Temporal flooding of regular islands by chaotic wave packets

We investigate the time evolution of wave packets in systems with a mixed phase space where regular islands and chaotic motion coexist. For wave packets started in the chaotic sea on average the weight on a quantized torus of the regular island increases due to dynamical tunneling. This flooding weight initially increases linearly and saturates to a value which varies from torus to torus. We demonstrate for the asymptotic flooding weight universal scaling with an effective tunneling coupling for quantum maps and the mushroom billiard. This universality is reproduced by a suitable random matrix model

A unified theory for excited-state, fragmented, and equilibrium-like Bose condensation in pumped photonic many-body systems

We derive a theory for Bose condensation in nonequilibrium steady states of bosonic quantum gases that are coupled both to a thermal heat bath and to a pumped reservoir (or gain medium), while suffering from loss. Such a scenario describes photonic many-body systems such as exciton-polariton gases. Our analysis is based on a set of kinetic equations for a gas of noninteracting bosons. By identifying a dimensionless scaling parameter controlling the boson density, we derive a sharp criterion for which system states become selected to host a macroscopic occupation. We show that with increasing pump power, the system generically undergoes a sequence of nonequilibrum phase transitions. At each transition a state either becomes or ceases to be Bose selected (i.e. to host a condensate): The state which first acquires a condensate when the pumping exceeds a threshold is the one with the largest ratio of pumping to loss. This intuitive behavior resembles simple lasing. In the limit of strong pumping, the coupling to the heat bath becomes dominant so that eventually the ground state is selected, corresponding to equilibrium(-like) Bose condensation. For intermediate pumping strengths, several states become selected giving rise to fragmented nonequilibrium Bose condensation. We compare these predictions to experimental results obtained for excitons polaritons in a double-pillar structure [Phys. Rev. Lett. 108, 126403 (2012)] and find good agreement. Our theory, moreover, predicts that the reservoir occupation is clamped at a constant value whenever the system hosts an odd number of Bose condensates

Visualization and comparison of classical structures and quantum states of 4D maps

For generic 4D symplectic maps we propose the use of 3D phase-space slices which allow for the global visualization of the geometrical organization and coexistence of regular and chaotic motion. As an example we consider two coupled standard maps. The advantages of the 3D phase-space slices are presented in comparison to standard methods like 3D projections of orbits, the frequency analysis, and a chaos indicator. Quantum mechanically, the 3D phase-space slices allow for the first comparison of Husimi functions of eigenstates of 4D maps with classical phase space structures. This confirms the semi-classical eigenfunction hypothesis for 4D maps.Comment: For videos with rotated view of the 3D phase-space slices in high resolution see http://www.comp-phys.tu-dresden.de/supp

Coupling of bouncing-ball modes to the chaotic sea and their counting function

We study the coupling of bouncing-ball modes to chaotic modes in two-dimensional billiards with two parallel boundary segments. Analytically, we predict the corresponding decay rates using the fictitious integrable system approach. Agreement with numerically determined rates is found for the stadium and the cosine billiard. We use this result to predict the asymptotic behavior of the counting function N_bb(E) ~ E^\delta. For the stadium billiard we find agreement with the previous result \delta = 3/4. For the cosine billiard we derive \delta = 5/8, which is confirmed numerically and is well below the previously predicted upper bound \delta=9/10.Comment: 10 pages, 6 figure

Localization of Chaotic Resonance States due to a Partial Transport Barrier

Chaotic eigenstates of quantum systems are known to localize on either side of a classical partial transport barrier if the flux connecting the two sides is quantum mechanically not resolved due to Heisenberg's uncertainty. Surprisingly, in open systems with escape chaotic resonance states can localize even if the flux is quantum mechanically resolved. We explain this using the concept of conditionally invariant measures from classical dynamical systems by introducing a new quantum mechanically relevant class of such fractal measures. We numerically find quantum-to-classical correspondence for localization transitions depending on the openness of the system and on the decay rate of resonance states.Comment: 5+1 pages, 4 figure

High-temperature nonequilibrium Bose condensation induced by a hot needle

We investigate theoretically a one-dimensional ideal Bose gas that is driven into a steady state far from equilibrium via the coupling to two heat baths: a global bath of temperature $T$ and a "hot needle", a bath of temperature $T_h\gg T$ with localized coupling to the system. Remarkably, this system features a crossover to finite-size Bose condensation at temperatures $T$ that are orders of magnitude larger than the equilibrium condensation temperature. This counterintuitive effect is explained by a suppression of long-wavelength excitations resulting from the competition between both baths. Moreover, for sufficiently large needle temperatures ground-state condensation is superseded by condensation into an excited state, which is favored by its weaker coupling to the hot needle. Our results suggest a general strategy for the preparation of quantum degenerate nonequilibrium steady states with unconventional properties and at large temperatures

3D billiards: visualization of regular structures and trapping of chaotic trajectories

The dynamics in three-dimensional billiards leads, using a Poincar\'e section, to a four-dimensional map which is challenging to visualize. By means of the recently introduced 3D phase-space slices an intuitive representation of the organization of the mixed phase space with regular and chaotic dynamics is obtained. Of particular interest for applications are constraints to classical transport between different regions of phase space which manifest in the statistics of Poincar\'e recurrence times. For a 3D paraboloid billiard we observe a slow power-law decay caused by long-trapped trajectories which we analyze in phase space and in frequency space. Consistent with previous results for 4D maps we find that: (i) Trapping takes place close to regular structures outside the Arnold web. (ii) Trapping is not due to a generalized island-around-island hierarchy. (iii) The dynamics of sticky orbits is governed by resonance channels which extend far into the chaotic sea. We find clear signatures of partial transport barriers. Moreover, we visualize the geometry of stochastic layers in resonance channels explored by sticky orbits.Comment: 20 pages, 11 figures. For videos of 3D phase-space slices and time-resolved animations see http://www.comp-phys.tu-dresden.de/supp

Complex-Path Prediction of Resonance-Assisted Tunneling in Mixed Systems

We present a semiclassical prediction of regular-to-chaotic tunneling in systems with a mixed phase space, including the effect of a nonlinear resonance chain. We identify complex paths for direct and resonance-assisted tunneling in the phase space of an integrable approximation with one nonlinear resonance chain. We evaluate the resonance-assisted contribution analytically and give a prediction based on just a few properties of the classical phase space. For the standard map excellent agreement with numerically determined tunneling rates is observed. The results should similarly apply to ionization rates and quality factors.Comment: 6 pages, 2 figure

Bifurcations of families of 1D-tori in 4D symplectic maps

The regular structures of a generic 4D symplectic map with a mixed phase space are organized by one-parameter families of elliptic 1D-tori. Such families show prominent bends, gaps, and new branches. We explain these features in terms of bifurcations of the families when crossing a resonance. For these bifurcations no external parameter has to be varied. Instead, the longitudinal frequency, which varies along the family, plays the role of the bifurcation parameter. As an example we study two coupled standard maps by visualizing the elliptic and hyperbolic 1D-tori in a 3D phase-space slice, local 2D projections, and frequency space. The observed bifurcations are consistent with analytical predictions previously obtained for quasi-periodically forced oscillators. Moreover, the new families emerging from such a bifurcation form the skeleton of the corresponding resonance channel.Comment: 14 pages, 10 figures. For videos of 3D phase-space slices see http://www.comp-phys.tu-dresden.de/supp