668 research outputs found
Microscopic formula for transport coefficients of causal hydrodynamics
The Green-Kubo-Nakano formula should be modified in relativistic
hydrodynamics because of the problem of acausality and the breaking of sum
rules. In this work, we propose a formula to calculate the transport
coefficients of causal hydrodynamics based on the projection operator method.
As concrete examples, we derive the expressions for the diffusion coefficient,
the shear viscosity coefficient, and corresponding relaxation times.Comment: 4 pages, title was modified, final version published in Phys. Rev.
Thermal Conductivity and Chiral Critical Point in Heavy Ion Collisions
Background: Quantum Chromodynamics is expected to have a phase transition in
the same static universality class as the 3D Ising model and the liquid-gas
phase transition. The properties of the equation of state, the transport
coefficients, and especially the location of the critical point are under
intense theoretical investigation. Some experiments are underway, and many more
are planned, at high energy heavy ion accelerators. Purpose: Develop a model of
the thermal conductivity, which diverges at the critical point, and use it to
study the impact of hydrodynamic fluctuations on observables in high energy
heavy ion collisions. Methods: We apply mode coupling theory, together with a
previously developed model of the free energy that incorporates the critical
exponents and amplitudes, to construct a model of the thermal conductivity in
the vicinity of the critical point. The effect of the thermal conductivity on
correlation functions in heavy ion collisions is studied in a boost invariant
hydrodynamic model via fluctuations, or noise. Results: We find that the closer
a thermodynamic trajectory comes to the critical point the greater is the
magnitude of the fluctuations in thermodynamic variables and in the 2-particle
correlation functions in momentum space. Conclusions: It may be possible to
discern the existence of a critical point, its location, and thermodynamic and
transport properties near to it in heavy ion collisions using the methods
developed here.Comment: 36 pages, 8 figures. Version published in Phys.Rev.C86, 054911
(2012). It contains some minor improvements with respect to v1: further
clarifications, small changes on figures and two extra reference
Interference effects in the counting statistics of electron transfers through a double quantum dot
We investigate the effect of quantum interferences and Coulomb interaction on
the counting statistics of electrons crossing a double quantum dot in a
parallel geometry using a generating function technique based on a quantum
master equation approach. The skewness and the average residence time of
electrons in the dots are shown to be the quantities most sensitive to
interferences and Coulomb coupling. The joint probabilities of consecutive
electron transfer processes show characteristic temporal oscillations due to
interference. The steady-state fluctuation theorem which predicts a universal
connection between the number of forward and backward transfer events is shown
to hold even in the presence of Coulomb coupling and interference.Comment: 11 pages, 12 figure
A homogenization theorem for Langevin systems with an application to Hamiltonian dynamics
This paper studies homogenization of stochastic differential systems. The
standard example of this phenomenon is the small mass limit of Hamiltonian
systems. We consider this case first from the heuristic point of view,
stressing the role of detailed balance and presenting the heuristics based on a
multiscale expansion. This is used to propose a physical interpretation of
recent results by the authors, as well as to motivate a new theorem proven
here. Its main content is a sufficient condition, expressed in terms of
solvability of an associated partial differential equation ("the cell
problem"), under which the homogenization limit of an SDE is calculated
explicitly. The general theorem is applied to a class of systems, satisfying a
generalized detailed balance condition with a position-dependent temperature.Comment: 32 page
Survival probability (heat content) and the lowest eigenvalue of Dirichlet Laplacian
We study the survival probability of a particle diffusing in a
two-dimensional domain, bounded by a smooth absorbing boundary. The short-time
expansion of this quantity depends on the geometric characteristics of the
boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue
of the Dirichlet Laplacian defined on the domain. We present a simple algorithm
for calculation of the short-time expansion for an arbitrary "star-shaped"
domain. The coefficients are expressed in terms of powers of boundary
curvature, integrated around the circumference of the domain. Based on this
expansion, we look for a Pad\'e interpolation between the short-time and the
long-time behavior of the survival probability, i.e. between geometric
characteristics of the boundary and the lowest eigenvalue of the Dirichlet
Laplacian.Comment: Accepted in IJMP
Dynamics of Atom-Field Entanglement from Exact Solutions: Towards Strong Coupling and Non-Markovian Regimes
We examine the dynamics of bipartite entanglement between a two-level atom
and the electromagnetic field. We treat the Jaynes-Cummings model with a single
field mode and examine in detail the exact time evolution of entanglement,
including cases where the atomic state is initially mixed and the atomic
transition is detuned from resonance. We then explore the effects of other
nearby modes by calculating the exact time evolution of entanglement in more
complex systems with two, three, and five field modes. For these cases we can
obtain exact solutions which include the strong coupling regimes. Finally, we
consider the entanglement of a two-level atom with the infinite collection of
modes present in the intracavity field of a Fabre-Perot cavity. In contrast to
the usual treatment of atom-field interactions with a continuum of modes using
the Born-Markov approximation, our treatment in all cases describes the full
non-Markovian dynamics of the atomic subsystem. Only when an analytic
expression for the infinite mode case is desired do we need to make a weak
coupling assumption which at long times approximates Markovian dynamics.Comment: 12 pages, 5 figures; minor changes in grammar, wording, and
formatting. One unnecessary figure removed. Figure number revised (no longer
counts subfigures separately
Confinement and Viscoelastic effects on Chain Closure Dynamics
Chemical reactions inside cells are typically subject to the effects both of
the cell's confining surfaces and of the viscoelastic behavior of its contents.
In this paper, we show how the outcome of one particular reaction of relevance
to cellular biochemistry - the diffusion-limited cyclization of long chain
polymers - is influenced by such confinement and crowding effects. More
specifically, starting from the Rouse model of polymer dynamics, and invoking
the Wilemski-Fixman approximation, we determine the scaling relationship
between the mean closure time t_{c} of a flexible chain (no excluded volume or
hydrodynamic interactions) and the length N of its contour under the following
separate conditions: (a) confinement of the chain to a sphere of radius D, and
(b) modulation of its dynamics by colored Gaussian noise. Among other results,
we find that in case (a) when D is much smaller than the size of the chain,
t_{c}\simND^{2}, and that in case (b), t_{c}\simN^{2/(2-2H)}, H being a number
between 1/2 and 1 that characterizes the decay of the noise correlations. H is
not known \`a priori, but values of about 0.7 have been used in the successful
characterization of protein conformational dynamics. At this value of H
(selected for purposes of illustration), t_{c}\simN^3.4, the high scaling
exponent reflecting the slow relaxation of the chain in a viscoelastic medium
Measuring the energy landscape roughness and the transition state location of biomolecules using single molecule mechanical unfolding experiments
Single molecule mechanical unfolding experiments are beginning to provide
profiles of the complex energy landscape of biomolecules. In order to obtain
reliable estimates of the energy landscape characteristics it is necessary to
combine the experimental measurements with sound theoretical models and
simulations. Here, we show how by using temperature as a variable in mechanical
unfolding of biomolecules in laser optical tweezer or AFM experiments the
roughness of the energy landscape can be measured without making any
assumptions about the underlying reaction oordinate. The efficacy of the
formalism is illustrated by reviewing experimental results that have directly
measured roughness in a protein-protein complex. The roughness model can also
be used to interpret experiments on forced-unfolding of proteins in which
temperature is varied. Estimates of other aspects of the energy landscape such
as free energy barriers or the transition state (TS) locations could depend on
the precise model used to analyze the experimental data. We illustrate the
inherent difficulties in obtaining the transition state location from loading
rate or force-dependent unfolding rates. Because the transition state moves as
the force or the loading rate is varied it is in general difficult to invert
the experimental data unless the curvature at the top of the one dimensional
free energy profile is large, i.e the barrier is sharp. The independence of the
TS location on force holds good only for brittle or hard biomolecules whereas
the TS location changes considerably if the molecule is soft or plastic. We
also comment on the usefulness of extension of the molecule as a surrogate
reaction coordinate especially in the context of force-quench refolding of
proteins and RNA.Comment: 44 pages, 7 figure
Bubbling the False Vacuum Away
We investigate the role of nonperturbative, bubble-like inhomogeneities on
the decay rate of false-vacuum states in two and three-dimensional scalar field
theories. The inhomogeneities are induced by setting up large-amplitude
oscillations of the field about the false vacuum as, for example, after a rapid
quench or in certain models of cosmological inflation. We show that, for a wide
range of parameters, the presence of large-amplitude bubble-like
inhomogeneities greatly accelerates the decay rate, changing it from the
well-known exponential suppression of homogeneous nucleation to a power-law
suppression. It is argued that this fast, power-law vacuum decay -- known as
resonant nucleation -- is promoted by the presence of long-lived oscillons
among the nonperturbative fluctuations about the false vacuum. A phase diagram
is obtained distinguishing three possible mechanisms for vacuum decay:
homogeneous nucleation, resonant nucleation, and cross-over. Possible
applications are briefly discussed.Comment: 13 Pages, 16 figures, revtex4, submitted to pr
On solutions of a class of non-Markovian Fokker-Planck equations
We show that a formal solution of a rather general non-Markovian
Fokker-Planck equation can be represented in a form of an integral
decomposition and thus can be expressed through the solution of the Markovian
equation with the same Fokker-Planck operator. This allows us to classify
memory kernels into safe ones, for which the solution is always a probability
density, and dangerous ones, when this is not guaranteed. The first situation
describes random processes subordinated to a Wiener process, while the second
one typically corresponds to random processes showing a strong ballistic
component. In this case the non-Markovian Fokker-Planck equation is only valid
in a restricted range of parameters, initial and boundary conditions.Comment: A new ref.12 is added and discusse
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