77 research outputs found
Perturbation theory for a stochastic process with Ornstein-Uhlenbeck noise
The Ornstein-Uhlenbeck process may be used to generate a noise signal with a
finite correlation time. If a one-dimensional stochastic process is driven by
such a noise source, it may be analysed by solving a Fokker-Planck equation in
two dimensions. In the case of motion in the vicinity of an attractive fixed
point, it is shown how the solution of this equation can be developed as a
power series. The coefficients are determined exactly by using algebraic
properties of a system of annihilation and creation operators.Comment: 7 pages, 0 figure
Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle
Recently Wang et al. carried out a laboratory experiment, where a Brownian
particle was dragged through a fluid by a harmonic force with constant velocity
of its center. This experiment confirmed a theoretically predicted work related
integrated (I) Transient Fluctuation Theorem (ITFT), which gives an expression
for the ratio for the probability to find positive or negative values for the
fluctuations of the total work done on the system in a given time in a
transient state. The corresponding integrated stationary state fluctuation
theorem (ISSFT) was not observed. Using an overdamped Langevin equation and an
arbitrary motion for the center of the harmonic force, all quantities of
interest for these theorems and the corresponding non-integrated ones (TFT and
SSFT, resp.) are theoretically explicitly obtained in this paper. While the
(I)TFT is satisfied for all times, the (I)SSFT only holds asymptotically in
time. Suggestions for further experiments with arbitrary velocity of the
harmonic force and in which also the ISSFT could be observed, are given. In
addition, a non-trivial long-time relation between the ITFT and the ISSFT was
discovered, which could be observed experimentally, especially in the case of a
resonant circular motion of the center of the harmonic force.Comment: 20 pages, 3 figure
Phenomenological approach to non-linear Langevin equations
In this paper we address the problem of consistently construct Langevin
equations to describe fluctuations in non-linear systems. Detailed balance
severely restricts the choice of the random force, but we prove that this
property together with the macroscopic knowledge of the system is not enough to
determine all the properties of the random force. If the cause of the
fluctuations is weakly coupled to the fluctuating variable, then the
statistical properties of the random force can be completely specified. For
variables odd under time-reversal, microscopic reversibility and weak coupling
impose symmetry relations on the variable-dependent Onsager coefficients. We
then analyze the fluctuations in two cases: Brownian motion in position space
and an asymmetric diode, for which the analysis based in the master equation
approach is known. We find that, to the order of validity of the Langevin
equation proposed here, the phenomenological theory is in agreement with the
results predicted by more microscopic models.Comment: LaTex file, 2 figures available upon request, to appear in Phys.Rev.
The bremsstrahlung equation for the spin motion in LHC
The influence of the bremsstrahlung on the spin motion is expressed by the
equation which is the analogue and generalization of the
Bargmann-Michel-Telegdi equation. The new constant is involved in this
equation. This constant can be immediately determined by the experimental
measurement of the spin motion, or it follows from the classical limit of
quantum electrodynamics with radiative corrections.Comment: 9 page
On the theory of cosmic-ray showers I the furry model and the fluctuation problem
The main problems regarding the shower formation by fast electrons are reviewed on the basis of a simplified model first proposed by Furry ( S S 1 and 2). A general method is developed for calculating the fluctuation in the number of particles after a thickness x of matter ( S 3). It is shown in S 4 that can always be found when the average energy distribution F(E, x) is known. Using the approximate "cut-off" method the numerical values of have been computed for the Furry model (see table on p. 358). The approach to the normal value of the fluctuation (corresponding to the Poisson distribution) is much slower than has been expected.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32597/1/0000737.pd
Diffusion over a saddle with a Langevin equation
The diffusion problem over a saddle is studied using a multi-dimensional
Langevin equation. An analytical solution is derived for a quadratic potential
and the probability to pass over the barrier deduced. A very simple solution is
given for the one dimension problem and a general scheme is shown for higher
dimensions.Comment: 13 pages, use revTeX, to appear in Phys. Rev. E6
Multispecies virial expansions
We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange–Good inversion formula, which has other applications such as counting coloured trees or studying probability generating functions in multi-type branching processes. We prove that the virial expansion converges absolutely in a domain of small densities. In addition, we establish that the virial coefficients can be expressed in terms of two-connected graphs
Enhancement of fusion rates due to quantum effects in the particles momentum distribution in nonideal media
This study concerns a situation when measurements of the nonresonant
cross-section of nuclear reactions appear highly dependent on the environment
in which the particles interact. An appealing example discussed in the paper is
the interaction of a deuteron beam with a target of deuterated metal Ta. In
these experiments, the reaction cross section for d(d,p)t was shown to be
orders of magnitude greater than what the conventional model predicts for the
low-energy particles. In this paper we take into account the influence of
quantum effects due to the Heisenberg uncertainty principle for particles in a
non-ideal medium elastically interacting with the medium particles. In order to
calculate the nuclear reaction rate in the non-ideal environment we apply both
the Monte Carlo technique and approximate analytical calculation of the Feynman
diagram using nonrelativistic kinetic Green's functions in the medium which
correspond to the generalized energy and momentum distribution functions of
interacting particles. We show a possibility to reduce the 12-fold integral
corresponding to this diagram to a fivefold integral. This can significantly
speed up the computation and control accuracy. Our calculations show that
quantum effects significantly influence reaction rates such as p +7Be, 3He
+4He, p +7Li, and 12C +12C. The new reaction rates may be much higher than the
classical ones for the interior of the Sun and supernova stars. The possibility
to observe the theoretical predictions under laboratory conditions is
discussed
Diffusive spin transport
Information to be stored and transported requires physical carriers. The
quantum bit of information (qubit) can for instance be realised as the spin 1/2
degree of freedom of a massive particle like an electron or as the spin 1
polarisation of a massless photon. In this lecture, I first use irreducible
representations of the rotation group to characterise the spin dynamics in a
least redundant manner. Specifically, I describe the decoherence dynamics of an
arbitrary spin S coupled to a randomly fluctuating magnetic field in the
Liouville space formalism. Secondly, I discuss the diffusive dynamics of the
particle's position in space due to the presence of randomly placed impurities.
Combining these two dynamics yields a coherent, unified picture of diffusive
spin transport, as applicable to mesoscopic electronic devices or photons
propagating in cold atomic clouds.Comment: Lecture notes, published in A. Buchleitner, C. Viviescas, and M.
Tiersch (Eds.), "Entanglement and Decoherence. Foundations and Modern
Trends", Lecture Notes in Physics 768, Springer, Berlin (2009
Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces
Higgs bundles and non-abelian Hodge theory provide holomorphic methods with
which to study the moduli spaces of surface group representations in a
reductive Lie group G. In this paper we survey the case in which G is the
isometry group of a classical Hermitian symmetric space of non-compact type.
Using Morse theory on the moduli spaces of Higgs bundles, we compute the number
of connected components of the moduli space of representations with maximal
Toledo invariant.Comment: v2: added due credits to the work of Burger, Iozzi and Wienhard. v3:
corrected count of connected components for G=SU(p,q) (p \neq q); added due
credits to the work of Xia and Markman-Xia; minor corrections and
clarifications. 31 page
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