448 research outputs found
Semiclassical time evolution of the density matrix and tunneling
The time dependent density matrix of a system with potential barrier is
studied using path integrals. The characterization of the initial state, which
is assumed to be restricted to one side of the barrier, and the time evolution
of the density matrix lead to a three-fold path integral which is evaluated in
the semiclassical limit. The semiclassical trajectories are found to move in
the complex coordinate plane and barrier penetration only arises due to
fluctuations. Both the form of the semiclassical paths and the relevant
fluctuations change significantly as a function of temperature. The
semiclassical analysis leads to a detailed picture of barrier penetration in
the real time domain and the changeover from thermal activation to quantum
tunneling. Deep tunneling is associated with quasi-zero modes in the
fluctuation spectrum about the semiclassical orbits in the long time limit. The
connection between this real time description of tunneling and the standard
imaginary time instanton approach is established. Specific results are given
for a double well potential and an Eckart barrier.Comment: 27 pages, 8 figures, to be published in Phys. Rev.
Precision Measurements of Stretching and Compression in Fluid Mixing
The mixing of an impurity into a flowing fluid is an important process in
many areas of science, including geophysical processes, chemical reactors, and
microfluidic devices. In some cases, for example periodic flows, the concepts
of nonlinear dynamics provide a deep theoretical basis for understanding
mixing. Unfortunately, the building blocks of this theory, i.e. the fixed
points and invariant manifolds of the associated Poincare map, have remained
inaccessible to direct experimental study, thus limiting the insight that could
be obtained. Using precision measurements of tracer particle trajectories in a
two-dimensional fluid flow producing chaotic mixing, we directly measure the
time-dependent stretching and compression fields. These quantities, previously
available only numerically, attain local maxima along lines coinciding with the
stable and unstable manifolds, thus revealing the dynamical structures that
control mixing. Contours or level sets of a passive impurity field are found to
be aligned parallel to the lines of large compression (unstable manifolds) at
each instant. This connection appears to persist as the onset of turbulence is
approached.Comment: 5 pages, 5 figure
Floquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator
Using the parametrically driven harmonic oscillator as a working example, we
study two different Markovian approaches to the quantum dynamics of a
periodically driven system with dissipation. In the simpler approach, the
driving enters the master equation for the reduced density operator only in the
Hamiltonian term. An improved master equation is achieved by treating the
entire driven system within the Floquet formalism and coupling it to the
reservoir as a whole. The different ensuing evolution equations are compared in
various representations, particularly as Fokker-Planck equations for the Wigner
function. On all levels of approximation, these evolution equations retain the
periodicity of the driving, so that their solutions have Floquet form and
represent eigenfunctions of a non-unitary propagator over a single period of
the driving. We discuss asymptotic states in the long-time limit as well as the
conservative and the high-temperature limits. Numerical results obtained within
the different Markov approximations are compared with the exact path-integral
solution. The application of the improved Floquet-Markov scheme becomes
increasingly important when considering stronger driving and lower
temperatures.Comment: 29 pages, 7 figure
Opportunities for use of exact statistical equations
Exact structure function equations are an efficient means of obtaining
asymptotic laws such as inertial range laws, as well as all measurable effects
of inhomogeneity and anisotropy that cause deviations from such laws. "Exact"
means that the equations are obtained from the Navier-Stokes equation or other
hydrodynamic equations without any approximation. A pragmatic definition of
local homogeneity lies within the exact equations because terms that explicitly
depend on the rate of change of measurement location appear within the exact
equations; an analogous statement is true for local stationarity. An exact
definition of averaging operations is required for the exact equations. Careful
derivations of several inertial range laws have appeared in the literature
recently in the form of theorems. These theorems give the relationships of the
energy dissipation rate to the structure function of acceleration increment
multiplied by velocity increment and to both the trace of and the components of
the third-order velocity structure functions. These laws are efficiently
derived from the exact velocity structure function equations. In some respects,
the results obtained herein differ from the previous theorems. The
acceleration-velocity structure function is useful for obtaining the energy
dissipation rate in particle tracking experiments provided that the effects of
inhomogeneity are estimated by means of displacing the measurement location.Comment: accepted by Journal of Turbulenc
Mycobacterium tuberculosis Responds to Chloride and pH as Synergistic Cues to the Immune Status of its Host Cell
PubMed ID: 23592993This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Acute Renal Failure in Association with Community-Acquired Clostridium difficile Infection and McKittrick-Wheelock Syndrome
We report the case of a 65-year-old Caucasian woman who experienced two separate episodes of acute renal failure within an 18-month period, both requiring emergency admission and complicated treatment. Each episode was precipitated by hypovolaemia from intestinal fluid losses, but from two rare and independent pathologies. Her first admission was attributed to community-acquired Clostridium difficile-associated diarrhoea (CDAD) and was treated in the intensive therapy unit. She returned 18 months later with volume depletion and electrolyte disturbances, but on this occasion a giant hypersecretory villous adenoma of the rectum (McKittrick-Wheelock syndrome) was diagnosed following initial abnormal findings on digital rectal examination by a junior physician. Unlike hospital-acquired C. difficile, community-acquired infection is not common, although increasing numbers are being reported. Whilst community-acquired CDAD can be severe, it rarely causes acute renal failure. This case report highlights the pathological mechanisms whereby C. difficile toxin and hypersecretory villous adenoma of the rectum can predispose to acute renal failure, as well as the values of thorough clinical examination in the emergency room, and early communication with intensivist colleagues in dire situations
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