Related papers: Chaotic vibrations and strong scars
We discuss a number of basic physical mechanisms relevant to the formation of the proximity effect in superconductor/normal metal (SN) systems. Specifically, we review why the proximity effect sharply discriminates between systems with…
Protecting coherent quantum dynamics from chaotic environment is key to realizations of fragile many-body phenomena and their applications in quantum technology. We present a general construction that embeds a desired periodic orbit into a…
In the field of quantum chaos, the study of energy levels plays an important role. The aim of this review paper is to critically discuss some of the main contributions regarding the connection between classical dynamics, semi-classical…
We conjecture that chaotic resonance modes in scattering systems are a product of a conditionally invariant measure from classical dynamics and universal exponentially distributed fluctuations. The multifractal structure of the first factor…
We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling…
We investigate measures of chaos in the measurement record of a quantum system which is being observed. Such measures are attractive because they can be directly connected to experiment. Two measures of chaos in the measurement record are…
Numerical calculations studying bound eigenstates in chaotic regions of phase space, including those of the stadium billiard, are summarized. These calculations demonstrate that the scars of periodic orbit model is seriously flawed. An…
Ergodicity and chaos play an integral role in the dynamical behavior of many-particle systems and are crucial to the formulation of statistical mechanics. Still, a general understanding of how randomness and chaos emerge in the dynamical…
A semiclassical method to determine if the classical limit of a quantum system is chaotic or not, based on Pesin theorem, is presented. The method is applied to a phenomenological Gamow--type model and it is concluded that its classical…
Even as we understand for long that the world is quantal and buried in it is classical dynamics which is chaotic, finding eigenfunctions analytically from the the Schroedinger equation has turned out to be a near-impossibility. Here, we…
We compute numerically eigenvalues and eigenfunctions of the quantum Hamiltonian that describes the quantum mechanics of a point particle moving freely in a particular three-dimensional hyperbolic space of finite volume and investigate the…
Recent years have seen an increasing interest in quantum chaos and related aspects of spatially extended systems, such as spin chains. However, the results are strongly system dependent, generic approaches suggest the presence of many-body…
We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian,…
We study the competing order and chaos in a first-order quantum phase transition with a high barrier. The boson model Hamiltonian employed, interpolates between its U(5) (spherical) and SU(3) (deformed) limits. A classical analysis reveals…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset 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…
We study the response of the quasi-energy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis. The systematic…
Quantum groups have a long and fruitful history of applications in integrable systems. Can quantum group symmetries exist in the absence of integrability? We provide an explicit example of a system with quantum group global symmetry which…
In this work we semiclassically analyzed the high lying eigenstates of a mixed type Hamiltonian system. For the regular states we employ the Einstein-Brillouin-Keller quantization, while for the chaotic states, following the principle of…
A detailed discussion of semiclassical trace formulae is presented and it is demonstrated how a regularized trace formula can be derived while dealing only with finite and convergent expressions. Furthermore, several applications of trace…