Related papers: Semiclassical quantization of the diamagnetic hydr…
Gutzwiller's trace formula has a central place in quantum chaos because it provides semiclassical approximations for quantum energy levels in classically chaotic systems by linking them to classical periodic orbits. In this didactic…
In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information…
We present a semiclassical description of the level density of a two-dimensional circular quantum dot in a homogeneous magnetic field. We model the total potential (including electron-electron interaction) of the dot containing many…
The Gutzwiller's trace formula for the anisotropic Kepler problem is Fourier transformed with a convenient variable $u=1/\sqrt{-2E}$ which takes care of the scaling property of the AKP action $S(E)$. Proper symmetrization procedure…
A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher $\hbar$ contributions to the spectral determinant. We apply the theory to billiard…
Long periodic orbits of hyperbolic dynamics do not exist as independent individuals but rather come in closely packed bunches. Under weak resolution a bunch looks like a single orbit in configuration space, but close inspection reveals…
Closed-orbit theory provides a general approach to the semiclassical description of photo-absorption spectra of arbitrary atoms in external fields, the simplest of which is the hydrogen atom in an electric field. Yet, despite its apparent…
We formulate a semiclassical theory for systems with spin-orbit interactions. Using spin coherent states, we start from the path integral in an extended phase space, formulate the classical dynamics of the coupled orbital and spin degrees…
We determine semiclassical quasienergy spectra from periodic orbits for a system with a mixed phase space, the kicked top. Throughout the transition from integrability to well developed chaos the standard error incurred for the…
While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…
A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples…
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…
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…
We present an analytical calculation of periodic orbits in the homogeneous quartic oscillator potential. Exploiting the properties of the periodic Lam{\'e} functions that describe the orbits bifurcated from the fundamental linear orbit in…
We study interaction effects on the orbital magnetism of diffusive mesoscopic quantum systems. By combining many-body perturbation theory with semiclassical techniques, we show that the interaction contribution to the ensemble averaged…
Determination of periodic orbits for a Hamiltonian system together with their semi-classical quantization has been a long standing problem. We consider here resonances for a $h$-Pseudo-Differential Operator $H(y,hD_y;h)$ induced by a…
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 study how the singular behaviour of classical systems at bifurcations is reflected by their quantum counterpart. The semiclassical contributions of individual periodic orbits to trace formulae of Gutzwiller type are known to diverge when…
In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical…
Semiclassical spectra beyond the Gutzwiller and Berry-Tabor approximation for chaotic and regular systems, respectively, are obtained by harmonic inversion of the hbar expansion of the periodic orbit signal. The method is illustrated for…