1,862 research outputs found
Long Range Hops and the Pair Annihilation Reaction A+A->0: Renormalization Group and Simulation
A simple example of a non-equilibrium system for which fluctuations are
important is a system of particles which diffuse and may annihilate in pairs on
contact. The renormalization group can be used to calculate the time dependence
of the density of particles, and provides both an exact value for the exponent
governing the decay of particles and an epsilon-expansion for the amplitude of
this power law. When the diffusion is anomalous, as when the particles perform
Levy flights, the critical dimension depends continuously on the control
parameter for the Levy distribution. The epsilon-expansion can then become an
expansion in a small parameter. We present a renormalization group calculation
and compare these results with those of a simulation.Comment: As-published version; two significant errors fixed, two references
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Optimal quantum control in nanostructures: Theory and application to generic three-level system
Coherent carrier control in quantum nanostructures is studied within the
framework of Optimal Control. We develop a general solution scheme for the
optimization of an external control (e.g., lasers pulses), which allows to
channel the system's wavefunction between two given states in its most
efficient way; physically motivated constraints, such as limited laser
resources or population suppression of certain states, can be accounted for
through a general cost functional. Using a generic three-level scheme for the
quantum system, we demonstrate the applicability of our approach and identify
the pertinent calculation and convergence parameters.Comment: 7 pages; to appear in Phys. Rev.
Local threshold field for dendritic instability in superconducting MgB2 films
Using magneto-optical imaging the phenomenon of dendritic flux penetration in
superconducting films was studied. Flux dendrites were abruptly formed in a 300
nm thick film of MgB2 by applying a perpendicular magnetic field. Detailed
measurements of flux density distributions show that there exists a local
threshold field controlling the nucleation and termination of the dendritic
growth. At 4 K the local threshold field is close to 12 mT in this sample,
where the critical current density is 10^7 A/cm^2. The dendritic instability in
thin films is believed to be of thermo-magnetic origin, but the existence of a
local threshold field, and its small value are features that distinctly
contrast the thermo-magnetic instability (flux jumps) in bulk superconductors.Comment: 6 pages, 6 figures, submitted to Phys. Rev.
Self-replication and evolution of DNA crystals
Is it possible to create a simple physical system that is capable of replicating itself? Can such a system evolve interesting behaviors, thus allowing it to adapt to a wide range of environments? This paper presents a design for such a replicator constructed exclusively from synthetic DNA. The basis for the replicator is crystal growth: information is stored in the spatial arrangement of monomers and copied from layer to layer by templating. Replication is achieved by fragmentation of crystals, which produces new crystals that carry the same information. Crystal replication avoids intrinsic problems associated with template-directed mechanisms for replication of one-dimensional polymers. A key innovation of our work is that by using programmable DNA tiles as the crystal monomers, we can design crystal growth processes that apply interesting selective pressures to the evolving sequences. While evolution requires that copying occur with high accuracy, we show how to adapt error-correction techniques from algorithmic self-assembly to lower the replication error rate as much as is required
A threshold phenomenon for embeddings of into Orlicz spaces
We consider a sequence of positive smooth critical points of the
Adams-Moser-Trudinger embedding of into Orlicz spaces. We study its
concentration-compactness behavior and show that if the sequence is not
precompact, then the liminf of the -norms of the functions is greater
than or equal to a positive geometric constant.Comment: 14 Page
Experimental realization of the one qubit Deutsch-Jozsa algorithm in a quantum dot
We perform quantum interference experiments on a single self-assembled
semiconductor quantum dot. The presence or absence of a single exciton in the
dot provides a qubit that we control with femtosecond time resolution. We
combine a set of quantum operations to realize the single-qubit Deutsch-Jozsa
algorithm. The results show the feasibility of single qubit quantum logic in a
semiconductor quantum dot using ultrafast optical control.Comment: REVTex4, 4 pages, 3 figures. Now includes more details about the
dephasing in the quantum dots. The introduction has been reworded for
clarity. Minor readability fixe
Searching a bitstream in linear time for the longest substring of any given density
Given an arbitrary bitstream, we consider the problem of finding the longest
substring whose ratio of ones to zeroes equals a given value. The central
result of this paper is an algorithm that solves this problem in linear time.
The method involves (i) reformulating the problem as a constrained walk through
a sparse matrix, and then (ii) developing a data structure for this sparse
matrix that allows us to perform each step of the walk in amortised constant
time. We also give a linear time algorithm to find the longest substring whose
ratio of ones to zeroes is bounded below by a given value. Both problems have
practical relevance to cryptography and bioinformatics.Comment: 22 pages, 19 figures; v2: minor edits and enhancement
Size-dependent decoherence of excitonic states in semiconductor microcrystallites
The size-dependent decoherence of the exciton states resulting from the
spontaneous emission is investigated in a semiconductor spherical
microcrystallite under condition . In general, the
larger size of the microcrystallite corresponds to the shorter coherence time.
If the initial state is a superposition of two different excitonic coherent
states, the coherence time depends on both the overlap of two excitonic
coherent states and the size of the microcrystallite. When the system with
fixed size is initially in the even or odd coherent states, the larger average
number of the excitons corresponds to the faster decoherence. When the average
number of the excitons is given, the bigger size of the microcrystallite
corresponds to the faster decoherence. The decoherence of the exciton states
for the materials GaAs and CdS is numerically studied by our theoretical
analysis.Comment: 4 pages, two figure
Resonant nature of phonon-induced damping of Rabi oscillations in quantum dots
Optically controlled coherent dynamics of charge (excitonic) degrees of
freedom in a semiconductor quantum dot under the influence of lattice dynamics
(phonons) is discussed theoretically. We show that the dynamics of the lattice
response in the strongly non-linear regime is governed by a semiclassical
resonance between the phonon modes and the optically driven dynamics. We stress
on the importance of the stability of intermediate states for the truly
coherent control.Comment: 4 pages, 2 figures; final version; moderate changes, new titl
Generation of maximum spin entanglement induced by cavity field in quantum-dot systems
Equivalent-neighbor interactions of the conduction-band electron spins of
quantum dots in the model of Imamoglu et al. [Phys. Rev. Lett. 83, 4204 (1999)]
are analyzed. Analytical solution and its Schmidt decomposition are found and
applied to evaluate how much the initially excited dots can be entangled to the
remaining dots if all of them are initially disentangled. It is demonstrated
that the perfect maximally entangled states (MES) can only be generated in the
systems of up to 6 dots with a single dot initially excited. It is also shown
that highly entangled states, approximating the MES with a good accuracy, can
still be generated in systems of odd number of dots with almost half of them
being excited. A sudden decrease of entanglement is observed by increasing the
total number of dots in a system with a fixed number of excitations.Comment: 6 pages, 7 figures, to appear in Phys. Rev.
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