectangular quantum dot containing soft potential walls in contact with a superconductor are calculated by solving the Bogoliubov-de Gennes (BdG) equation. We compare the quantum mechanical…
The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number $N$. We show that the many-body density of states can be expressed as a coherent sum over oscillating…