41,459 research outputs found
Vortex Dynamics within the BCS Theory
We outline a conventional path integral derivation of the transverse force
and the friction for a vortex in a superconductor based on the BCS theory. The
derivation is valid in both clean and dirty limits at both zero and finite
temperatures. The transverse force is found to be precisely as what has been
obtained by Ao and Thouless using the Berry's phase method. The friction is
essentially the same as the Bardeen and Stephen's result.
Errors in some previous representive microscopic derivations are discussed.Comment: Revtex. the Invited Talk in M2S-HTSC-V conference in Beijing, Feb.
28-March 4, 1997. to appear in Physica
Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. II: construction of SDS with nonlinear force and multiplicative noise
There is a whole range of emergent phenomena in non-equilibrium behaviors can
be well described by a set of stochastic differential equations. Inspired by an
insight gained during our study of robustness and stability in phage lambda
genetic switch in modern biology, we found that there exists a classification
of generic nonequilibrium processes: In the continuous description in terms of
stochastic differential equations, there exists four dynamical elements: the
potential function , the friction matrix , the anti-symmetric matrix
, and the noise. The generic feature of absence of detailed balance is
then precisely represented by . For dynamical near a fixed point, whether or
not it is stable or not, the stochastic dynamics is linear. A rather complete
analysis has been carried out (Kwon, Ao, Thouless, cond-mat/0506280; PNAS, {\bf
102} (2005) 13029), referred to as SDS I. One important and persistent question
is the existence of a potential function with nonlinear force and with
multiplicative noise, with both nice local dynamical and global steady state
properties. Here we demonstrate that a dynamical structure built into
stochastic differential equation allows us to construct such a global
optimization potential function. First, we provide the construction. One of
most important ingredient is the generalized Einstein relation. We then present
an approximation scheme: The gradient expansion which turns every order into
linear matrix equations. The consistent of such methodology with other known
stochastic treatments will be discussed in next paper, SDS III; and the
explicitly connection to statistical mechanics and thermodynamics will be
discussed in a forthcoming paper, SDS IV.Comment: Latex, 9 page
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