Related papers: Relativistic Trace Formula for Bound States in Ter…
A recently proposed convolution technique for the calculation of local density of states is described more thouroughly and new results of its application are presented. For separable systems the exposed method allows to construct the ldos…
We derive a powerful yet simple method for analyzing the local density of states in gapless one dimensional fermionic systems, including extensions such as momentum dependent interaction parameters and hard-wall boundaries. We study the…
We investigate the resonance spectrum of the H\'enon-Heiles potential up to twice the barrier energy. The quantum spectrum is obtained by the method of complex coordinate rotation. We use periodic orbit theory to approximate the oscillating…
We consider methods for obtaining local lower bounds on characteristics of quantum (correspondingly, classical) systems, i.e. lower bounds valid in the trace norm $\epsilon$-neighborhood of a given state (correspondingly, probability…
We investigate the Dirac equation in the semiclassical limit \hbar --> 0. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two…
We present in this talk a series of new results on the nature of a bound state or resonance based on the calculation of the expectation values of the number operators of the free particles in the state of interest. In this way, a new…
We show that the pattern of tunnelling rates can display a vivid and regular pattern when the classical dynamics is of mixed chaotic/regular type. We consider the situation in which the dominant tunnelling route connects to a stable…
Is there a version of the notions of "state" and "observable" wide enough to apply naturally and in a covariant manner to relativistic systems? I discuss here a tentative answer.
Radar-holonomic congruences of wordlines are proposed as a weaker substitute for the too restrictive class of Born-rigid motions. The definition is expressed as a set of differential equations. Integrability conditions and Cauchy data are…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
We consider the use of the energy density for describing a localization of relativistic particles. This method is consistent with the causality requirements. The related positive operator valued measure is presented. The probability…
Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The…
The relative entropy of entanglement is defined in terms of the relative entropy between an entangled state and its closest separable state (CSS). Given a multipartite-state on the boundary of the set of separable states, we find a closed…
Trace formulae provide one of the most elegant descriptions of the classical-quantum correspondence. One side of a formula is given by a trace of a quantum object, typically derived from a quantum Hamiltonian, and the other side is…
Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix…
The Gutzwiller trace formula establishes a profound connection between the quantum spectrum and classical periodic orbits. However, its application is limited by its reliance on the semiclassical saddle point approximation. In this work, we…
We analyze the consequences of a recent argument justifying the validity of the "geodesic rule" which can be used to determine the density of global topological defects. We derive a formula that provides a rough estimate of the number of…
The local trace formula gives strong relations between two types of invariant distributions on a reductive group defined over a local field: orbital integrals and characters of representations. For connected reductive groups, the formula…
Bound states around an impurity are investigated for a two dimensional electron system in a strong magnetic field. Long-range Coulomb potential and related potentials are considered. Schr\"odinger equation is solved numerically to obtain…
A generalisation of the Faulhaber polynomials and Bernoulli numbers related to elliptic curves is introduced and investigated. This is applied to compute the density of states for the classical Lam\'e operators.