392 research outputs found
Multiple phases in stochastic dynamics: geometry and probabilities
Stochastic dynamics is generated by a matrix of transition probabilities.
Certain eigenvectors of this matrix provide observables, and when these are
plotted in the appropriate multi-dimensional space the phases (in the sense of
phase transitions) of the underlying system become manifest as extremal points.
This geometrical construction, which we call an
\textit{observable-representation of state space}, can allow hierarchical
structure to be observed. It also provides a method for the calculation of the
probability that an initial points ends in one or another asymptotic state
Ratcheting up energy by means of measurement
The destruction of quantum coherence can pump energy into a system. For our
examples this is paradoxical since the destroyed correlations are ordinarily
considered negligible. Mathematically the explanation is straightforward and
physically one can identify the degrees of freedom supplying this energy.
Nevertheless, the energy input can be calculated without specific reference to
those degrees of freedom.Comment: To appear in Phys. Rev. Let
Path integral in a magnetic field using the Trotter product formula
The derivation of the Feynman path integral based on the Trotter product
formula is extended to the case where the system is in a magnetic field.Comment: To appear in the American Journal of Physics, 200
Imaging geometry through dynamics: the observable representation
For many stochastic processes there is an underlying coordinate space, ,
with the process moving from point to point in or on variables (such as
spin configurations) defined with respect to . There is a matrix of
transition probabilities (whether between points in or between variables
defined on ) and we focus on its ``slow'' eigenvectors, those with
eigenvalues closest to that of the stationary eigenvector. These eigenvectors
are the ``observables,'' and they can be used to recover geometrical features
of
A Kinetic Model of the Muscular Contraction
In this article, we build a self consistent mean field deterministic model for the muscular contraction. The two main variables are the number of free myosin heads and the number of myosin heads attached to the actin, just after attachment. The model is natural in the sense that it respects the physico-chemical natural constraints. We calculate the stationary state,
prove that it is stable and calculate the efficiency
Slow relaxation, confinement, and solitons
Millisecond crystal relaxation has been used to explain anomalous decay in
doped alkali halides. We attribute this slowness to Fermi-Pasta-Ulam solitons.
Our model exhibits confinement of mechanical energy released by excitation.
Extending the model to long times is justified by its relation to solitons,
excitations previously proposed to occur in alkali halides. Soliton damping and
observation are also discussed
Topological methods for searching barriers and reaction paths
We present a family of algorithms for the fast determination of reaction
paths and barriers in phase space and the computation of the corresponding
rates. The method requires the reaction times be large compared to the
microscopic time, irrespective of the origin - energetic, entropic, cooperative
- of the timescale separation. It lends itself to temperature cycling as in
simulated annealing and to activation-relaxation routines. The dynamics is
ultimately based on supersymmetry methods used years ago to derive Morse
theory. Thus, the formalism automatically incorporates all relevant topological
information.Comment: 4 pages, 4 figures, RevTex
Nonlinear Dirac and diffusion equations in 1 + 1 dimensions from stochastic considerations
We generalize the method of obtaining the fundamental linear partial
differential equations such as the diffusion and Schrodinger equation, Dirac
and telegrapher's equation from a simple stochastic consideration to arrive at
certain nonlinear form of these equations. The group classification through one
parameter group of transformation for two of these equations is also carried
out.Comment: 18 pages, Latex file, some equations corrected and group analysis in
one more case adde
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