189 research outputs found
On the theory of electric dc-conductivity : linear and non-linear microscopic evolution and macroscopic behaviour
We consider the Schrodinger time evolution of charged particles subject to a
static substrate potential and to a homogeneous, macroscopic electric field (a
magnetic field may also be present). We investigate the microscopic velocities
and the resulting macroscopic current. We show that the microscopic velocities
are in general non-linear with respect to the electric field. One kind of
non-linearity arises from the highly non-linear adiabatic evolution and (or)
from an admixture of parts of it in so-called intermediate states, and the
other kind from non-quadratic transition rates between adiabatic states. The
resulting macroscopic dc-current may or may not be linear in the field. Three
cases can be distinguished : (a) The microscopic non-linearities can be
neglected. This is assumed to be the case in linear response theory (Kubo
formalism, ...). We give arguments which make it plausible that often such an
assumption is indeed justified, in particular for the current parallel to the
field. (b) The microscopic non-linearitites lead to macroscopic
non-linearities. An example is the onset of dissipation by increasing the
electric field in the breakdown of the quantum Hall effect. (c) The macroscopic
current is linear although the microscopic non-linearities constitute an
essential part of it and cannot be neglected. We show that the Hall current of
a quantized Hall plateau belongs to this case. This illustrates that
macroscopic linearity does not necessarily result from microscopic linearity.
In the second and third cases linear response theory is inadequate. We
elucidate also some other problems related to linear response theory.Comment: 24 pages, 6 figures, some typing errors have been corrected. Remark :
in eq. (1) of the printed article an obvious typing error remain
Relaxation Phenomena in a System of Two Harmonic Oscillators
We study the process by which quantum correlations are created when an
interaction Hamiltonian is repeatedly applied to a system of two harmonic
oscillators for some characteristic time interval. We show that, for the case
where the oscillator frequencies are equal, the initial Maxwell-Boltzmann
distributions of the uncoupled parts evolve to a new equilibrium
Maxwell-Boltzmann distribution through a series of transient Maxwell-Boltzmann
distributions. Further, we discuss why the equilibrium reached when the two
oscillator frequencies are unequal, is not a thermal one. All the calculations
are exact and the results are obtained through an iterative process, without
using perturbation theory.Comment: 22 pages, 6 Figures, Added contents, to appear in PR
Current-driven vortex oscillations in metallic nanocontacts
We present experimental evidence of sub-GHz spin-transfer oscillations in
metallic nano-contacts that are due to the translational motion of a magnetic
vortex. The vortex is shown to execute large-amplitude orbital motion outside
the contact region. Good agreement with analytical theory and micromagnetics
simulations is found.Comment: 4 pages, 3 figure
Modeling transcription factor binding events to DNA using a random walker/jumper representation on a 1D/2D lattice with different affinity sites
Surviving in a diverse environment requires corresponding organism responses.
At the cellular level, such adjustment relies on the transcription factors
(TFs) which must rapidly find their target sequences amidst a vast amount of
non-relevant sequences on DNA molecules. Whether these transcription factors
locate their target sites through a 1D or 3D pathway is still a matter of
speculation. It has been suggested that the optimum search time is when the
protein equally shares its search time between 1D and 3D diffusions. In this
paper, we study the above problem using a Monte Carlo simulation by considering
a very simple physical model. A 1D strip, representing a DNA, with a number of
low affinity sites, corresponding to non-target sites, and high affinity sites,
corresponding to target sites, is considered and later extended to a 2D strip.
We study the 1D and 3D exploration pathways, and combinations of the two modes
by considering three different types of molecules: a walker that randomly walks
along the strip with no dissociation; a jumper that represents dissociation and
then re-association of a TF with the strip at later time at a distant site; and
a hopper that is similar to the jumper but it dissociates and then
re-associates at a faster rate than the jumper. We analyze the final
probability distribution of molecules for each case and find that TFs can
locate their targets fast enough even if they spend 15% of their search time
diffusing freely in the solution. This indeed agrees with recent experimental
results obtained by Elf et al. 2007 and is in contrast with theoretical
expectation.Comment: 24 pages, 9 figure
Quasiprobabilistic Interpretation of Weak measurements in Mesoscopic Junctions
The impossibility of measuring noncommuting quantum mechanical observables is
one of the most fascinating consequences of the quantum mechanical postulates.
Hence, to date the investigation of quantum measurement and projection is a
fundamentally interesting topic. We propose to test the concept of weak
measurement of noncommuting observables in mesoscopic transport experiments,
using a quasiprobablistic description. We derive an inequality for current
correlators, which is satisfied by every classical probability but violated by
high-frequency fourth-order cumulants in the quantum regime for experimentally
feasible parameters.Comment: 4 pages, published versio
Kinetic theory of age-structured stochastic birth-death processes
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-–Born–-Green–-Kirkwood-–Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution
Noninvasiveness and time symmetry of weak measurements
Measurements in classical and quantum physics are described in fundamentally
different ways. Nevertheless, one can formally define similar measurement
procedures with respect to the disturbance they cause. Obviously, strong
measurements, both classical and quantum, are invasive -- they disturb the
measured system. We show that it is possible to define general weak
measurements, which are noninvasive: the disturbance becomes negligible as the
measurement strength goes to zero. Classical intuition suggests that
noninvasive measurements should be time symmetric (if the system dynamics is
reversible) and we confirm that correlations are time-reversal symmetric in the
classical case. However, quantum weak measurements -- defined analogously to
their classical counterparts -- can be noninvasive but not time symmetric. We
present a simple example of measurements on a two-level system which violates
time symmetry and propose an experiment with quantum dots to measure the
time-symmetry violation in a third-order current correlation function.Comment: 19 pages, 5 figures, more information at
http://www.fuw.edu.pl/~abednorz/tasym
Phase-space approach to dynamical density functional theory
We consider a system of interacting particles subjected to Langevin inertial
dynamics and derive the governing time-dependent equation for the one-body
density. We show that, after suitable truncations of the
Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale
analysis, we obtain a self-consistent equation involving only the one-body
density. This study extends to arbitrary dimensions previous work on a
one-dimensional fluid and highlights the subtelties of kinetic theory in the
derivation of dynamical density functional theory
From chemical Langevin equations to Fokker-Planck equation: application of Hodge decomposition and Klein-Kramers equation
The stochastic systems without detailed balance are common in various
chemical reaction systems, such as metabolic network systems. In studies of
these systems, the concept of potential landscape is useful. However, what are
the sufficient and necessary conditions of the existence of the potential
function is still an open problem. Use Hodge decomposition theorem in
differential form theory, we focus on the general chemical Langevin equations,
which reflect complex chemical reaction systems. We analysis the conditions for
the existence of potential landscape of the systems. By mapping the stochastic
differential equations to a Hamiltonian mechanical system, we obtain the
Fokker-Planck equation of the chemical reaction systems. The obtained
Fokker-Planck equation can be used in further studies of other steady
properties of complex chemical reaction systems, such as their steady state
entropies.Comment: 6 pages, 0 figure, submitted to J. Phys. A: Math. Theo
Modeling long-range memory with stationary Markovian processes
In this paper we give explicit examples of power-law correlated stationary
Markovian processes y(t) where the stationary pdf shows tails which are
gaussian or exponential. These processes are obtained by simply performing a
coordinate transformation of a specific power-law correlated additive process
x(t), already known in the literature, whose pdf shows power-law tails 1/x^a.
We give analytical and numerical evidence that although the new processes (i)
are Markovian and (ii) have gaussian or exponential tails their autocorrelation
function still shows a power-law decay =1/T^b where b grows with a
with a law which is compatible with b=a/2-c, where c is a numerical constant.
When a<2(1+c) the process y(t), although Markovian, is long-range correlated.
Our results help in clarifying that even in the context of Markovian processes
long-range dependencies are not necessarily associated to the occurrence of
extreme events. Moreover, our results can be relevant in the modeling of
complex systems with long memory. In fact, we provide simple processes
associated to Langevin equations thus showing that long-memory effects can be
modeled in the context of continuous time stationary Markovian processes.Comment: 5 figure
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