7 research outputs found
Exact transformation of a Langevin equation to a fluctuating response equation
We demonstrate that a Langevin equation that describes the motion of a
Brownian particle under non-equilibrium conditions can be exactly transformed
to a special equation that explicitly exhibits the response of the velocity to
a time dependent perturbation. This transformation is constructed on the basis
of an operator formulation originally used in nonlinear perturbation theory for
differential equations by extending it to stochastic analysis. We find that the
obtained expression is useful for the calculation of fundamental quantities of
the system, and that it provides a physical basis for the decomposition of the
forces in the Langevin description into effective driving, dissipative, and
random forces in a large-scale description.Comment: 14 pages, to appear in J. Phys. A: Math. Ge
Slow light in photonic crystals
The problem of slowing down light by orders of magnitude has been extensively
discussed in the literature. Such a possibility can be useful in a variety of
optical and microwave applications. Many qualitatively different approaches
have been explored. Here we discuss how this goal can be achieved in linear
dispersive media, such as photonic crystals. The existence of slowly
propagating electromagnetic waves in photonic crystals is quite obvious and
well known. The main problem, though, has been how to convert the input
radiation into the slow mode without loosing a significant portion of the
incident light energy to absorption, reflection, etc. We show that the
so-called frozen mode regime offers a unique solution to the above problem.
Under the frozen mode regime, the incident light enters the photonic crystal
with little reflection and, subsequently, is completely converted into the
frozen mode with huge amplitude and almost zero group velocity. The linearity
of the above effect allows to slow light regardless of its intensity. An
additional advantage of photonic crystals over other methods of slowing down
light is that photonic crystals can preserve both time and space coherence of
the input electromagnetic wave.Comment: 96 pages, 12 figure
Dynamical Reduction of Discrete Systems Based on the Renormalization Group Method
The renormalization group (RG) method is extended for global asymptotic
analysis of discrete systems. We show that the RG equation in the discretized
form leads to difference equations corresponding to the Stuart-Landau or
Ginzburg-Landau equations. We propose a discretization scheme which leads to a
faithful discretization of the reduced dynamics of the original differential
equations.Comment: LaTEX. 12pages. 1 figure include