1,979 research outputs found
The triangle map: a model of quantum chaos
We study an area preserving parabolic map which emerges from the Poincar\' e
map of a billiard particle inside an elongated triangle. We provide numerical
evidence that the motion is ergodic and mixing. Moreover, when considered on
the cylinder, the motion appear to follow a gaussian diffusive process.Comment: 4 pages in RevTeX with 4 figures (in 6 eps-files
Quantum chaos and the double-slit experiment
We report on the numerical simulation of the double-slit experiment, where
the initial wave-packet is bounded inside a billiard domain with perfectly
reflecting walls. If the shape of the billiard is such that the classical ray
dynamics is regular, we obtain interference fringes whose visibility can be
controlled by changing the parameters of the initial state. However, if we
modify the shape of the billiard thus rendering classical (ray) dynamics fully
chaotic, the interference fringes disappear and the intensity on the screen
becomes the (classical) sum of intensities for the two corresponding one-slit
experiments. Thus we show a clear and fundamental example in which transition
to chaotic motion in a deterministic classical system, in absence of any
external noise, leads to a profound modification in the quantum behaviour.Comment: 5 pages, 4 figure
The Sato Grassmannian and the CH hierarchy
We discuss how the Camassa-Holm hierarchy can be framed within the geometry
of the Sato Grassmannian.Comment: 10 pages, no figure
Asymmetric Wave Propagation in Nonlinear Systems
A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As
a reference system, we consider a layered nonlinear, non mirror-symmetric model
described by the one-dimensional Discrete Nonlinear Schreodinger equation with
spatially varying coefficients embedded in an otherwise linear lattice. We
construct a class of exact extended solutions such that waves with the same
frequency and incident amplitude impinging from left and right directions have
very different transmission coefficients. This effect arises already for the
simplest case of two nonlinear layers and is associated with the shift of
nonlinear resonances. Increasing the number of layers considerably increases
the complexity of the family of solutions. Finally, numerical simulations of
asymmetric wavepacket transmission are presented which beautifully display the
rectifying effect
A 3-component extension of the Camassa-Holm hierarchy
We introduce a bi-Hamiltonian hierarchy on the loop-algebra of sl(2) endowed
with a suitable Poisson pair. It gives rise to the usual CH hierarchy by means
of a bi-Hamiltonian reduction, and its first nontrivial flow provides a
3-component extension of the CH equation.Comment: 15 pages; minor changes; to appear in Letters in Mathematical Physic
Translationally invariant conservation laws of local Lindblad equations
We study the conditions under which one can conserve local translationally
invariant operators by local translationally invariant Lindblad equations in
one-dimensional rings of spin-1/2 particles. We prove that for any 1-local
operator (e.g., particle density) there exist Lindblad dissipators that
conserve that operator, while on the other hand we prove that among 2-local
operators (e.g., energy density) only trivial ones of the Ising type can be
conserved, while all the other cannot be conserved, neither locally nor
globally, by any 2- or 3-local translationally invariant Lindblad equation. Our
statements hold for rings of any finite length larger than some minimal length
determined by the locality of Lindblad equation. These results show in
particular that conservation of energy density in interacting systems is
fundamentally more difficult than conservation of 1-local quantities.Comment: 15 pages, no fig
Directed deterministic classical transport: symmetry breaking and beyond
We consider transport properties of a double delta-kicked system, in a regime
where all the symmetries (spatial and temporal) that could prevent directed
transport are removed. We analytically investigate the (non trivial) behavior
of the classical current and diffusion properties and show that the results are
in good agreement with numerical computations. The role of dissipation for a
meaningful classical ratchet behavior is also discussed.Comment: 10 pages, 20 figure
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
Steering Bose-Einstein condensates despite time symmetry
A Bose-Einstein condensate in an oscillating spatially asymmetric potential
is shown to exhibit a directed current for unbiased initial conditions despite
time symmetry. This phenomenon occurs only if the interaction between atoms,
treated in mean-field approximation, exceeds a critical value. Our findings can
be described with a three-mode model (TMM). These TMM results corroborate well
with a many-body study over a time scale which increases with increasing atom
number. The duration of this time scale probes the validity of the used
mean-field approximation.Comment: 4 pages, 5 figure
Accelerator dynamics of a fractional kicked rotor
It is shown that the Weyl fractional derivative can quantize an open system.
A fractional kicked rotor is studied in the framework of the fractional
Schrodinger equation. The system is described by the non-Hermitian Hamiltonian
by virtue of the Weyl fractional derivative. Violation of space symmetry leads
to acceleration of the orbital momentum. Quantum localization saturates this
acceleration, such that the average value of the orbital momentum can be a
direct current and the system behaves like a ratchet. The classical counterpart
is a nonlinear kicked rotor with absorbing boundary conditions.Comment: Submitted for publication in Phys. Rev.
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