12,949 research outputs found
Loschmidt echo decay from local boundary perturbations
We investigate the sensitivity of the time evolution of semiclassical wave
packets in two-dimensional chaotic billiards with respect to local
perturbations of their boundaries. For this purpose, we address, analytically
and numerically, the time decay of the Loschmidt echo (LE). We find the LE to
decay exponentially in time, with the rate equal to the classical escape rate
from an open billiard obtained from the original one by removing the
perturbation-affected region of its boundary. Finally, we propose a principal
scheme for the experimental observation of the LE decay.Comment: Final version; 4 pages, 3 figure
Overdamped Stress Relaxation in Buckled Rods
We present a comprehensive theoretical analysis of the stress relaxation in a
multiply but weakly buckled incompressible rod in a viscous solvent. In the
bulk two interesting regimes of generic self--similar intermediate asymptotics
are distinguished, which give rise to two classes of approximate and exact
power--law solutions, respectively. For the case of open boundary conditions
the corresponding non--trivial boundary--layer scenarios are derived by a
multiple--scale perturbation (``adiabatic'') method. Our results compare well
with -- and provide the theoretical explanation for -- previous results from
numerical simulations, and they suggest new directions for further fruitful
numerical and experimental investigations.Comment: 20 pages, 12 figure
The field inside a random distribution of parallel dipoles
We determine the probability distribution for the field inside a random
uniform distribution of electric or magnetic dipoles.
For parallel dipoles, simulations and an analytical derivation show that
although the average contribution from any spherical shell around the probe
position vanishes, the Levy stable distribution of the field is symmetric
around a non-vanishing field amplitude.
In addition we show how omission of contributions from a small volume around
the probe leads to a field distribution with a vanishing mean, which, in the
limit of vanishing excluded volume, converges to the shifted distribution.Comment: RevTeX, 4 pages, 3 figures. Submitted to Phys. Rev. Let
Optimal control of the propagation of a graph in inhomogeneous media
We study an optimal control problem for viscosity solutions of a HamiltonâJacobi equation describing the propagation of a one-dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the -norm. We prove convergence of a discrete optimal control problem based on a monotone finite difference scheme and describe some numerical results
Photon number states generated from a continuous-wave light source
Conditional preparation of photon number states from a continuous-wave
nondegenerate optical parametric oscillator is investigated. We derive the
phase space Wigner function for the output state conditioned on photo detection
events that are not necessarily simultaneous, and we maximize its overlap with
the desired photon number state by choosing the optimal temporal output state
mode function. We present a detailed numerical analysis for the case of
two-photon state generation from a parametric oscillator driven with an
arbitrary intensity below threshold, and in the low intensity limit, we present
a formalism that yields the optimal output state mode function and fidelity for
higher photon number states.Comment: 8 pages, 7 figures, v2: shortened versio
Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states
We study the influence of different edge types on the electronic density of
states of graphene nanostructures. To this end we develop an exact expansion
for the single particle Green's function of ballistic graphene structures in
terms of multiple reflections from the system boundary, that allows for a
natural treatment of edge effects. We first apply this formalism to calculate
the average density of states of graphene billiards. While the leading term in
the corresponding Weyl expansion is proportional to the billiard area, we find
that the contribution that usually scales with the total length of the system
boundary differs significantly from what one finds in semiconductor-based,
Schr\"odinger type billiards: The latter term vanishes for armchair and
infinite mass edges and is proportional to the zigzag edge length, highlighting
the prominent role of zigzag edges in graphene. We then compute analytical
expressions for the density of states oscillations and energy levels within a
trajectory based semiclassical approach. We derive a Dirac version of
Gutzwiller's trace formula for classically chaotic graphene billiards and
further obtain semiclassical trace formulae for the density of states
oscillations in regular graphene cavities. We find that edge dependent
interference of pseudospins in graphene crucially affects the quantum spectrum.Comment: to be published in Phys. Rev.
Spatial Coherence of a Polariton Condensate
We perform Young's double-slit experiment to study the spatial coherence
properties of a two-dimensional dynamic condensate of semiconductor microcavity
polaritons. The coherence length of the system is measured as a function of the
pump rate, which confirms a spontaneous buildup of macroscopic coherence in the
condensed phase. An independent measurement reveals that the position and
momentum uncertainty product of the condensate is close to the Heisenberg
limit. An experimental realization of such a minimum uncertainty wave packet of
the polariton condensate opens a door to coherent matter-wave phenomena such as
Josephson oscillation, superfluidity, and solitons in solid state condensate
systems
Scalable designs for quantum computing with rare-earth-ion-doped crystals
Due to inhomogeneous broadening, the absorption lines of rare-earth-ion
dopands in crystals are many order of magnitudes wider than the homogeneous
linewidths. Several ways have been proposed to use ions with different
inhomogeneous shifts as qubit registers, and to perform gate operations between
such registers by means of the static dipole coupling between the ions.
In this paper we show that in order to implement high-fidelity quantum gate
operations by means of the static dipole interaction, we require the
participating ions to be strongly coupled, and that the density of such
strongly coupled registers in general scales poorly with register size.
Although this is critical to previous proposals which rely on a high density of
functional registers, we describe architectures and preparation strategies that
will allow scalable quantum computers based on rare-earth-ion doped crystals.Comment: Submitted to Phys. Rev.
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