相关论文: Quantum Fractal Eigenstates
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
In this paper I discuss the formation of topological defects in quantum field theory and the relation between fractals and coherent states. The study of defect formation is particularly useful in the understanding of the same mathematical…
While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be…
Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems associated with violations of thermalization for special non-equilibrium initial states. Their various systematic constructions require…
A quantum eigenstate of a classically chaotic system is referred as scarred by an unstable periodic orbit if its probability density is concentrated in the vicinity of that orbit. Recently, a new class of scarring - variational scarring -…
Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective…
We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behavior of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics…
We examine whether the chaotic behavior of classical systems with a limited number of degrees of freedom can produce quantum dephasing, against the conventional idea that dephasing takes place only in large systems with a huge number of…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
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…
Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the…
Unstable periodic orbits (UPOs) play a key role in the theory of chaos, constituting the "skeleton" of classical chaotic systems and "scarring" the eigenstates of the corresponding quantum system. Recently, nonthermal many-body eigenstates…
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…
We study quantum chaos for systems with more than one degree of freedom, for which we present an analysis of the dynamics of entanglement. Our analysis explains the main features of entanglement dynamics and identifies entanglement-based…
We study quantum chaos in a non-KAM system, i.e. a kicked particle in a one-dimensional infinite square potential well. Within the perturbative regime the classical phase space displays stochastic web structures, and the diffusion…
The environment surrounding a quantum system can, in effect, monitor some of the systems observables. As a result, the eigenstates of these observables continuously decohere and can behave like classical states.
We have studied two complementary decoherence measures purity and fidelity for a generic diffusive noise in two different chaotic systems (the baker and the cat maps). For both quantities, we have found classical structures in quantum…
Formation of chaos in the parametric dependent system of interacting oscillators for the both classical and quantum cases has been investigated. Domain in which classical motion is chaotic is defined. It has been shown that for certain…
Properties related to entanglement in quantum systems, are known to be associated with distinct properties of the corresponding classical systems, as for example stability, integrability and chaos. This means that the detailed topology,…