相关论文: Intermediate statistics in quantum maps

We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the…

We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…

A previous paper by the authors found explicit contour integral formulas for certain joint moments of the multi-species q-TAZRP (totally asymmetric zero range process), using algebraic methods. These contour integral formulas have a…

We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…

A compact review is given, and a few new numerical results are added to the recent studies of the q-pointed one-dimensional star-shaped quantum graphs. These graphs are assumed endowed with certain specific, manifestly non-Hermitian point…

The computation of the two-point correlation form factor K(t) is performed for a rectangular billiard with a small size impurity inside for both periodic or Dirichlet boundary conditions. It is demonstrated that all terms of perturbation…

We present the asymptotic analysis of the quantum two-port interferometer in the $n \rightarrow \infty$ limit of $n$ partially indistinguishable photons. Using the unitary-unitary duality between port and inner-mode degrees of freedom, the…

The correlation spectrum of fully developed one-dimensional mappings are studied near and at a weakly intermittent situation. Using a suitable infinite matrix representation, the eigenvalue equation of the Frobenius-Perron operator is…

We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure.

We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use this framework to formulate a 2-categorical theory of quantum…

This is the second of a series of papers dealing with the asymptotic behavior of certain integrals occuring in the description of the spectrum of an invariant elliptic operator on a compact Riemannian manifold carrying the action of a…

Some of the subtleties of the integrability of the elliptic quantum billiard are discussed. A well known classical constant of the motion has in the quantum case an ill-defined commutator with the Hamiltonian. It is shown how this problem…

We study quantum causal inference in a set-up proposed by Ried et al. [Nat. Phys. 11, 414 (2015)] in which a common-cause scenario can be mixed with a cause-effect scenario, and for which it was found that quantum mechanics can bring an…

In this paper we investigate the distribution of the set of values of a quadratic form Q, at integral points. In particular we are interested in the n-point correlations of the this set. The asymptotic behaviour of the counting function…

The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…

We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the…

We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices…

The spectral statistics in the strongly chaotic cardioid billiard are studied. The analysis is based on the first 11000 quantal energy levels for odd and even symmetry respectively. It is found that the level-spacing distribution is in good…

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…