229 research outputs found
Universal Power-law Decay in Hamiltonian Systems?
The understanding of the asymptotic decay of correlations and of the
distribution of Poincar\'e recurrence times has been a major challenge
in the field of Hamiltonian chaos for more than two decades. In a recent
Letter, Chirikov and Shepelyansky claimed the universal decay for Hamiltonian systems. Their reasoning is based on renormalization
arguments and numerical findings for the sticking of chaotic trajectories near
a critical golden torus in the standard map. We performed extensive numerics
and find clear deviations from the predicted asymptotic exponent of the decay
of . We thereby demonstrate that even in the supposedly simple case, when
a critical golden torus is present, the fundamental question of asymptotic
statistics in Hamiltonian systems remains unsolved.Comment: Phys. Rev. Lett., in pres
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
Efficient Diagonalization of Kicked Quantum Systems
We show that the time evolution operator of kicked quantum systems, although
a full matrix of size NxN, can be diagonalized with the help of a new method
based on a suitable combination of fast Fourier transform and Lanczos algorithm
in just N^2 ln(N) operations. It allows the diagonalization of matrizes of
sizes up to N\approx 10^6 going far beyond the possibilities of standard
diagonalization techniques which need O(N^3) operations. We have applied this
method to the kicked Harper model revealing its intricate spectral properties.Comment: Text reorganized; part on the kicked Harper model extended. 13 pages
RevTex, 1 figur
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
Isolated resonances in conductance fluctuations in ballistic billiards
We study numerically quantum transport through a billiard with a classically
mixed phase space. In particular, we calculate the conductance and Wigner delay
time by employing a recursive Green's function method. We find sharp, isolated
resonances with a broad distribution of resonance widths in both the
conductance and the Wigner time, in contrast to the well-known smooth
conductance fluctuations of completely chaotic billiards. In order to elucidate
the origin of the isolated resonances, we calculate the associated scattering
states as well as the eigenstates of the corresponding closed system. As a
result, we find a one-to-one correspondence between the resonant scattering
states and eigenstates of the closed system. The broad distribution of
resonance widths is traced to the structure of the classical phase space.
Husimi representations of the resonant scattering states show a strong overlap
either with the regular regions in phase space or with the hierarchical parts
surrounding the regular regions. We are thus lead to a classification of the
resonant states into regular and hierarchical, depending on their phase space
portrait.Comment: 2 pages, 5 figures, to be published in J. Phys. Soc. Jpn.,
proceedings Localisation 2002 (Tokyo, Japan
Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space
The lifetimes of optical modes in whispering-gallery cavities depend crucially on the underlying classical ray dynamics, and they may be spoiled by the presence of classical nonlinear resonances due to resonance-assisted tunneling. Here we present an intuitive semiclassical picture that allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space, and we find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths
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