1,176 research outputs found
Quantum Resonances of Kicked Rotor and SU(q) group
The quantum kicked rotor (QKR) map is embedded into a continuous unitary
transformation generated by a time-independent quasi-Hamiltonian. In some
vicinity of a quantum resonance of order , we relate the problem to the {\it
regular} motion along a circle in a -component inhomogeneous
"magnetic" field of a quantum particle with intrinsic degrees of freedom
described by the group. This motion is in parallel with the classical
phase oscillations near a non-linear resonance.Comment: RevTeX, 4 pages, 3 figure
Quantum Resonances and Regularity Islands in Quantum Maps
We study analytically as well as numerically the dynamics of a quantum map
near a quantum resonance of an order q. The map is embedded into a continuous
unitary transformation generated by a time-independent quasi-Hamiltonian. Such
a Hamiltonian generates at the very point of the resonance a local gauge
transformation described the unitary unimodular group SU(q). The resonant
energy growth of is attributed to the zero Liouville eigenmodes of the
generator in the adjoint representation of the group while the non-zero modes
yield saturating with time contribution. In a vicinity of a given resonance,
the quasi-Hamiltonian is then found in the form of power expansion with respect
to the detuning from the resonance. The problem is related in this way to the
motion along a circle in a (q^2-1)-component inhomogeneous "magnetic" field of
a quantum particle with intrinsic degrees of freedom described by the SU(q)
group. This motion is in parallel with the classical phase oscillations near a
non-linear resonance. The most important role is played by the resonances with
the orders much smaller than the typical localization length, q << l. Such
resonances master for exponentially long though finite times the motion in some
domains around them. Explicit analytical solution is possible for a few lowest
and strongest resonances.Comment: 28 pages (LaTeX), 11 ps figures, submitted to PR
Quantum dephasing and decay of classical correlation functions in chaotic systems
We discuss the dephasing induced by the internal classical chaotic motion in
the absence of any external environment. To this end we consider a suitable
extension of fidelity for mixed states which is measurable in a Ramsey
interferometry experiment. We then relate the dephasing to the decay of this
quantity which, in the semiclassical limit, is expressed in terms of an
appropriate classical correlation function. Our results are derived
analytically for the example of a nonlinear driven oscillator and then
numerically confirmed for the kicked rotor model.Comment: 14 pages, 1 figur
Complexity of Quantum States and Reversibility of Quantum Motion
We present a quantitative analysis of the reversibility properties of
classically chaotic quantum motion. We analyze the connection between
reversibility and the rate at which a quantum state acquires a more and more
complicated structure in its time evolution. This complexity is characterized
by the number of harmonics of the (initially isotropic, i.e.
) Wigner function, which are generated during quantum evolution
for the time . We show that, in contrast to the classical exponential
increase, this number can grow not faster than linearly and then relate this
fact with the degree of reversibility of the quantum motion. To explore the
reversibility we reverse the quantum evolution at some moment immediately
after applying at this moment an instant perturbation governed by a strength
parameter . It follows that there exists a critical perturbation strength,
, below which the initial state is well
recovered, whereas reversibility disappears when . In the
classical limit the number of harmonics proliferates exponentially with time
and the motion becomes practically irreversible. The above results are
illustrated in the example of the kicked quartic oscillator model.Comment: 15 pages, 13 figures; the list of references is update
Negative differential thermal resistance and thermal transistor
We report on the first model of a thermal transistor to control heat flow.
Like its electronic counterpart, our thermal transistor is a three-terminal
device with the important feature that the current through the two terminals
can be controlled by small changes in the temperature or in the current through
the third terminal. This control feature allows us to switch the device between
"off" (insulating) and "on" (conducting) states or to amplify a small current.
The thermal transistor model is possible because of the negative differential
thermal resistance.Comment: 4 pages, 4 figures. SHortened. To appear in Applied Physics Letter
Anomalous diffusion and dynamical localization in a parabolic map
We study numerically classical and quantum dynamics of a piecewise parabolic
area preserving map on a cylinder which emerges from the bounce map of
elongated triangular billiards. The classical map exhibits anomalous diffusion.
Quantization of the same map results in a system with dynamical localization
and pure point spectrum.Comment: 4 pages in RevTeX (4 ps-figures included
Quantum Poincare Recurrences for Hydrogen Atom in a Microwave Field
We study the time dependence of the ionization probability of Rydberg atoms
driven by a microwave field, both in classical and in quantum mechanics. The
quantum survival probability follows the classical one up to the Heisenberg
time and then decays algebraically as P(t) ~ 1/t. This decay law derives from
the exponentially long times required to escape from some region of the phase
space, due to tunneling and localization effects. We also provide parameter
values which should allow to observe such decay in laboratory experiments.Comment: revtex, 4 pages, 4 figure
A semiquantal approach to finite systems of interacting particles
A novel approach is suggested for the statistical description of quantum
systems of interacting particles. The key point of this approach is that a
typical eigenstate in the energy representation (shape of eigenstates, SE) has
a well defined classical analog which can be easily obtained from the classical
equations of motion. Therefore, the occupation numbers for single-particle
states can be represented as a convolution of the classical SE with the quantum
occupation number operator for non-interacting particles. The latter takes into
account the wavefunctions symmetry and depends on the unperturbed energy
spectrum only. As a result, the distribution of occupation numbers can be
numerically found for a very large number of interacting particles. Using the
model of interacting spins we demonstrate that this approach gives a correct
description of even in a deep quantum region with few single-particle
orbitals.Comment: 4 pages, 2 figure
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