Related papers: Hierarchical Structure in the Trace Formula
We develop the semiclassical method of complex trajectories in application to chaotic dynamical tunneling. First, we suggest a systematic numerical technique for obtaining complex tunneling trajectories by the gradual deformation of the…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these…
Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…
It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is…
We study the level statistics of an interacting multi-qubit system, namely the kicked Ising spin chain, in the regime of quantum chaos. Long range quasi-energy level statistics show effects analogous to the ones observed in semi-classical…
We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behavior of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics…
We develop a statistical theory that describes quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of physical systems, ranging from…
A theory of rank $k\ge 2$ perturbation of symplectic matrices and Hamiltonian systems with periodic coefficients using a base of isotropic subspaces, is presented. After showing that the fundamental matrix ${\displaystyle…
We consider a class of simple quasi one-dimensional classically non-integrable systems which capture the essence of the periodic orbit structure of general hyperbolic nonintegrable dynamical systems. Their behavior is simple enough to allow…
zeta-regularized traces, resp. super-traces, are defined on a classical pseudo-differential operator A by: tr^Q(A):= f.p.tr(A Q^{-z})_{|_{z=0}}, resp. str^Q(A):= f.p.str(A Q^{-z})_{|_{z=0}}, where f.p. refers to the finite part and Q is an…
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…
Recent developments in many-body quantum chaos have raised the issue of correlations between different families of levels in the spectra of random fermionic systems. It seems that rotational invariance is sufficient to force an otherwise…
States supported by chaotic open quantum systems fall into two categories: a majority showing instantaneous ballistic decay, and a set of quantum resonances of classically vanishing support in phase space. We present a theory describing…
Topological properties of energy spectra of general one-dimensional quasiperiodic systems, describing also Bloch electrons in magnetic fields, are studied for an infinity of irrational modulation frequencies corresponding to irrational…
While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
We investigate spatial reflection and associated nonlocal order in spin chain quantum systems. The proposed string order parameters, e.g., reflected via operations of the spatial reflection or combinations of it with spin reflection, are…
The existing periodic orbit theory of spectral correlations for classically chaotic systems relies on the Riemann-Siegel-like representation of the spectral determinants which is still largely hypothetical. We suggest a simpler derivation…
Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…