Related papers: Spectra of regular quantum graphs
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…
We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the…
A system of two initially homogeneous, physically real fields uniformly attracted to each other is considered as the simplest basis of the self-developing world structure. It is shown that the system is unstable against periodic cycles of…
We define a monodromy, directly from the spectrum of small non-selfadjoint perturbations of a selfadjoint semiclassical operator with two degrees of freedom, which is classically integrable. It is a combinatorial invariant that obstructs…
Can classical systems be described analytically at all orders in their interaction strength? For periodic and approximately periodic systems, the answer is yes, as we show in this work. Our analytical approach, which we call the…
We present a semiclassical approach to n-point spectral correlation functions of quantum systems whose classical dynamics is chaotic, for arbitrary n. The basic ingredients are sets of periodic orbits that have nearly the same action and…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…
Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
The existing periodic orbit theory of spectral correlations for classically chaotic systems relies on the Riemann-Siegel-like representation of the spectral determinants which is still largely hypothetical. We suggest a simpler derivation…
We introduce a new model for investigating spectral properties of quantum graphs, a quantum circulant graph. Circulant graphs are the Cayley graphs of cyclic groups. Quantum circulant graphs with standard vertex conditions maintain…
Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently…
Based on earlier work on regular quantum graphs we show that a large class of scaling quantum graphs with arbitrary topology are explicitly analytically solvable. This is surprising since quantum graphs are excellent models of quantum chaos…
We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
Generic low-dimensional Hamiltonian systems feature a structured, mixed classical phase-space. The traditional Percival classification of quantum spectra into regular states supported by quasi-integrable regions and irregular states…
We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing.…
We summarize recent work showing that the $1/r^2$ model of interacting particles in 1-dimension is a universal Hamiltonian for quantum chaotic systems. The problem is analyzed in terms of random matrices and of the evolution of their…