Related papers: Spectra of regular quantum graphs
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are…
We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural…
I review the appearance of classical integrable systems as an effective tool for the description of non-perturbative exact results in quantum string and gauge theories. Various aspects of this relation: spectral curves, action-angle…
Nonclassicality cannot be a single-observable property since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior from the joint measurement of…
We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(tau) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown…
In the framework of semiclassical theory the universal properties of quantum systems with classically chaotic dynamics can be accounted for through correlations between partner periodic orbits with small action differences. So far, however,…
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
The classical Bernoulli and baker maps are two simple models of deterministic chaos. On the level of ensembles, it has been shown that the time evolution operator for these maps admits generalized spectral representations in terms of…
We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems, with a focus on molecular systems. The method combines classical preparation of a perturbed…
An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling…
Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space…
Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs…
We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the non-commutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the…
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation.…
We examine quantum normal typicality and ergodicity properties for quantum systems whose dynamics are generated by Hamiltonians which have residual degeneracy in their spectrum and resonance in their energy gaps. Such systems can be…
In the present note, we uncover a remarkable connection between the length of periodic orbit of a classical particle enclosed in a class of 2-dimensional planar billiards and the energy of a quantum particle confined to move in an identical…
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…