A ug 1 99 9 Semiclassical density of degeneracies in quantum regular systems
نویسنده
چکیده
The spectrum of eigenenergies of a quantum integrable system whose hamil-tonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings in the plane energy-parameter, that is the number of crossings per unit of energy and unit of parameter, in terms of classical periodic orbits. We compare the results of the semiclassical formula with exact quantum calculations for two specific quantum integrable billiards.
منابع مشابه
Semiclassical density of degeneracies in quantum regular systems
The spectrum of eigenenergies of a quantum integrable system whose hamiltonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings in the plane energy-parameter, that is the number of crossings per unit of energy and unit of parameter, in terms of classical periodic orbits. We compare the resul...
متن کامل/ 99 08 01 9 v 1 1 8 A ug 1 99 9 Uniform approximations for non - generic bifurcation scenarios
Gutzwiller's trace formula allows interpreting the density of states of a classically chaotic quantum system in terms of classical periodic orbits. It diverges when periodic orbits undergo bifurcations, and must be replaced with a uniform approximation in the vicinity of the bifurcations. As a characteristic feature, these approximations require the inclusion of complex " ghost orbits ". By stu...
متن کاملEigenvalue Statistics in Quantum Ideal Gases
The eigenvalue statistics of quantum ideal gases with single particle energies en = n α are studied. A recursion relation for the partition function allows to calculate the mean density of states from the asymptotic expansion for the single particle density. For integer α > 1 one expects and finds number theoretic degeneracies and deviations from the Poissonian spacing distribution. By semiclas...
متن کامل2 1 O ct 1 99 9 A semiclassical approach to the ground state and density oscillations of quantum dots
A semiclassical Thomas-Fermi method, including a Weizsäcker gradient term, is implemented to describe ground states of two dimensional nanostructures of arbitrary shape. Time dependent density oscillations are addressed in the same spirit using the corresponding semiclassical time-dependent equations. The validity of the approximations is tested, both for ground state and density oscillations, ...
متن کاملar X iv : c on d - m at / 9 60 80 58 v 1 1 3 A ug 1 99 6 Antiresonance and Localization in Quantum Dynamics
The phenomenon of quantum antiresonance (QAR), i.e., exactly periodic recurrences in quantum dynamics, is studied in a large class of nonintegrable systems, the modulated kicked rotors (MKRs). It is shown that asymptotic exponential localiza-tion generally occurs for η (a scaled ¯ h) in the infinitesimal vicinity of QAR points η 0. The localization length ξ 0 is determined from the analytical p...
متن کامل