Related papers: Quantum chaos with graphs: a silicon photonics pla…
Traveling waves triggered by a phase slip in coupled map lattices are studied. A local phase slip affects globally the system, which is in strong contrast with kink propagation. Attractors with different velocities coexist, and form…
An analysis is made of a moving disturbance using a directed cyclic graph. A statistical approach is used to calculate the alternative positions in space and state of the disturbance with a defined observed time. The probability for a…
Statistical distribution of energy levels for Dirac fermions confined in a quantum dot is studied numerically on the examples of triangular and hexagonal graphene flakes with random electrostatic potential landscape. When increasing the…
A discrete analog of quantum unique ergodicity was proved for Cayley graphs of quasirandom groups by Magee, Thomas and Zhao. They show that for large graphs there exist real orthonormal basis of eigenfunctions of the adjacency matrix such…
We semiclassically derive the leading off-diagonal correction to the spectral form factor of quantum systems with a chaotic classical counterpart. To this end we present a phase space generalization of a recent approach for uniformly…
We study the transport of few-photon states in an open disordered nonlinear photonic lattice. More specifically, we consider a waveguide quantum electrodynamics (QED) setup where photons are scattered from a chain of nonlinear resonators…
For time-reversal invariant graphs we prove the Bohigas-Giannoni-Schmit conjecture in its most general form: For graphs that are mixing in the classical limit, all spectral correlation functions coincide with those of the Gaussian…
We prove quantum ergodicity for a family of graphs that are obtained from ergodic one-dimensional maps of an interval using a procedure introduced by Pakonski et al (J. Phys. A, v. 34, 9303-9317 (2001)). As observables we take the L^2…
The authors review the evidence for the applicability of random--matrix theory to nuclear spectra. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately: quantum chaos) in nuclei whenever random--matrix…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
Quantum graphs were introduced to model free electrons in organic molecules using a self-adjoint Hamiltonian on a network of intervals. A second graph quantization describes wave propagation on a graph by specifying scattering matrices at…
We consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval. We investigate the possibility of having power-law tails in the invariant measure by approximate solution of the…
In this paper, we introduce a hybrid chaos map for image encryption method with high sensitivity. This new map is sensitive to small changes in the starting point and also in control parameters which result in having more computational…
Using a graph approach to quantum systems, we prove that descriptions of 3-dim Kochen-Specker (KS) setups as well as descriptions of 3-dim spin systems by means of Greechie lattices that we find in the literature are wrong. Correct lattices…
We study the dielectric annular billiard as a quantum chaotic model of a micro-optical resonator. It differs from conventional billiards with hard-wall boundary conditions in that it is partially open and composed of two dielectric media…
The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…
In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical…
Although electrons and photons produce the same interference patterns in the two-slit experiments, the description of these patters is markedly different. This difference was analyzed by Bohm. Later on Sanz and Miret-Artes and others were…
Programmable quantum devices provide a platform to control the coherent dynamics of quantum wavefunctions. Here we experimentally realize adaptive monitored quantum circuits, which incorporate conditional feedback into non-unitary…
We formulate a general theory of wave-particle duality for many-body quantum states, which quantifies how wave- and particle-like properties balance each other. Much as in the well-understood single-particle case, which-way information --…