2,618 research outputs found
Fluctuations and Ergodicity of the Form Factor of Quantum Propagators and Random Unitary Matrices
We consider the spectral form factor of random unitary matrices as well as of
Floquet matrices of kicked tops. For a typical matrix the time dependence of
the form factor looks erratic; only after a local time average over a suitably
large time window does a systematic time dependence become manifest. For
matrices drawn from the circular unitary ensemble we prove ergodicity: In the
limits of large matrix dimension and large time window the local time average
has vanishingly small ensemble fluctuations and may be identified with the
ensemble average. By numerically diagonalizing Floquet matrices of kicked tops
with a globally chaotic classical limit we find the same ergodicity. As a
byproduct we find that the traces of random matrices from the circular
ensembles behave very much like independent Gaussian random numbers. Again,
Floquet matrices of chaotic tops share that universal behavior. It becomes
clear that the form factor of chaotic dynamical systems can be fully faithful
to random-matrix theory, not only in its locally time-averaged systematic time
dependence but also in its fluctuations.Comment: 12 pages, RevTEX, 4 figures in eps forma
Field quantization for chaotic resonators with overlapping modes
Feshbach's projector technique is employed to quantize the electromagnetic
field in optical resonators with an arbitray number of escape channels. We find
spectrally overlapping resonator modes coupled due to the damping and noise
inflicted by the external radiation field. For wave chaotic resonators the mode
dynamics is determined by a non--Hermitean random matrix. Upon including an
amplifying medium, our dynamics of open-resonator modes may serve as a starting
point for a quantum theory of random lasing.Comment: 4 pages, 1 figur
Periodic-Orbit Theory of Level Correlations
We present a semiclassical explanation of the so-called
Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral
fluctuations in chaotic dynamics. We work with a generating function whose
semiclassical limit is determined by quadruplets of sets of periodic orbits.
The asymptotic expansions of both the non-oscillatory and the oscillatory part
of the universal spectral correlator are obtained. Borel summation of the
series reproduces the exact correlator of random-matrix theory.Comment: 4 pages, 1 figure (+ web-only appendix with 2 pages, 1 figure
Overdamping by weakly coupled environments
A quantum system weakly interacting with a fast environment usually undergoes
a relaxation with complex frequencies whose imaginary parts are damping rates
quadratic in the coupling to the environment, in accord with Fermi's ``Golden
Rule''. We show for various models (spin damped by harmonic-oscillator or
random-matrix baths, quantum diffusion, quantum Brownian motion) that upon
increasing the coupling up to a critical value still small enough to allow for
weak-coupling Markovian master equations, a new relaxation regime can occur. In
that regime, complex frequencies lose their real parts such that the process
becomes overdamped. Our results call into question the standard belief that
overdamping is exclusively a strong coupling feature.Comment: 4 figures; Paper submitted to Phys. Rev.
Non-Markovian generalization of the Lindblad theory of open quantum systems
A systematic approach to the non-Markovian quantum dynamics of open systems
is given by the projection operator techniques of nonequilibrium statistical
mechanics. Combining these methods with concepts from quantum information
theory and from the theory of positive maps, we derive a class of correlated
projection superoperators that take into account in an efficient way
statistical correlations between the open system and its environment. The
result is used to develop a generalization of the Lindblad theory to the regime
of highly non-Markovian quantum processes in structured environments.Comment: 10 pages, 1 figure, replaced by published versio
Chaotic Quantum Decay in Driven Biased Optical Lattices
Quantum decay in an ac driven biased periodic potential modeling cold atoms
in optical lattices is studied for a symmetry broken driving. For the case of
fully chaotic classical dynamics the classical exponential decay is quantum
mechanically suppressed for a driving frequency \omega in resonance with the
Bloch frequency \omega_B, q\omega=r\omega_B with integers q and r.
Asymptotically an algebraic decay ~t^{-\gamma} is observed. For r=1 the
exponent \gamma agrees with as predicted by non-Hermitian random matrix
theory for q decay channels. The time dependence of the survival probability
can be well described by random matrix theory. The frequency dependence of the
survival probability shows pronounced resonance peaks with sub-Fourier
character.Comment: 7 pages, 5 figure
Standing Up for Industry Standing in Environmental Regulatory Challenges
Article III of the U.S. Constitution limits courts to hearing only cases and controversies. To address this limitation, federal courts have developed the doctrine of standing, which requires a litigant to have suffered a cognizable injury in fact, which was caused by the challenged conduct and that will be redressable by a favorable outcome. Courts have struggled to balance these components and, in practice, different requirements have developed for meeting standing depending on the nature of the case and the type of party bringing suit. This Article explores the U.S. Court of Appeals for the District of Columbia Circuit’s recent decisions in Coalition for Responsible Regulation, Inc. v. EPA, Grocery Manufacturers Ass’n v. EPA, and Alliance of Automobile Manufacturers v. EPA. It argues that the D.C. Circuit’s findings in these cases—that industry petitioners lacked standing to sue—are the result of the court’s overly narrow analysis of EPA rulemakings as individual acts, without regard to the broader effect of the regulatory scheme of which the rulemakings are a part. In so doing, the D.C. Circuit has precluded industry petitioners from accounting for the practical financial harms they have suffered. The authors conclude that the consequence of this narrow review is a higher bar to establish standing for industry petitioners than for environmental plaintiffs. Ultimately, the D.C. Circuit’s decisions raise the specter that a regulatory program that has tangible impacts on a regulated industry will nonetheless be shielded from judicial review
Semiclassical spectral correlator in quasi one-dimensional systems
We investigate the spectral statistics of chaotic quasi one dimensional
systems such as long wires. To do so we represent the spectral correlation
function through derivatives of a generating function and
semiclassically approximate the latter in terms of periodic orbits. In contrast
to previous work we obtain both non-oscillatory and oscillatory contributions
to the correlation function. Both types of contributions are evaluated to
leading order in for systems with and without time-reversal
invariance. Our results agree with expressions from the theory of disordered
systems.Comment: 10 pages, no figure
Quantum resonance and anti-resonance for a periodically kicked Bose-Einstein Condensate in a one dimensional Box
We investigate the quantum dynamics of a periodically kicked Bose-Einstein
Condensate confined in a one dimensional (1D) Box both numerically and
theoretically, emphasizing on the phenomena of quantum resonance and
anti-resonance. The quantum resonant behavior of BEC is different from the
single particle case but the anti-resonance condition ( and ) is not affected by the atomic interaction. For the anti-resonance case, the
nonlinearity (atom interaction) causes the transition between oscillation and
quantum beating. For the quantum resonance case, because of the coherence of
BEC, the energy increase is oscillating and the rate is dramatically affected
by the many-body interaction. We also discuss the relation between the quantum
resonant behavior and the KAM or non-KAM property of the corresponding
classical system.Comment: 7 pages, 7 figure
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