Related papers: Semiclassical calculation of time delay statistics…
We solve the problem of resonance statistics in systems with broken time-reversal invariance by deriving the joint probability density of all resonances in the framework of a random matrix approach and calculating explicitly all n-point…
A semiclassical approximation for the matrix elements of a quantum chaotic propagator in the scar function basis has been derived. The obtained expression is solely expressed in terms of canonical invariant objects. For our purpose, we have…
Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities.…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
For chaotic scattering on quantum graphs, the semiclassical approximation is exact. We use this fact and employ supersymmetry, the colour-flavour transformation, and the saddle-point approximation to calculate the exact expression for the…
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…
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…
The purely classical counterpart of the Scattering Probability Matrix (SPM) $\mid S_{n,m}\mid^2$ of the quantum scattering matrix $S$ is defined for 2D quantum waveguides for an arbitrary number of propagating modes $M$. We compare the…
The usefulness of time-frequency analysis methods in the study of quasicrystals was pointed out in a previous paper, where we proved that a tempered distribution $\mu$ on ${\mathbb R}^d$ whose Wigner transform is a measure supported on the…
We describe an iterative approach to computing long-time semiclassical dynamics in the presence of chaos, which eliminates the need for summing over an exponentially large number of classical paths, and has good convergence properties even…
The scattering matrix S of a ballistic chaotic cavity is the direct sum of a `classical' and a `quantum' part, which describe the scattering of channels with typical dwell time smaller and larger than the Ehrenfest time, respectively.…
Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells…
We discuss general aspects of non-relativistic quantum chaos theory of scattering of a quantum particle on a system of a large number of naked singularities. We define such a system space-temporal Sinai billiard We dis- cuss the problem in…
We discuss the fluctuation properties of diagonal matrix elements in the semiclassical limit in chaotic systems. For extended observables, covering a phase space area of many times Planck's constant, both classical and quantal distributions…
Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic…
A number of approaches to the problem of defining arrival and dwell time probabilities in quantum theory make use of idealised models of clocks. An interesting question is the extent to which the probabilities obtained in this way are…
We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a…
In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for…
We consider the scattering by a one-dimensional random potential and derive the probability distribution of the corresponding Wigner time delay. It is shown that the limiting distribution is the same for two different models and coincides…
The surprisingly long-lasting oscillations observed in the dynamics of highly excited states of chains of Rydberg atoms defy the expectation that interacting systems should thermalize fast. The phenomenon is reminiscent of wavepackets in…