相关论文: Classical Resonances and Quantum Scarring

In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when…

Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, this leading to the appearance of different classical resonances. In this paper, we study the quantum manifestations of these classical…

The notion of many-body quantum scars is associated with special eigenstates, usually concentrated in certain parts of Hilbert space, that give rise to robust persistent oscillations in a regime that globally exhibits thermalization. Here…

A new type of localization - localization over the quantum resonance cells - in an intrinsically degenerate system is explored by using the quasienergy eigenstates.

We study theoretically two consequences of the mixed classical phase space for three repulsively-interacting bosonic particles in a circular trap. First, we show that the energy levels of the corresponding quantum system are well described…

For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states and quantum resonant states, except at negative integers where the correspondence involves…

The theory of scarring of eigenfunctions of classically chaotic systems by short periodic orbits is extended in several ways. The influence of short-time linear recurrences on correlations and fluctuations at long times is emphasized. We…

We study the classical and quantum mechanics of a free particle that collides elastically with the walls of a circular disk with the radius varying periodically in time. The quasi-energy spectral properties of the model are obtained from…

Correspondence in quantum chaotic systems is lost in short time scales. Introducing some noise we study the spectrum of the resulting coarse grained propagaor of density matrices. Some differen methods to compute the spectrum are reviewed.…

Quantum scars refer to eigenstates with enhanced probability density along unstable classical periodic orbits (POs). First predicted 40 years ago, scars are special eigenstates that counterintuitively defy ergodicity in quantum systems…

In this paper we construct a sequence of eigenfunctions of the ``quantum Arnold's cat map'' that, in the semiclassical limit, show a strong scarring phenomenon on the periodic orbits of the dynamics. More precisely, those states have a…

We present a novel extension of the concept of scars for the wave functions of classically chaotic few-body systems of identical particles with rotation and permutation symmetry. Generically there exist manifolds in classical phase space…

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…

Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This gives a new solution of the the long standing problem of quantizing the resonances generically appearing…

We study resonance patterns of a spiral-shaped dielectric microcavity with chaotic ray dynamics. Many resonance patterns of this microcavity, with refractive indices $n=2$ and 3, exhibit strong localization of simple geometric shape, and we…

Motivated by the rich variety of complex periodic and quasi-periodic patterns found in systems such as two-frequency forced Faraday waves, we study the interaction of two spatially periodic modes that are nearly resonant. Within the…

We perform quantum mechanically exact calculations of resonances in the spectrum of the hydrogen atom in crossed external fields and establish a close connection between the classical transition state in phase space and features in the…

We point out a correspondence between classical and quantum states, by showing that for every classical distribution over phase--space, one can construct a corresponding quantum state, such that in the classical limit of $\hbar\to 0$ the…

We reveal a feature of quantum scarring in systems with many particles: Quantum scars, living densely near an unstable periodic orbit, must be compensated by corresponding antiscarred states suppressed there to establish the uniformity of…

By analyzing a paradigmatic example of the theory of dissipative systems -- the classical and quantum dissipative standard map -- we are able to explain the main features of the decay to the quantum equilibrium state. The classical…