Related papers: Quantum and Arithmetical Chaos
Based on the acoustic analog, we investigate both of the effects : disorder and (Pauli-blocking) interaction to the possible localization in electron gases by using the quantum discrete kinetic model. Effects of the disorder (or…
We studied complex spectra of a two-level electron system coupled to two phonon (vibron) modes represented by the E$\otimes$e Jahn-Teller model. For particular rotation quantum numbers we found a coexistence of up to three regions of the…
Quantum gravity is expected to gauge all global symmetries of effective theories, in the ultraviolet. Inspired by this expectation, we explore the consequences of gauging CPT as a quantum boundary condition in phase space. We find that it…
Out-of-time-order correlators are widely used as an indicator of quantum chaos, but give false-positive quantum Lyapunov exponents for integrable systems with isolated saddle points. We propose an alternative indicator that fixes this…
In these Lectures a method is described to analyze the effect of quantum fluctuations on topological defect backgrounds up to the one-loop level. The method is based on the spectral heat kernel/zeta function regularization procedure, and it…
Chaos quantization conditions, which relate the eigenvalues of a Hermitian operator (the Riemann operator) with the non-trivial zeros of the Riemann zeta function are considered, and their geometrical interpretation is discussed.
Mesoscopic devices, with system sizes in the range of several to several dozens wavelengths, represent paradigmatic model systems for the observation of quantum chaotic behaviour based on semiclassical concepts. Those electronic and…
These notes are based on my four lectures given at the Newton Institute in April 2004 during the Recent Perspectives in Random Matrix Theory and Number Theory Workshop. Their purpose is to introduce the reader to the analytic number theory…
Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger…
Recent work has suggested an intriguing relation between quantum chaos and energy density correlations, known as pole skipping. We investigate this relationship in two dimensional conformal field theories on a finite size spatial circle by…
The model of an open Fermi-system is used for studying the interplay of intrinsic chaos and irreversible decay into open continuum channels. Two versions of the model are characterized by one-body chaos coming from disorder or by many-body…
We use semiconductors as an example to show that quantum chaos manifests itself in the energy spectrum of crystals. We analyze the {\it ab initio} band structure of silicon and the tight-binding spectrum of the alloy $Al_xGa_{1-x}As$, and…
Based on periodic orbit theory we address the individual-system versus ensemble interpretation of quantum gravity from a quantum chaos perspective. To this end we show that the spectrum of geodesic motion on high-dimensional hyperbolic…
In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the Laplace-Beltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple…
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in…
Applying random matrix theory to quantum transport in chaotic cavities, we develop a novel approach to computation of the moments of the conductance and shot-noise (including their joint moments) of arbitrary order and at any number of open…
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation…
Transition from regular to chaotic dynamics in a crystal made of singular scatterers $U(r)=\lambda |r|^{-\sigma}$ can be reached by varying either sigma or lambda. We map the problem to a localization problem, and find that in all space…
The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of…
This is a continuation of our preceding paper devoted to signatures of quantum chaos in the geometric collective model of atomic nuclei. We apply the method by Peres to study ordered and disordered patterns in quantum spectra drawn as…