Related papers: Path integration over closed loops and Gutzwiller'…
We have derived an analytical trace formula for the level density of the H\'enon-Heiles potential using the improved stationary phase method, based on extensions of Gutzwiller's semiclassical path integral approach. This trace formula has…
We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur…
It is shown that there is a generalization of the Conley-Zehnder index for periodic trajectories of a classical Hamiltonian system $(Q, \omega, H)$ from the case $Q = T^*R^n$ to arbitrary symplectic manifolds. As it turns out, it is…
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 Gutzwiller trace formula establishes a profound connection between the quantum spectrum and classical periodic orbits. However, its application is limited by its reliance on the semiclassical saddle point approximation. In this work, we…
The mixed density operator for coarsegrained eigenlevels of a static Hamiltonian is represented in phase space by the spectral Wigner function, which has its peak on the corresponding classical energy shell. The action of trajectory…
A trajectory segment in an energy shell, which combines to form a closed curve with a segment in another canonically driven energy shell, adds an oscillatory semiclassical contribution to the smooth classical background of the quantum…
This work studies the semiclassical methods in multi-dimensional quantum systems bounded by finite potentials. By replacing the Maslov index by the scattering phase, the modified transfer operator method gives rather accurate corrections to…
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…
A short survey of the semiclassical periodic orbit theory, initiated by M. Gutzwiller and generalized by many other authors, is given. Via so-called semiclassical trace formmulae, gross-shell effects in bound fermion systems can be…
We present a semiclassical analysis for a dissipative quantum map with an area-nonpreserving classical limit. We show that in the limit of Planck's constant to 0 the trace of an arbitrary natural power of the propagator is dominated by…
We have extended the semi-classical theory to include a general account of matrix valued Hamiltonians, i.e. those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for…
Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular…
We develop a semiclassical approximation for the dynamics of quantum systems in finite-dimensional Hilbert spaces whose classical counterparts are defined on a toroidal phase space. In contrast to previous models of quantum maps, the time…
While detailed information about the semiclassics for single-particle systems is available, much less is known about the connection between quantum and classical dynamics for many-body systems. As an example, we focus on spin chains which…
We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit…
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…
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows over closed prequantized symplectic manifolds in the context of geometric quantization…
We discuss the semiclassical approaches for describing systems with spin-orbit interactions by Littlejohn and Flynn (1991, 1992), Frisk and Guhr (1993), and by Bolte and Keppeler (1998, 1999). We use these methods to derive trace formulae…