16,173 research outputs found
Two hard spheres in a pore: Exact Statistical Mechanics for different shaped cavities
The Partition function of two Hard Spheres in a Hard Wall Pore is studied
appealing to a graph representation. The exact evaluation of the canonical
partition function, and the one-body distribution function, in three different
shaped pores are achieved. The analyzed simple geometries are the cuboidal,
cylindrical and ellipsoidal cavities. Results have been compared with two
previously studied geometries, the spherical pore and the spherical pore with a
hard core. The search of common features in the analytic structure of the
partition functions in terms of their length parameters and their volumes,
surface area, edges length and curvatures is addressed too. A general framework
for the exact thermodynamic analysis of systems with few and many particles in
terms of a set of thermodynamic measures is discussed. We found that an exact
thermodynamic description is feasible based in the adoption of an adequate set
of measures and the search of the free energy dependence on the adopted measure
set. A relation similar to the Laplace equation for the fluid-vapor interface
is obtained which express the equilibrium between magnitudes that in extended
systems are intensive variables. This exact description is applied to study the
thermodynamic behavior of the two Hard Spheres in a Hard Wall Pore for the
analyzed different geometries. We obtain analytically the external work, the
pressure on the wall, the pressure in the homogeneous zone, the wall-fluid
surface tension, the line tension and other similar properties
Non-retracing orbits in Andreev billiards
The validity of the retracing approximation in the semiclassical quantization
of Andreev billiards is investigated. The exact energy spectrum and the
eigenstates of normal-conducting, ballistic quantum dots in contact with a
superconductor are calculated by solving the Bogoliubov-de Gennes equation and
compared with the semiclassical Bohr-Sommerfeld quantization for periodic
orbits which result from Andreev reflections. We find deviations that are due
to the assumption of exact retracing electron-hole orbits rather than the
semiclassical approximation, as a concurrently performed
Einstein-Brillouin-Keller quantization demonstrates. We identify three
different mechanisms producing non-retracing orbits which are directly
identified through differences between electron and hole wave functions.Comment: 9 pages, 12 figures, Phys. Rev. B (in print), high resolution images
available upon reques
Scaled Particle Theory for Hard Sphere Pairs. I. Mathematical Structure
We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle
theory that can serve as a predictive method for the hard sphere pair
correlation function g(r). The reversible cavity creation work is analyzed both
for a single spherical cavity of arbitrary size, as well as for a pair of
identical such spherical cavities with variable center-to-center separation.
These quantities lead directly to prediction of g(r). Smooth connection
conditions have been identified between the small-cavity situation where the
work can be exactly and completely expressed in terms of g(r), and the
large-cavity regime where macroscopic properties become relevant. Closure
conditions emerge which produce a nonlinear integral equation that must be
satisfied by the pair correlation function. This integral equation has a
structure which straightforwardly generates a solution that is a power series
in density. The results of this series replicate the exact second and third
virial coefficients for the hard sphere system via the contact value of the
pair correlation function. The predicted fourth virial coefficient is
approximately 0.6 percent lower than the known exact value. Detailed numerical
analysis of the nonlinear integral equation has been deferred to the sequel
(following paper
Photonic currents in driven and dissipative resonator lattices
Arrays of coupled photonic cavities driven by external lasers represent a
highly controllable setup to explore photonic transport. In this paper we
address (quasi)-steady states of this system that exhibit photonic currents
introduced by engineering driving and dissipation. We investigate two
approaches: in the first one, photonic currents arise as a consequence of a
phase difference of applied lasers and in the second one, photons are injected
locally and currents develop as they redistribute over the lattice. Effects of
interactions are taken into account within a mean-field framework. In the first
approach, we find that the current exhibits a resonant behavior with respect to
the driving frequency. Weak interactions shift the resonant frequency toward
higher values, while in the strongly interacting regime in our mean-field
treatment the effect stems from multiphotonic resonances of a single driven
cavity. For the second approach, we show that the overall lattice current can
be controlled by incorporating few cavities with stronger dissipation rates
into the system. These cavities serve as sinks for photonic currents and their
effect is maximal at the onset of quantum Zeno dynamics.Comment: 12 pages, 11 figure
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