55,328 research outputs found
Time-reversible Dynamical Systems for Turbulence
Dynamical Ensemble Equivalence between hydrodynamic dissipative equations and
suitable time-reversible dynamical systems has been investigated in a class of
dynamical systems for turbulence. The reversible dynamics is obtained from the
original dissipative equations by imposing a global constraint. We find that,
by increasing the input energy, the system changes from an equilibrium state to
a non-equilibrium stationary state in which an energy cascade, with the same
statistical properties of the original system, is clearly detected.Comment: 16 pages Latex, 4 PS figures, on press on J. Phy
Time Quasilattices in Dissipative Dynamical Systems
We establish the existence of `time quasilattices' as stable trajectories in
dissipative dynamical systems. These tilings of the time axis, with two unit
cells of different durations, can be generated as cuts through a periodic
lattice spanned by two orthogonal directions of time. We show that there are
precisely two admissible time quasilattices, which we term the infinite Pell
and Clapeyron words, reached by a generalization of the period-doubling
cascade. Finite Pell and Clapeyron words of increasing length provide
systematic periodic approximations to time quasilattices which can be verified
experimentally. The results apply to all systems featuring the universal
sequence of periodic windows. We provide examples of discrete-time maps, and
periodically-driven continuous-time dynamical systems. We identify quantum
many-body systems in which time quasilattices develop rigidity via the
interaction of many degrees of freedom, thus constituting dissipative discrete
`time quasicrystals'.Comment: 38 pages, 14 figures. This version incorporates "Pell and Clapeyron
Words as Stable Trajectories in Dynamical Systems", arXiv:1707.09333.
Submission to SciPos
Dynamical regimes of dissipative quantum systems
We reveal several distinct regimes of the relaxation dynamics of a small
quantum system coupled to an environment within the plane of the dissipation
strength and the reservoir temperature. This is achieved by discriminating
between coherent dynamics with damped oscillatory behavior on all time scales,
partially coherent behavior being nonmonotonic at intermediate times but
monotonic at large ones, and purely monotonic incoherent decay. Surprisingly,
elevated temperature can render the system `more coherent' by inducing a
transition from the partially coherent to the coherent regime. This provides a
refined view on the relaxation dynamics of open quantum systems.Comment: 5 pages, 3 figure
Nonintegrability, Chaos, and Complexity
Two-dimensional driven dissipative flows are generally integrable via a
conservation law that is singular at equilibria. Nonintegrable dynamical
systems are confined to n*3 dimensions. Even driven-dissipative deterministic
dynamical systems that are critical, chaotic or complex have n-1 local
time-independent conservation laws that can be used to simplify the geometric
picture of the flow over as many consecutive time intervals as one likes. Those
conserevation laws generally have either branch cuts, phase singularities, or
both. The consequence of the existence of singular conservation laws for
experimental data analysis, and also for the search for scale-invariant
critical states via uncontrolled approximations in deterministic dynamical
systems, is discussed. Finally, the expectation of ubiquity of scaling laws and
universality classes in dynamics is contrasted with the possibility that the
most interesting dynamics in nature may be nonscaling, nonuniversal, and to
some degree computationally complex
Simulating Quantum Dissipation in Many-Body Systems
An efficient Path Integral Monte Carlo procedure is proposed to simulate the
behavior of quantum many-body dissipative systems described within the
framework of the influence functional. Thermodynamic observables are obtained
by Monte Carlo sampling of the partition function after discretization and
Fourier transformation in imaginary time of the dynamical variables. The method
is tested extensively for model systems, using realistic dissipative kernels.
Results are also compared with the predictions of a recently proposed
semiclassical approximation, thus testing the reliability of the latter
approach for weak quantum coupling. Our numerical method opens the possibility
to quantitatively describe real quantum dissipative systems as, e.g., Josephson
junction arrays.Comment: 10 pages, 4 figure
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