Related papers: Spectral statistics of a pseudo-integrable map: th…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution…
In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries. The structure of the generalized spectral function is described in terms of…
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…
For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study…
Generically, spectral statistics of spinless systems with time reversal invariance (TRI) and chaotic dynamics are well described by the Gaussian Orthogonal ensemble (GOE). However, if an additional symmetry is present, the spectrum can be…
Design of filters for graph signal processing benefits from knowledge of the spectral decomposition of matrices that encode graphs, such as the adjacency matrix and the Laplacian matrix, used to define the shift operator. For shift matrices…
There being no precise definition of the quantum integrability, the separability of variables can serve as its practical substitute. For any quantum integrable model generated by the Yangian Y[sl(3)] the canonical coordinates and the…
We review a surprising correspondence between certain two-dimensional integrable models and the spectral theory of ordinary differential equations. Particular emphasis is given to the relevance of this correspondence to certain problems in…
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide…
We describe a plausible-speculative form of quantum computation which exploits particle (fermionic, bosonic) statistics, under a generalized, counterfactual interpretation thereof. In the idealized situation of an isolated system, it seems…
The spectrum of a real and symmetric $N\times N$ matrix determines the matrix up to unitary equivalence. More spectral data is needed together with some sign indicators to remove the unitary ambiguities. In the first part of this work we…
We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental…
We derive a Gutzwiller-type trace formula for quantum chaotic systems that accounts for both particle spin precession and discrete geometrical symmetries. This formula generalises previous results that were obtained either for systems with…
We present quantum graphs with remarkably regular spectral characteristics. We call them {\it regular quantum graphs}. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly…
We review arXiv:1308.3444 and arXiv:1104.1891. The structure of the spectrum of a quantum integrable system is crucial to understand its properties. In his seminar 1971 paper, Baxter observed that the spectrum of the "ice model" has a very…
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present…
We study the pseudospectrum of the non-selfadjoint Zakharov-Shabat system in the semiclassical regime. The pseudospectrum may be defined as the union of the spectra of perturbations of the Zakharov-Shabat system, thus it is relevant to the…
We study the spectral statistics for quantized skew translations on the torus, which are ergodic but not mixing for irrational parameters. It is shown explicitly that in this case the level--spacing distribution and other common spectral…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…