Related papers: A Gutzwiller trace formula for singular potentials
We present evidence that anomalous transport in the classical standard map results in strong enhancement of fluctuations in the localization length of quasienergy states in the corresponding quantum dynamics. This generic effect occurs even…
We generalize the scattering approach to quantum graphs to quantum graphs with with piecewise constant potentials and multiple excitation modes. The free single-mode case is well-known and leads to the trace formulas of Roth, Kottos and…
The Loewner equation describes the time development of an analytic map into the upper half of the complex plane in the presence of a "forcing", a defined singularity moving around the real axis. The applications of this equation use the…
We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…
A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear…
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 present the quantum mechanics of "partial-trace" non-linear sigma models, on the grounds of a fully symmetry-based procedure. After the general scheme is sketched, the particular example of a particle on the two-sphere is explicitly…
We consider motion in a periodic potential in a classical, quantum, and semiclassical context. Various results on the distribution of asymptotic velocities are proven.
The trace anomaly and the cosmological constant problem are two typical breakdowns when applying the quantum principle to a general covariant or gravitational system. A quantum theory of spacetime reference frame is proposed and reviewed.…
In this paper we investigate the trace anomaly in a spacetime where single events are de-localized as a consequence of short distance quantum coordinate fluctuations. We obtain a modified form of heat kernel asymptotic expansion which does…
We give a general expression for the static potential energy of the gravitational interaction of two massive particles, in terms of an invariant vacuum expectation value of the quantized gravitational field. This formula holds for…
We study the dynamics of a particle in a one-dimensional Gaussian random potential with logarithmic correlations. It was shown in previous studies that the model exhibits a dynamical transition between two subdiffusive phases. We…
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…
Semiclassical trace formulas are examined using phase space path integrals. Our main concern in this paper is the Maslov index of the periodic orbit, which seems not fully understood in previous works. We show that the calculation of the…
We prove an exact trace formula for the Laplacian with a delta potential - also known as a point scatterer - on a non-compact hyperbolic surface of finite volume with one cusp. Our formula is an analogue of the Selberg trace formula. We…
A brief review of the manifestations of classical chaos observed in atomic systems is presented. Particular attention is paid to the analysis of atomic spectra by periodic orbit-type theories. For diamagnetic non-hydrogenic Rydberg atoms,…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
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…
We study the quantum tunnel effect through a potential barrier employing a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution…
Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian…