719 research outputs found
Multiscaling for Systems with a Broad Continuum of Characteristic Lengths and Times: Structural Transitions in Nanocomposites
The multiscale approach to N-body systems is generalized to address the broad
continuum of long time and length scales associated with collective behaviors.
A technique is developed based on the concept of an uncountable set of time
variables and of order parameters (OPs) specifying major features of the
system. We adopt this perspective as a natural extension of the commonly used
discrete set of timescales and OPs which is practical when only a few,
widely-separated scales exist. The existence of a gap in the spectrum of
timescales for such a system (under quasiequilibrium conditions) is used to
introduce a continuous scaling and perform a multiscale analysis of the
Liouville equation. A functional-differential Smoluchowski equation is derived
for the stochastic dynamics of the continuum of Fourier component order
parameters. A continuum of spatially non-local Langevin equations for the OPs
is also derived. The theory is demonstrated via the analysis of structural
transitions in a composite material, as occurs for viral capsids and molecular
circuits.Comment: 28 pages, 1 figur
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
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
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
On measuring colloidal volume fractions
Hard-sphere colloids are popular as models for testing fundamental theories
in condensed matter and statistical physics, from crystal nucleation to the
glass transition. A single parameter, the volume fraction (phi), characterizes
an ideal, monodisperse hard-sphere suspension. In comparing experiments with
theories and simulation, researchers to date have paid little attention to
likely uncertainties in experimentally-quoted phi values. We critically review
the experimental measurement of phi in hard-sphere colloids, and show that
while statistical uncertainties in comparing relative values of phi can be as
low as 0.0001, systematic errors of 3-6% are probably unavoidable. The
consequences of this are illustrated by way of a case study comparing
literature data sets on hard-sphere viscosity and diffusion.Comment: 11 page
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
Dynamics of the Density Matrix in Contact with a Thermal Bath and the Quantum Master Equation
We study the structure of the time evolution of the density matrix in contact
with a thermal bath in a standard projection operator sheme. The reduced
density matrix of the system in the steady state is obtained by tracing out the
degree of freedom of the thermal bath from the equilibrium density matrix of
the total system. This reduced density matrix is modified by the interaction,
and is different from that of the equilibrium of the system alone. We
explicitly calculate the contribution of each term in quantum master equation
to the realization of the steady state density matrix, and make clear roles of
each term. By making use of the role of each term, the properties of the
commonly used quantum master equation are examined.Comment: 17 pages, to appear in JPS
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