相关论文: Exact, convergent periodic-orbit expansions of ind…

Quantum periodic cluster methods for strongly correlated electron systems are reformulated and developed. The reformulation and development are based on a canonical transformation which periodizes the fermions in the cluster space. The…

The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.

The three-disk system, which for many years has served as a paradigm for the usefulness of cycle expansion methods, represents an extremely hard problem to semiclassical quantization when the disks are moved closer and closer together,…

We numerically investigate the stability of exceptional periodic classical trajectories in rather generic chaotic many-body systems and explore a possible connection between these trajectories and exceptional nonthermal quantum eigenstates…

We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the two cells touch. The general theory is illustrated with…

We use quantum graphs as a model to study various mathematical aspects of the vacuum energy, such as convergence of periodic path expansions, consistency among different methods (trace formulae versus method of images) and the possible…

We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing…

In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when…

We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…

Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is…

Energy spectra of quasi-one-dimensional quantum rings with a few electrons are studied using several different theoretical methods. Discrete Hubbard models and continuum models are shown to give similar results governed by the special…

We study the electronic band structure for a model one-dimensional periodic potential in the presence of a spacially homogeneous laser field. The statistical properties of the energy bands depend on the coupling between the crystal and the…

Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the…

The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out…

We generalize the known solution of the Schr\"odinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the…

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…

Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…

We discuss spectral properties of an periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links, assuming that the vertex coupling is manifestly non-invariant with respect to the time…

We calculate the first order maximal acceleration corrections to the classical electrodynamics of a particle in external electromagnetic fields. These include additional dissipation terms, the presence of a critical electric field, a…

Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…