Related papers: Periodic Orbit Quantization beyond Semiclassics
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
We study diffraction corrections to the semiclassical spectral density of dispersing (Sinai) billiards. They modify the contributions of periodic orbits (PO's), with at least one segment which is almost tangent to the concave part of the…
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…
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…
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…
Gutzwiller's trace formula for the semiclassical density of states diverges at the bifurcation points of periodic orbits and has to be replaced with uniform semiclassical approximations. We present a method to derive these expressions from…
We study absolutely periodic points and trajectories of Hamiltonian systems. Our main result is a necessary and sufficient for a Hamiltonian system to have the following property: if there exists one absolutely periodic trajectory then all…
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…
The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated…
Periodic orbit theory for classical hyperbolic system is very significant matter of how we can interpret spectral statistics in terms of semiclassical theory. Although pruning is significant and generic property for almost all hyperbolic…
Although hydrogen in external fields is a paradigm for the application of periodic orbits and the Gutzwiller trace formula to a real system, the trace formula has never been applied successfully to other Rydberg atoms. We show that spectral…
In the present note, we uncover a remarkable connection between the length of periodic orbit of a classical particle enclosed in a class of 2-dimensional planar billiards and the energy of a quantum particle confined to move in an identical…
We give a path integral formulation of the time evolution of qudits of odd dimension. This allows us to consider semiclassical evolution of discrete systems in terms of an expansion of the propagator in powers of $\hbar$. The largest power…
The classical and quantum behavior of a particle inside a square box under the influence of the gravitational field is studied. Detailed calculations on periodic orbits, probability densities as well as expectation values and uncertainties…
We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all…
Quantum chaos of many-body systems has been swiftly developing into a vibrant research area at the interface between various disciplines, ranging from statistical physics to condensed matter to quantum information and to cosmology. In…
We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the…
Let $G$ be the complex general linear group and $g$ its Lie algebra equipped with a factorizable Lie bialgebra structure; let $U_h$ be the corresponding quantum group. We construct explicit $U_h$-equivariant quantization of Poisson orbit…
The paper establishes the property of splittability of billiard boundary sequences in n dimensional cube into subsequences of fractional parts. This reveals a new property of integrable and weak perturbated Hamilton systems: under a simple…
We show that the contributions to the Gutzwiller formula with observable associated to the iterates of a given elliptic nondegenerate periodic trajectory $\gamma$ and to certain families of observables localized near $\gamma$ determine the…