Related papers: Semiclassical trace formulas in terms of phase spa…
A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables…
Starting from a semiclassical quantization condition based on the trace formula, we derive a periodic-orbit formula for the distribution of spacings of eigenvalues with k intermediate levels. Numerical tests verify the validity of this…
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…
The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. When the dimensionality of the system…
The Gutzwiller trace formula relates the asymptotic spacing of quantum-mechanical energy levels in the semiclassical limit to the dynamics of periodic classical particle trajectories. We generalize this result to the case of non-smooth…
We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…
We derive a semiclassical trace formula for quantized chaotic transformations of the torus coupled to a two-spinor precessing in a magnetic field. The trace formula is applied to semiclassical correlation densities of the quantum map,…
A new form of the Bohr-Sommerfeld quantization is given of the motion of guiding center in strong magnetic field. This is obtained by the effective action for the degree of guiding center which is deduced from the coherent state path…
Gutzwiller's trace formula and Bogomolny's formula are applied to a non--specific, non--scalable Hamiltonian system, a two--dimensional anharmonic oscillator. These semiclassical theories reproduce well the exact quantal results over a…
The semiclassical propagator in the representation of SU(n) coherent states is characterized by isolated classical trajectories subjected to boundary conditions in a doubled phase space. In this paper we recast this expression in terms of…
We analyze the spectrum of the 3-site Bose-Hubbard model with periodic boundary conditions using a semiclassical method. The Bohr-Sommerfeld quantization is applied to an effective classical Hamiltonian which we derive using resonance…
We apply the semiclassical spin coherent state method for the density of states by Pletyukhov et al. (2002) in the weak spin-orbit coupling limit and recover the modulation factor in the semiclassical trace formula found by Bolte and…
Semiclassical spectra weighted with products of diagonal matrix elements of operators A_{alpha}, i.e., g_{alpha alpha'}(E) = sum_n <n|A_{alpha}|n><n|A_{alpha'}|n>/(E-E_n) are obtained by harmonic inversion of a cross-correlation signal…
Since its first appearance in 1971, Gutzwiller's trace formula has been extended to systems with continuous symmetries, in which not all periodic orbits are isolated. In order to avoid the divergences occurring in connection with symmetry…
Spectral determinants have proven to be valuable tools for resumming the periodic orbits in the Gutzwiller trace formula of chaotic systems. We investigate these tools in the context of integrable systems to which these techniques have not…
The purpose of the paper is to suggest a new method which allows one to study multiple coherent reflection/transmissions by partially transparent interfaces (e.g. in multi-layer mesoscopic structures or grain boundaries in high-Tc's) in the…
We apply recent results on semi-classical trace formulae and on Birkhoff normal forms for semi-classical Fourier integral operators to a wide range of semi-classical and high energy spectral inverse problems.
The Maslov correction to the wave function is to the jump of $-\pi/2$ in the phase when the system passes through a caustic point. This phenomenon is related to the second variation and to the geometry of paths, as conveniently explained in…
We derive semiclassical expressions for the Kubo conductivity tensor. Within our approach the oscillatory parts of the diagonal and Hall conductivity are given as sums over contributions from classical periodic orbits in close relation to…
The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the…