1,881 research outputs found
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
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.
Coarse-Grained Picture for Controlling Complex Quantum Systems
We propose a coarse-grained picture to control ``complex'' quantum dynamics,
i.e., multi-level-multi-level transition with a random interaction. Assuming
that optimally controlled dynamics can be described as a Rabi-like oscillation
between an initial and final state, we derive an analytic optimal field as a
solution to optimal control theory. For random matrix systems, we numerically
confirm that the analytic optimal field steers an initial state to a target
state which both contains many eigenstates.Comment: jpsj2.cls, 2 pages, 3 figure files; appear in J. Phys. Soc. Jpn.
Vol.73, No.11 (Nov. 15, 2004
Weak localization of the open kicked rotator
We present a numerical calculation of the weak localization peak in the
magnetoconductance for a stroboscopic model of a chaotic quantum dot. The
magnitude of the peak is close to the universal prediction of random-matrix
theory. The width depends on the classical dynamics, but this dependence can be
accounted for by a single parameter: the level curvature around zero magnetic
field of the closed system.Comment: 8 pages, 8 eps figure
Universality of Decoherence
We consider environment induced decoherence of quantum superpositions to
mixtures in the limit in which that process is much faster than any competing
one generated by the Hamiltonian of the isolated system. While
the golden rule then does not apply we can discard . By allowing
for simultaneous couplings to different reservoirs, we reveal decoherence as a
universal short-time phenomenon independent of the character of the system as
well as the bath and of the basis the superimposed states are taken from. We
discuss consequences for the classical behavior of the macroworld and quantum
measurement: For the decoherence of superpositions of macroscopically distinct
states the system Hamiltonian is always negligible.Comment: 4 revtex pages, no figure
The statistical properties of the city transport in Cuernavaca (Mexico) and Random matrix ensembles
We analyze statistical properties of the city bus transport in Cuernavaca
(Mexico) and show that the bus arrivals display probability distributions
conforming those given by the Unitary Ensemble of random matrices.Comment: 4 pages, 3 figure
Splitting of Andreev levels in a Josephson junction by spin-orbit coupling
We consider the effect of spin-orbit coupling on the energy levels of a
single-channel Josephson junction below the superconducting gap. We investigate
quantitatively the level splitting arising from the combined effect of
spin-orbit coupling and the time-reversal symmetry breaking by the phase
difference between the superconductors. Using the scattering matrix approach we
establish a simple connection between the quantum mechanical time delay matrix
and the effective Hamiltonian for the level splitting. As an application we
calculate the distribution of level splittings for an ensemble of chaotic
Josephson junctions. The distribution falls off as a power law for large
splittings, unlike the exponentially decaying splitting distribution given by
the Wigner surmise -- which applies for normal chaotic quantum dots with
spin-orbit coupling in the case that the time-reversal symmetry breaking is due
to a magnetic field.Comment: 6 pages, 3 figure
Coherence and Decoherence in Radiation off Colliding Heavy Ions
We discuss the kinetics of a disoriented chiral condensate, treated as an
open quantum system. We suggest that the problem is analogous to that of a
damped harmonic oscillator. Master equations are used to establish a hierarchy
of relevant time scales. Some phenomenological consequences are briefly
outlined.Comment: 15 latex pages, LPTHE Orsay 93/19, e-mail: [email protected]
Anomalous power law of quantum reversibility for classically regular dynamics
The Loschmidt Echo M(t) (defined as the squared overlap of wave packets
evolving with two slightly different Hamiltonians) is a measure of quantum
reversibility. We investigate its behavior for classically quasi-integrable
systems. A dominant regime emerges where M(t) ~ t^{-alpha} with alpha=3d/2
depending solely on the dimension d of the system. This power law decay is
faster than the result ~ t^{-d} for the decay of classical phase space
densities
Fidelity and Purity Decay in Weakly Coupled Composite Systems
We study the stability of unitary quantum dynamics of composite systems (for
example: central system + environment) with respect to weak interaction between
the two parts. Unified theoretical formalism is applied to study different
physical situations: (i) coherence of a forward evolution as measured by purity
of the reduced density matrix, (ii) stability of time evolution with respect to
small coupling between subsystems, and (iii) Loschmidt echo measuring dynamical
irreversibility. Stability has been measured either by fidelity of pure states
of a composite system, or by the so-called reduced fidelity of reduced density
matrices within a subsystem. Rigorous inequality among fidelity,
reduced-fidelity and purity is proved and a linear response theory is developed
expressing these three quantities in terms of time correlation functions of the
generator of interaction. The qualitatively different cases of regular
(integrable) or mixing (chaotic in the classical limit) dynamics in each of the
subsystems are discussed in detail. Theoretical results are demonstrated and
confirmed in a numerical example of two coupled kicked tops.Comment: 21 pages, 12 eps figure
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