Related papers: Is there quantum chaos in the prime numbers?
Quantum small-worlds are quantum many-body systems that interpolate between completely ordered (nearest-neighbour, next-to-nearest-neighbour etc.) and completely random interactions. As such, they furnish a novel new laboratory to study…
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…
An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although…
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
The Prime state of $n$ qubits, $|\mathbb{P}_n\rangle$, is defined as the uniform superposition of all the computational-basis states corresponding to prime numbers smaller than $2^n$. This state encodes, quantum mechanically, arithmetic…
A recent quasiclassical description of a tunneling universe model is shown to exhibit chaotic dynamics by an analysis of fractal dimensions in the plane of initial values. This result relies on non-adiabatic features of the quantum…
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…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
We numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered…
We derive a set of spectral statistics whose power spectrum is characterized, in the case of chaotic quantum systems, by colored noise $1/f^{\gamma}$, where the integer parameter $\gamma$ critically depends on the specific energy-level…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular…
We study statistical properties of excited levels of the E x (b_1+b_2) Jahn-Teller model. The multitude of avoided crossings of energy levels is generally claimed to be a testimony of quantum chaos. We found that apart from two limiting…
Differences between measured nuclear masses and those calculated using the Finite Range Droplet Model are analyzed. It is shown that they have a well defined, clearly correlated oscillatory component as a function of the proton and neutron…
The quantum and classical dynamics of particles kicked by a gaussian attractive potential are studied. Classically, it is an open mixed system (the motion in some parts of the phase space is chaotic, and in some parts it is regular). The…
The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…