Related papers: On Geometry, Arithmetics and Chaos
We consider two coupled quantum tops with angular momentum vectors $\mathbf{L}$ and $\mathbf{M}$. The coupling Hamiltonian defines the Feinberg-Peres model which is a known paradigm of quantum chaos. We show that this model has a…
This is a short review in the theory of chaos in Bohmian Quantum Mechanics based on our series of works in this field. Our first result is the development of a generic theoretical mechanism responsible for the generation of chaos in an…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
A class of time independent and physically meaningful Hamiltonians leads to evolution of observable quantities whose Ehrenfest times are arbitrarily large. This fact contradicts the popular claim that the true chaos is in quantum mechanics…
We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions,…
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…
We address the problem of quantum chaos: Is there a rigorous, physically meaningful definition of chaos in quantum physics? Can the tools of classical chaos theory, like Lyapunov exponents, Poincar\'e sections etc. be carried over to…
Quantum dots are small conducting devices containing up to several thousand electrons. We focus here on closed dots whose single-electron dynamics are mostly chaotic. The mesoscopic fluctuations of the conduction properties of such dots…
Parrondo's paradox (PP) is a fundamental principle in nonlinear science where the alternation of individually losing strategies leads to a winning outcome. In this topical review, we provide the first systematic panorama of the synergy…
We report a novel mechanism for the occurrence of chaos at the macroscopic level induced by the frustration of interaction, namely frustration-induced chaos, in a non-monotonic sequential associative memory model. We succeed in deriving…
A new micro-irreversible 3D theory of quantum multichannel scattering in the three-body system is developed. The quantum approach is constructed on the generating trajectory tubes which allow taking into account influence of classical…
The manner in which unpredictable chaotic dynamics manifests itself in quantum mechanics is a key question in the field of quantum chaos. Indeed, very distinct quantum features can appear due to underlying classical nonlinear dynamics. Here…
Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to…
We consider stable periodic helixes as a generalization of stable periodic orbits. We see that in the studied class of iterated functions Chaos always arise suddenly. Therefore, we shall study the route from chaos to order rather than the…
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the "frame potential," which is minimized by unitary $k$-designs and measures the $2$-norm…
The main idea of "Quantum Chaos" studies is that Quantum Mechanics introduces two energy scales into the study of chaotic systems: One is obviously the mean level spacing $\Delta\propto\hbar^d$, where $d$ is the dimensionality; The other is…
We study the spatiotemporally chaotic dynamics of holes and defects in the 1D complex Ginzburg--Landau equation (CGLE). We focus particularly on the self--disordering dynamics of holes and on the variation in defect profiles. By enforcing…
The orbits of fluid particles in two dimensions effectively act as topological obstacles to material lines. A spacetime plot of the orbits of such particles can be regarded as a braid whose properties reflect the underlying dynamics. For a…
Chaos as typical property of non-linear systems has revealed its crucial role in various problems of astrophysics and cosmology. The problems discussed at these lectures include planetary dynamics, galactic dynamics, reconstruction of the…
In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of…