Related papers: Nodal Domain Distribution for a Nonintegrable Two-…
We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2-$d$ quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic…
Nodal domains are regions where a function has definite sign. In recent paper [nlin.CD/0109029] it is conjectured that the distribution of nodal domains for quantum eigenfunctions of chaotic systems is universal. We propose a…
Classical counterparts of a great variety of quantum systems, from atomic physics to quantum wells and quantum dots, to optical, microwave, and acoustic resonators exhibit partially chaotic dynamics. Since it is often impossible to measure…
We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and…
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength…
We investigate the emergence of chaotic dynamics in a quantum Fermi - Pasta - Ulam problem for anharmonic vibrations in atomic chains applying semi-quantitative analysis of resonant interactions complemented by exact diagonalization…
The nodal structure of bound-state wave functions for one-dimensional quantum systems with quartic energy-momentum dispersion and polynomial potentials is analysed by using the semiclassical approximation and variational approach. For…
Recent experimental and theoretical studies on the magnetization dynamics driven by an electric current have uncovered a number of unprecedented rich dynamic phenomena. We predict an intrinsic chaotic dynamics that has not been previously…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
The statistics of the nodal lines and nodal domains of the eigenfunctions of quantum billiards have recently been observed to be fingerprints of the chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett., Vol. 88…
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum…
We investigate the robustness of a dynamical phase transition against quantum fluctuations by studying the impact of a ferromagnetic nearest-neighbour spin interaction in one spatial dimension on the non-equilibrium dynamical phase diagram…
A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory numbers statistics for the model of nonlinear dissipative oscillator. It is shown by numerical simulation of an ensemble of quantum trajectories…
The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of…
The harmonic oscillator is an essential tool, widely used in all branches of Physics in order to understand more realistic systems, from classical to quantum and relativistic regimes. We know that the harmonic oscillator is integrable in…
The transition from a chaotic to a periodic oscillatory state can be smooth or abrupt in real-world turbulent systems. Although there have been several mathematical studies, the occurrence of abrupt transitions in real-world systems such as…
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…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external…
We study the dynamics of a three-mode bosonic system with mode-changing interactions. For large mode occupations the short-time dynamics is well described by classical mean-field equations allowing us to study chaotic dynamics in the…
We discuss the connection between the out-of-time-ordered correlator and the number of harmonics of the phase-space Wigner distribution function. In particular, we show that both quantities grow exponentially for chaotic dynamics, with a…