365 research outputs found
Diagnostic criterion for crystallized beams
Small ion crystals in a Paul trap are stable even in the absence of laser
cooling. Based on this theoretically and experimentally well-established fact
we propose the following diagnostic criterion for establishing the presence of
a crystallized beam: Absence of heating following the shut-down of all cooling
devices. The validity of the criterion is checked with the help of detailed
numerical simulations.Comment: REVTeX, 11 pages, 4 figures; submitted to PR
Conductance Distribution of a Quantum Dot with Non-Ideal Single-Channel Leads
We have computed the probability distribution of the conductance of a
ballistic and chaotic cavity which is connected to two electron reservoirs by
leads with a single propagating mode, for arbitrary values of the transmission
probability Gamma of the mode, and for all three values of the symmetry index
beta. The theory bridges the gap between previous work on ballistic leads
(Gamma = 1) and on tunneling point contacts (Gamma << 1). We find that the
beta-dependence of the distribution changes drastically in the crossover from
the tunneling to the ballistic regime. This is relevant for experiments, which
are usually in this crossover regime. ***Submitted to Physical Review B.***Comment: 7 pages, REVTeX-3.0, 4 postscript figures appended as self-extracting
archive, INLO-PUB-940607
One-dimensional quantum chaos: Explicitly solvable cases
We present quantum graphs with remarkably regular spectral characteristics.
We call them {\it regular quantum graphs}. Although regular quantum graphs are
strongly chaotic in the classical limit, their quantum spectra are explicitly
solvable in terms of periodic orbits. We present analytical solutions for the
spectrum of regular quantum graphs in the form of explicit and exact periodic
orbit expansions for each individual energy level.Comment: 9 pages and 4 figure
Classical dynamics on graphs
We consider the classical evolution of a particle on a graph by using a
time-continuous Frobenius-Perron operator which generalizes previous
propositions. In this way, the relaxation rates as well as the chaotic
properties can be defined for the time-continuous classical dynamics on graphs.
These properties are given as the zeros of some periodic-orbit zeta functions.
We consider in detail the case of infinite periodic graphs where the particle
undergoes a diffusion process. The infinite spatial extension is taken into
account by Fourier transforms which decompose the observables and probability
densities into sectors corresponding to different values of the wave number.
The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a
Frobenius-Perron operator corresponding to a given sector. The diffusion
coefficient is obtained from the hydrodynamic modes of diffusion and has the
Green-Kubo form. Moreover, we study finite but large open graphs which converge
to the infinite periodic graph when their size goes to infinity. The lifetime
of the particle on the open graph is shown to correspond to the lifetime of a
system which undergoes a diffusion process before it escapes.Comment: 42 pages and 8 figure
Fractal templates in the escape dynamics of trapped ultracold atoms
We consider the dynamic escape of a small packet of ultracold atoms launched
from within an optical dipole trap. Based on a theoretical analysis of the
underlying nonlinear dynamics, we predict that fractal behavior can be seen in
the escape data. This data would be collected by measuring the time-dependent
escape rate for packets launched over a range of angles. This fractal pattern
is particularly well resolved below the Bose-Einstein transition temperature--a
direct result of the extreme phase space localization of the condensate. We
predict that several self-similar layers of this novel fractal should be
measurable and we explain how this fractal pattern can be predicted and
analyzed with recently developed techniques in symbolic dynamics.Comment: 11 pages with 5 figure
Explicitly solvable cases of one-dimensional quantum chaos
We identify a set of quantum graphs with unique and precisely defined
spectral properties called {\it regular quantum graphs}. Although chaotic in
their classical limit with positive topological entropy, regular quantum graphs
are explicitly solvable. The proof is constructive: we present exact periodic
orbit expansions for individual energy levels, thus obtaining an analytical
solution for the spectrum of regular quantum graphs that is complete, explicit
and exact
Mesoscopic Transport Through Ballistic Cavities: A Random S-Matrix Theory Approach
We deduce the effects of quantum interference on the conductance of chaotic
cavities by using a statistical ansatz for the S matrix. Assuming that the
circular ensembles describe the S matrix of a chaotic cavity, we find that the
conductance fluctuation and weak-localization magnitudes are universal: they
are independent of the size and shape of the cavity if the number of incoming
modes, N, is large. The limit of small N is more relevant experimentally; here
we calculate the full distribution of the conductance and find striking
differences as N changes or a magnetic field is applied.Comment: 4 pages revtex 3.0 (2-column) plus 2 postscript figures (appended),
hub.pam.94.
Correlations and pair emission in the escape dynamics of ions from one-dimensional traps
We explore the non-equilibrium escape dynamics of long-range interacting ions
in one-dimensional traps. The phase space of the few ion setup and its impact
on the escape properties are studied. As a main result we show that an
instantaneous reduction of the trap's potential depth leads to the synchronized
emission of a sequence of ion pairs if the initial configurations are close to
the crystalline ionic configuration. The corresponding time-intervals of the
consecutive pair emission as well as the number of emitted pairs can be tuned
by changing the final trap depth. Correlations between the escape times and
kinetic energies of the ions are observed and analyzed.Comment: 17 pages, 9 figure
Failure of Effective Potential Approach: Nucleus-Electron Entanglement in the He-Ion
Entanglement may be considered a resource for quantum-information processing,
as the origin of robust and universal equilibrium behaviour, but also as a
limit to the validity of an effective potential approach, in which the
influence of certain interacting subsystems is treated as a potential. Here we
show that a closed three particle (two protons, one electron) model of a He-ion
featuring realistic size, interactions and energy scales of electron and
nucleus, respectively, exhibits different types of dynamics depending on the
initial state: For some cases the traditional approach, in which the nucleus
only appears as the center of a Coulomb potential, is valid, in others this
approach fails due to entanglement arising on a short time-scale. Eventually
the system can even show signatures of thermodynamical behaviour, i.e. the
electron may relax to a maximum local entropy state which is, to some extent,
independent of the details of the initial state.Comment: Submitted to Europhysics Letter
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