Related papers: Generalized multibaker maps for open dissipative s…
Dynamical maps are the principal subject of the open system theory. Formally, the dynamical map of a given open quantum system is a density matrix transformation that takes any initial state and sends it to the state at a later time.…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
Consider a finite number of balls initially placed in $L$ bins. At each time step a ball is taken from each non-empty bin. Then all the balls are uniformly reassigned into bins. This finite Markov chain is called Repeated Balls-into-Bins…
Recently, a concept of generalized multifractality, which characterizes fluctuations and correlations of critical eigenstates, was introduced and explored for all ten symmetry classes of disordered systems. Here, by using the non-linear…
The universal mechanism resulting in the generalized synchronization regime arising in the chaotic oscillators with the dissipative coupling has been described. The reasons of the generalized synchronization occurrence may be clarified by…
Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via…
It is shown that a coupled map model for open flow may exhibit spatial chaos and spatial quasiperiodicity with temporal periodicity. The locations of these patterns, which cover a substantial part of parameter space, are indicated in a…
In shear flows like pipe flow and plane Couette flow there is an extended range of parameters where linearly stable laminar flow coexists with a transient turbulent dynamics. When increasing the amplitude of a perturbation on top of the…
Non-linear dynamics is not a usually covered topic in undergraduate physics courses. However, its importance within classical mechanics and the general theory of dynamical systems is unquestionable. In this work we show that this subject…
We derive an expression for the mean square displacement of a particle whose motion is governed by a uniform, periodic, quantum multi-baker map. The expression is a function of both time, $t$, and Planck's constant, $\hbar$, and allows a…
We investigate the universal dissipationless dynamics of Gaussian continuous-variable systems in the presence of a band-gapped bosonic environment. Our results show that environmental band gaps can induce localized modes, which give rise to…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
We discuss an open driven-dissipative many-body system, in which the competition of unitary Hamiltonian and dissipative Liouvillian dynamics leads to a nonequilibrium phase transition. It shares features of a quantum phase transition in…
We treat three cubic recurrences, two of which generalize the famous iterated map $x \mapsto x (1-x)$ from discrete chaos theory. A feature of each asymptotic series developed here is a constant, dependent on the initial condition but…
Understanding how external driving and dissipation jointly influence the dynamics of open quantum systems is essential for advancing the study of non-equilibrium quantum phenomena and developing quantum technologies. The present study…
We critically evaluate the most widespread assumption in the theoretical description of coherent control strategies for open quantum systems. We show that, for non-Markovian open systems dynamics, this fixed-dissipator assumption leads to a…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
The quantum baker's map is the quantization of a simple classically chaotic system, and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study…
Integrable systems offer rare examples of solvable many-body problems in the quantum world. Due to the fine-tuned structure, their realization in nature and experiment is never completely accurate, therefore effects of integrability are…