相关论文: Action Correlations in Integrable Systems

Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the…

Semiclassical sum rules, such as the Gutzwiller trace formula, depend on the properties of periodic, closed, or homoclinic (heteroclinic) orbits. The interferences embedded in such orbit sums are governed by classical action functions and…

The correlations in the spectra of quantum systems are intimately related to correlations which are of genuine classical origin, and which appear in the spectra of actions of the classical periodic orbits of the corresponding classical…

We present a semiclassical approach to n-point spectral correlation functions of quantum systems whose classical dynamics is chaotic, for arbitrary n. The basic ingredients are sets of periodic orbits that have nearly the same action and…

An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…

Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in…

It is shown that the atomic inversion in the Jaynes-Cummings model has an exact representation as an integral over the Hankel contour. For a field in a coherent state, the integral is evaluated using the saddle point method. The…

Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. Semiclassical periodic orbit formulae together with universal spectral statistics in the corresponding quantum Baker map suggest the…

Excited electronic states of molecules and solids play a fundamental role in fields such as catalysis and electronics. In electronic structure calculations, excited states typically correspond to saddle points on the surface described by…

We develop a bootstrap approach to Euclidean two-point correlators, in the thermal or ground state of quantum mechanical systems. We formulate the problem of bounding the two-point correlator as a semidefinite programming problem, subject…

The value of a highly oscillatory integral is typically determined asymptotically by the behaviour of the integrand near a small number of critical points. These include the endpoints of the integration domain and the so-called stationary…

We apply the saddle-point method to derive asymptotic estimates or asymptotic series for the number of partitions of a natural integer into parts chosen from a subset of the positive integers whose associated Dirichlet series satisfies…

We prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics, which serves as a powerful instrument in finding saddle points and constructing the solution landscapes of constrained systems…

The 2-point correlation form factor, $K_2(\tau)$, for small values of $\tau$ is computed analytically for typical examples of pseudo-integrable systems. This is done by explicit calculation of periodic orbit contributions in the diagonal…

A common measure of a function's complexity is the count of its stationary points. For complicated functions, this count grows exponentially with the volume and dimension of their domain. In practice, the count is averaged over a class of…

The saddle point approximation to the partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which…

The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical…

We consider a reduction procedure in Wiener-type path integral for a finite-dimensional mechanical system with a symmetry representing the motion of two interacting scalar particles on a manifold that is the product of the total space of…

Recent developments in the theory of integrable models have provided the means of calculating dynamical correlation functions of some important observables in systems such as Heisenberg spin chains and one-dimensional atomic gases. This…

The construction of discrete velocity models or numerical methods for the Boltzmann equation, may lead to the necessity of computing the collision operator as a sum over lattice points. The collision operator involves an integral over a…