5,401 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.
Super and Sub-Poissonian photon statistics for single molecule spectroscopy
We investigate the distribution of the number of photons emitted by a single
molecule undergoing a spectral diffusion process and interacting with a
continuous wave laser field. The spectral diffusion is modeled based on a
stochastic approach, in the spirit of the Anderson-Kubo line shape theory.
Using a generating function formalism we solve the generalized optical Bloch
equations, and obtain an exact analytical formula for the line shape and
Mandel's Q parameter. The line shape exhibits well known behaviors, including
motional narrowing when the stochastic modulation is fast, and power
broadening. The Mandel parameter, describing the line shape fluctuations,
exhibits a transition from a Quantum sub-Poissonian behavior in the fast
modulation limit, to a classical super-Poissonian behavior found in the slow
modulation limit. Our result is applicable for weak and strong laser field,
namely for arbitrary Rabi frequency. We show how to choose the Rabi frequency
in such a way that the Quantum sub-Poissonian nature of the emission process
becomes strongest. A lower bound on is found, and simple limiting behaviors
are investigated. A non-trivial behavior is obtained in the intermediate
modulation limit, when the time scales for spectral diffusion and the life time
of the excited state, become similar. A comparison is made between our results,
and previous ones derived based on the semi-classical generalized
Wiener--Khintchine theorem.Comment: 14 Phys. Rev style pages, 10 figure
Quadratic short-range order corrections to the mean-field free energy
A method for calculating the short-range order part of the free energy of
order-disorder systems is proposed. The method is based on the apllication of
the cumulant expansion to the exact configurational entropy. Second-order
correlation corrections to the mean-field approximation for the free energy are
calculated for arbitrary thermodynamic phase and type of interactions. The
resulting quadratic approximation for the correlation entropy leads to
substantially better values of transition temperatures for the
nearest-neighbour cubic Ising ferromagnets.Comment: 7 pages, no figures, IOP-style LaTeX, submitted to J. Phys. Condens.
Matter (Letter to the Editor
Stochastic Transition between Turbulent Branch and Thermodynamic Branch of an Inhomogeneous Plasma
Transition phenomena between thermodynamic branch and turbulent branch in
submarginal turbulent plasma are analyzed with statistical theory.
Time-development of turbulent fluctuation is obtained by numerical simulations
of Langevin equation which contains submarginal characteristics. Probability
density functions and transition rates between two states are analyzed.
Transition from turbulent branch to thermodynamic branch occurs in almost
entire region between subcritical bifurcation point and linear stability
boundary.Comment: 10 pages, 8 figures, to be published in J. Phys. Soc. Jp
Nonequilibrium charge-Kondo transport through negative-U molecules
Low-temperature transport through molecules with effectively negative
charging energy U exhibits a charge-Kondo effect. We explore this regime
analytically by establishing an exact mapping between the negative-U and the
positive-U Anderson models, which is suitable for the description of
nonequilibrium transport. We employ this mapping to demonstrate the intimate
relation between nonequilibrium tranport in the spin-Kondo and charge-Kondo
regimes, and derive analytical expressions for the nonlinear current-voltage
chracteristics as well as the shot noise in the latter regime. Applying the
mapping in the opposite direction, we elucidate the finding of super-Poissonian
noise in the positive-U Anderson model at high temperatures, by relating the
correlations between spin flips to pair-tunneling processes at negative U.Comment: 11 pages, 5 figure
Brownian dynamics around the core of self-gravitating systems
We derive the non-Maxwellian distribution of self-gravitating -body
systems around the core by a model based on the random process with the
additive and the multiplicative noise. The number density can be obtained
through the steady state solution of the Fokker-Planck equation corresponding
to the random process. We exhibit that the number density becomes equal to that
of the King model around the core by adjusting the friction coefficient and the
intensity of the multiplicative noise. We also show that our model can be
applied in the system which has a heavier particle. Moreover, we confirm the
validity of our model by comparing with our numerical simulation.Comment: 11 pages, 4 figure
Entropy, non-ergodicity and non-Gaussian behaviour in ballistic transport
Ballistic transportation introduces new challenges in the thermodynamic
properties of a gas of particles. For example, violation of mixing, ergodicity
and of the fluctuation-dissipation theorem may occur, since all these processes
are connected. In this work, we obtain results for all ranges of diffusion,
i.e., both for subdiffusion and superdiffusion, where the bath is such that it
gives origin to a colored noise. In this way we obtain the skewness and the
non-Gaussian factor for the probability distribution function of the dynamical
variable. We put particular emphasis on ballistic diffusion, and we demonstrate
that in this case, although the second law of thermodynamics is preserved, the
entropy does not reach a maximum and a non-Gaussian behavior occurs. This
implies the non-applicability of the central limit theorem.Comment: 9 pages, 2 figure
Non-exponential relaxation for anomalous diffusion
We study the relaxation process in normal and anomalous diffusion regimes for
systems described by a generalized Langevin equation (GLE). We demonstrate the
existence of a very general correlation function which describes the relaxation
phenomena. Such function is even; therefore, it cannot be an exponential or a
stretched exponential. However, for a proper choice of the parameters, those
functions can be reproduced within certain intervals with good precision. We
also show the passage from the non-Markovian to the Markovian behaviour in the
normal diffusion regime. For times longer than the relaxation time, the
correlation function for anomalous diffusion becomes a power law for broad-band
noise.Comment: 6 pages, 2 figure
Fractional time random walk subdiffusion and anomalous transport with finite mean residence times: faster, not slower
Continuous time random walk (CTRW) subdiffusion along with the associated
fractional Fokker-Planck equation (FFPE) is traditionally based on the premise
of random clock with divergent mean period. This work considers an alternative
CTRW and FFPE description which is featured by finite mean residence times
(MRTs) in any spatial domain of finite size. Transient subdiffusive transport
can occur on a very large time scale which can greatly exceed mean
residence time in any trap, , and even not being related to
it. Asymptotically, on a macroscale transport becomes normal for .
However, mesoscopic transport is anomalous. Differently from viscoelastic
subdiffusion no long-range anti-correlations among position increments are
required. Moreover, our study makes it obvious that the transient subdiffusion
and transport are faster than one expects from their normal asymptotic limit on
a macroscale. This observation has profound implications for anomalous
mesoscopic transport processes in biological cells because of macroscopic
viscosity of cytoplasm is finite
Transition Probability to Turbulent Transport Regime
Transition phenomena between thermal noise state and turbulent state observed
in a submarginal turbulent plasma are analyzed with statistical theory.
Time-development of turbulent fluctuation is obtained by numerical simulations
of Langevin equation which contains hysteresis characteristics. Transition
rates between two states are analyzed. Transition from turbulent state to
thermal noise state occurs in entire region between subcritical bifurcation
point and linear stability boundary.Comment: 9 pages, 6 figures, to be published in Plasma Phys. Control. Fusio
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