447 research outputs found
Distance traveled by random walkers before absorption in a random medium
We consider the penetration length of random walkers diffusing in a
medium of perfect or imperfect absorbers of number density . We solve
this problem on a lattice and in the continuum in all dimensions , by means
of a mean-field renormalization group. For a homogeneous system in , we
find that , where is the absorber density
correlation length. The cases of D=1 and D=2 are also treated. In the presence
of long-range correlations, we estimate the temporal decay of the density of
random walkers not yet absorbed. These results are illustrated by exactly
solvable toy models, and extensive numerical simulations on directed
percolation, where the absorbers are the active sites. Finally, we discuss the
implications of our results for diffusion limited aggregation (DLA), and we
propose a more effective method to measure in DLA clusters.Comment: Final version: also considers the case of imperfect absorber
Aspects of the dynamics of colloidal suspensions: Further results of the mode-coupling theory of structural relaxation
Results of the idealized mode-coupling theory for the structural relaxation
in suspensions of hard-sphere colloidal particles are presented and discussed
with regard to recent light scattering experiments. The structural relaxation
becomes non-diffusive for long times, contrary to the expectation based on the
de Gennes narrowing concept. A semi-quantitative connection of the wave vector
dependences of the relaxation times and amplitudes of the final
-relaxation explains the approximate scaling observed by Segr{\`e} and
Pusey [Phys. Rev. Lett. {\bf 77}, 771 (1996)]. Asymptotic expansions lead to a
qualitative understanding of density dependences in generalized Stokes-Einstein
relations. This relation is also generalized to non-zero frequencies thereby
yielding support for a reasoning by Mason and Weitz [Phys. Rev. Lett {\bf 74},
1250 (1995)]. The dynamics transient to the structural relaxation is discussed
with models incorporating short-time diffusion and hydrodynamic interactions
for short times.Comment: 11 pages, 9 figures; to be published in Phys. Rev.
Qubit Decoherence and Non-Markovian Dynamics at Low Temperatures via an Effective Spin-Boson Model
Quantum Brownian oscillator model (QBM), in the Fock-space representation,
can be viewed as a multi-level spin-boson model. At sufficiently low
temperature, the oscillator degrees of freedom are dynamically reduced to the
lowest two levels and the system behaves effectively as a two-level (E2L)
spin-boson model (SBM) in this limit. We discuss the physical mechanism of
level reduction and analyze the behavior of E2L-SBM from the QBM solutions. The
availability of close solutions for the QBM enables us to study the
non-Markovian features of decoherence and leakage in a SBM in the
non-perturbative regime (e.g. without invoking the Born approximation) in
better details than before. Our result captures very well the characteristic
non-Markovian short time low temperature behavior common in many models.Comment: 19 pages, 8 figure
Diffusive Evolution of Stable and Metastable Phases II: Theory of Non-Equilibrium Behaviour in Colloid-Polymer Mixtures
By analytically solving some simple models of phase-ordering kinetics, we
suggest a mechanism for the onset of non-equilibrium behaviour in
colloid-polymer mixtures. These mixtures can function as models of atomic
systems; their physics therefore impinges on many areas of thermodynamics and
phase-ordering. An exact solution is found for the motion of a single, planar
interface separating a growing phase of uniform high density from a
supersaturated low density phase, whose diffusive depletion drives the
interfacial motion. In addition, an approximate solution is found for the
one-dimensional evolution of two interfaces, separated by a slab of a
metastable phase at intermediate density. The theory predicts a critical
supersaturation of the low-density phase, above which the two interfaces become
unbound and the metastable phase grows ad infinitum. The growth of the stable
phase is suppressed in this regime.Comment: 27 pages, Latex, eps
Time-convolutionless reduced-density-operator theory of a noisy quantum channel: a two-bit quantum gate for quantum information processing
An exact reduced-density-operator for the output quantum states in
time-convolutionless form was derived by solving the quantum Liouville equation
which governs the dynamics of a noisy quantum channel by using a projection
operator method and both advanced and retarded propagators in time. The
formalism developed in this work is general enough to model a noisy quantum
channel provided specific forms of the Hamiltonians for the system, reservoir,
and the mutual interaction between the system and the reservoir are given.
Then, we apply the formulation to model a two-bit quantum gate composed of
coupled spin systems in which the Heisenberg coupling is controlled by the
tunneling barrier between neighboring quantum dots. Gate Characteristics
including the entropy, fidelity, and purity are calculated numerically for both
mixed and entangled initial states
Numerical simulation of diffusion-controlled droplet growth: Dynamical correlation effects
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Crystal constructions in Number Theory
Weyl group multiple Dirichlet series and metaplectic Whittaker functions can
be described in terms of crystal graphs. We present crystals as parameterized
by Littelmann patterns and we give a survey of purely combinatorial
constructions of prime power coefficients of Weyl group multiple Dirichlet
series and metaplectic Whittaker functions using the language of crystal
graphs. We explore how the branching structure of crystals manifests in these
constructions, and how it allows access to some intricate objects in number
theory and related open questions using tools of algebraic combinatorics
The DNA Glycosylases Ogg1 and Nth1 Do Not Contribute to Ig Class Switching in Activated Mouse Splenic B Cells
During activation of B cells to undergo class switching, B cell metabolism is increased, and levels of reactive oxygen species (ROS) are increased. ROS can oxidize DNA bases resulting in substrates for the DNA glycosylases Ogg1 and Nth1. Ogg1 and Nth1 excise oxidized bases, and nick the resulting abasic sites, forming single-strand DNA breaks (SSBs) as intermediates during the repair process. In this study, we asked whether splenic B cells from mice deficient in these two enzymes would show altered class switching and decreased DNA breaks in comparison with wild-type mice. As the c-myc gene frequently recombines with the IgH S region in B cells induced to undergo class switching, we also analyzed the effect of deletion of these two glycosylases on DSBs in the c-myc gene. We did not detect a reduction in S region or c-myc DSBs or in class switching in splenic B cells from Ogg1- or Nth1-deficient mice or from mice deficient in both enzymes
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