Related papers: A semiclassical matrix model for quantum chaotic t…
Quantum transport through left-right symmetric chaotic cavities in the presence of the symplectic symmetry, is studied through the statistical distribution of the dimensionless conductance. With this particular point symmetry, their…
This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed…
We use semi--classical and perturbation methods to establish the quantum theory of the Neumann model, and explain the features observed in previous numerical computations.
For many classically chaotic systems, it is believed that in the semiclassical limit, the matrix elements of smooth observables approach the phase space average of the observable. In the approach to the limit the matrix elements can…
The semiclassical formula for the coherent-state propagator is written in terms of complex classical trajectories of an equivalent classical system. Depending on the parameters involved, more than one trajectory may contribute to the…
The interplay between classical chaos and quantum tunneling is examined in driven nonlinear systems, with emphasis on how semi classical phase space structures influence purely quantum transport phenomena. We show that, in the presence of…
During the last years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wave function statistics. In the first part of this review we give a detailed introduction to…
We derive a semiclassical trace formula for quantized chaotic transformations of the torus coupled to a two-spinor precessing in a magnetic field. The trace formula is applied to semiclassical correlation densities of the quantum map,…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
This review article will present some recent results and methods in the study of 1-particle quantum or wave scattering systems, in the semiclassical/high frequency limit, in cases where the corresponding classical/ray dynamics is chaotic.…
We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
We introduces the Quantum-Train(QT) framework, a novel approach that integrates quantum computing with classical machine learning algorithms to address significant challenges in data encoding, model compression, and inference hardware…
Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…
Digital circuits based on residue number systems have been considered to produce a pseudo-random behavior. The present work is an initial step towards the complete implementation of those systems for similar applications using quantum…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic $\sigma$-model approach. We analyze conditions of…
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
While plenty of results have been obtained for single-particle quantum systems with chaotic dynamics through a semiclassical theory, much less is known about quantum chaos in the many-body setting. We contribute to recent efforts to make a…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…