23 research outputs found
Scaling and front dynamics in Ising quantum chains
We study the relaxation dynamics of a quantum Ising chain initially prepared
in a product of canonical states corresponding each to an equilibrium state of
part of the chain at a given temperature. We focus our attention on the
transverse magnetization for which a general expression is given. Explicite
results are given for the completely factorized initial state, corresponding to
a situation where all the spins are thermalized independently, and for the
two-temperatures initial state, where part of the chain called the system is
thermalized at a temperature and the remaining part is at a temperature
.Comment: 7 pages, submitted to EPJ
Out-of-equilibrium bosons on a one-dimensional optical random lattice
We study the transport properties of a one-dimensional hard-core boson
lattice gas coupled to two particle reservoirs at different chemical potentials
generating a current flow through the system. In particular, the influence of
random fluctuations of the underlying lattice on the stationary state
properties is investigated. We show analytically that the steady-state density
presents a linear profile. The local steady-state current obeys the Fourier law
where is a typical timescale of the
lattice fluctuations and the density gradient imposed %on the
system by the reservoirs
Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins
In biophysics, the search for analytical solutions of stochastic models of
cellular processes is often a challenging task. In recent work on models of
gene expression, it was shown that a mapping based on partitioning of Poisson
arrivals (PPA-mapping) can lead to exact solutions for previously unsolved
problems. While the approach can be used in general when the model involves
Poisson processes corresponding to creation or degradation, current
applications of the method and new results derived using it have been limited
to date. In this paper, we present the exact solution of a variation of the
two-stage model of gene expression (with time dependent transition rates)
describing the arbitrary partitioning of proteins. The methodology proposed
makes full use of the the PPA-mapping by transforming the original problem into
a new process describing the evolution of three biological switches. Based on a
succession of transformations, the method leads to a hierarchy of reduced
models. We give an integral expression of the time dependent generating
function as well as explicit results for the mean, variance, and correlation
function. Finally, we discuss how results for time dependent parameters can be
extended to the three-stage model and used to make inferences about models with
parameter fluctuations induced by hidden stochastic variables.Comment: 15 pages, 6 figure
Regulation by small RNAs via coupled degradation: mean-field and variational approaches
Regulatory genes called small RNAs (sRNAs) are known to play critical roles
in cellular responses to changing environments. For several sRNAs, regulation
is effected by coupled stoichiometric degradation with messenger RNAs (mRNAs).
The nonlinearity inherent in this regulatory scheme indicates that exact
analytical solutions for the corresponding stochastic models are intractable.
Here, we present a variational approach to analyze a well-studied stochastic
model for regulation by sRNAs via coupled degradation. The proposed approach is
efficient and provides accurate estimates of mean mRNA levels as well as higher
order terms. Results from the variational ansatz are in excellent agreement
with data from stochastic simulations for a wide range of parameters, including
regions of parameter space where mean-field approaches break down. The proposed
approach can be applied to quantitatively model stochastic gene expression in
complex regulatory networks.Comment: 4 pages, 3 figure
Relaxation in the XX quantum chain
We present the results obtained on the magnetisation relaxation properties of
an XX quantum chain in a transverse magnetic field. We first consider an
initial thermal kink-like state where half of the chain is initially
thermalized at a very high temperature while the remaining half, called
the system, is put at a lower temperature . From this initial state, we
derive analytically the Green function associated to the dynamical behaviour of
the transverse magnetisation. Depending on the strength of the magnetic field
and on the temperature of the system, different regimes are obtained for the
magnetic relaxation. In particular, with an initial droplet-like state, that is
a cold subsystem of finite size in contact at both ends with an infinite
temperature environnement, we derive analytically the behaviour of the
time-dependent system magnetisation
Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes
Stochasticity in gene expression gives rise to fluctuations in protein levels
across a population of genetically identical cells. Such fluctuations can lead
to phenotypic variation in clonal populations, hence there is considerable
interest in quantifying noise in gene expression using stochastic models.
However, obtaining exact analytical results for protein distributions has been
an intractable task for all but the simplest models. Here, we invoke the
partitioning property of Poisson processes to develop a mapping that
significantly simplifies the analysis of stochastic models of gene expression.
The mapping leads to exact protein distributions using results for mRNA
distributions in models with promoter-based regulation. Using this approach, we
derive exact analytical results for steady-state and time-dependent
distributions for the basic 2-stage model of gene expression. Furthermore, we
show how the mapping leads to exact protein distributions for extensions of the
basic model that include the effects of post-transcriptional and
post-translational regulation. The approach developed in this work is widely
applicable and can contribute to a quantitative understanding of stochasticity
in gene expression and its regulation.Comment: 10 pages, 5 figure
Quantum Non-Equilibrium Steady States Induced by Repeated Interactions
We study the steady state of a finite XX chain coupled at its boundaries to
quantum reservoirs made of free spins that interact one after the other with
the chain. The two-point correlations are calculated exactly and it is shown
that the steady state is completely characterized by the magnetization profile
and the associated current. Except at the boundary sites, the magnetization is
given by the average of the reservoirs' magnetizations. The steady state
current, proportional to the difference in the reservoirs' magnetizations,
shows a non-monotonous behavior with respect to the system-reservoir coupling
strength, with an optimal current state for a finite value of the coupling.
Moreover, we show that the steady state can be described by a generalized Gibbs
state.Comment: to appear in Phys. Rev. Let
"The greatest Poet that has [n]ever existed" -- A Narrative Networks Analysis of the Poems of Ossian
Surprising as it may seem, applications of statistical methods to physics
were inspired by the social sciences, which in turn are linked to the
humanities. So perhaps it is not as unlikely as it might first appear for a
group of statistical physicists and humanists to come together to investigate
one of the subjects of Thomas Jefferson's poetic interests from a scientific
point of view. And that is the nature of this article: a collaborative
interdisciplinary analysis of the works of a figure Jefferson described as a
''rude bard of the North'' and ''the greatest Poet that has ever existed.'' In
2012, a subset of this team embraced an increase in interdisciplinary methods
to apply the new science of complex networks to longstanding questions in
comparative mythology. Investigations of network structures embedded in epic
narratives allowed universal properties to be identified and ancient texts to
be compared to each other. The approach inspired new challenges in mathematics,
physics and even processes in industry, thereby illustrating how collaborations
of this nature can be mutually beneficial and can capture the attention of a
public, often ill-served by academic communication and dissemination. This
article derives from these works, and from our consistent objective to help
bridge the perceived gap between the natural sciences and the humanities. First
we discuss the history of relationships between the two. Then we discuss the
origins of the poems of Ossian and Jefferson's interests. We follow with our
statistical approach in the next section. In the final section, we explore
ideas for future research on these themes and discuss the potential of
collaborative pursuits of human curiosity to overcome the two cultures
dichotomy and embrace a scientific- and humanities-literate information age.Comment: Contriution to book chapte
Work fluctuations in quantum spin chains
We study the work fluctuations of two types of finite quantum spin chains
under the application of a time-dependent magnetic field in the context of the
fluctuation relation and Jarzynski equality. The two types of quantum chains
correspond to the integrable Ising quantum chain and the nonintegrable XX
quantum chain in a longitudinal magnetic field. For several magnetic field
protocols, the quantum Crooks and Jarzynski relations are numerically tested
and fulfilled. As a more interesting situation, we consider the forcing regime
where a periodic magnetic field is applied. In the Ising case we give an exact
solution in terms of double-confluent Heun functions. We show that the
fluctuations of the work performed by the external periodic drift are maximum
at a frequency proportional to the amplitude of the field. In the nonintegrable
case, we show that depending on the field frequency a sharp transition is
observed between a Poisson-limit work distribution at high frequencies toward a
normal work distribution at low frequencies.Comment: 10 pages, 13 figure