33 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
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
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
Relative momentum for identical particles
Possible definitions for the relative momentum of identical particles are
considered
Violation of the zeroth law of thermodynamics for a non-ergodic interaction
The phenomenon described by our title should surprise no one. What may be
surprising though is how easy it is to produce a quantum system with this
feature; moreover, that system is one that is often used for the purpose of
showing how systems equilibrate. The violation can be variously manifested. In
our detailed example, bringing a detuned 2-level system into contact with a
monochromatic reservoir does not cause it to relax to the reservoir
temperature; rather, the system acquires the reservoir's
level-occupation-ratio
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
Efficiency of a thermodynamic motor at maximum power
Several recent theories address the efficiency of a macroscopic thermodynamic
motor at maximum power and question the so-called "Curzon-Ahlborn (CA)
efficiency." Considering the entropy exchanges and productions in an n-sources
motor, we study the maximization of its power and show that the controversies
are partly due to some imprecision in the maximization variables. When power is
maximized with respect to the system temperatures, these temperatures are
proportional to the square root of the corresponding source temperatures, which
leads to the CA formula for a bi-thermal motor. On the other hand, when power
is maximized with respect to the transitions durations, the Carnot efficiency
of a bi-thermal motor admits the CA efficiency as a lower bound, which is
attained if the duration of the adiabatic transitions can be neglected.
Additionally, we compute the energetic efficiency, or "sustainable efficiency,"
which can be defined for n sources, and we show that it has no other universal
upper bound than 1, but that in certain situations, favorable for power
production, it does not exceed 1/2