Nambu brackets with constraint functionals

If a Hamiltonian dynamical system with $n$ degrees of freedom admits $m$ constants of motion more than $2n-1$, then there exist some functional relations between the constants of motion. Among these relations the number of functionally independent ones are $s=m-(2n-1)$. It is shown that for such a system in which the constants of motion constitute a polynomial algebra closing in Poisson bracket, the Nambu brackets can be written in terms of these $s$ constraint functionals. The exemplification is very rich and several of them are analyzed in the text.Comment: 15 page

Vibrational properties of phonons in random binary alloys: An augmented space recursive technique in the k-representation

We present here an augmented space recursive technique in the k-representation which include diagonal, off-diagonal and the environmental disorder explicitly : an analytic, translationally invariant, multiple scattering theory for phonons in random binary alloys.We propose the augmented space recursion (ASR) as a computationally fast and accurate technique which will incorporate configuration fluctuations over a large local environment. We apply the formalism to $Ni_{55}Pd_{45}$, Ni_{88}Cr_12} and $Ni_{50}Pt_{50}$ alloys which is not a random choice. Numerical results on spectral functions, coherent structure factors, dispersion curves and disordered induced FWHM's are presented. Finally the results are compared with the recent itinerant coherent potential approximation (ICPA) and also with experiments.Comment: 20 pages, LaTeX, 23 figure

Repulsive Casimir Pistons

Casimir pistons are models in which finite Casimir forces can be calculated without any suspect renormalizations. It has been suggested that such forces are always attractive. We present three scenarios in which that is not true. Two of these depend on mixing two types of boundary conditions. The other, however, is a simple type of quantum graph in which the sign of the force depends upon the number of edges.Comment: 4 pages, 2 figures; RevTeX. Minor additions and correction

Scar Intensity Statistics in the Position Representation

We obtain general predictions for the distribution of wave function intensities in position space on the periodic orbits of chaotic ballistic systems. The expressions depend on effective system size N, instability exponent lambda of the periodic orbit, and proximity to a focal point of the orbit. Limiting expressions are obtained that include the asymptotic probability distribution of rare high-intensity events and a perturbative formula valid in the limit of weak scarring. For finite system sizes, a single scaling variable lambda N describes deviations from the semiclassical N -> infinity limit.Comment: To appear in Phys. Rev. E, 10 pages, including 4 figure

Localization of Eigenfunctions in the Stadium Billiard

We present a systematic survey of scarring and symmetry effects in the stadium billiard. The localization of individual eigenfunctions in Husimi phase space is studied first, and it is demonstrated that on average there is more localization than can be accounted for on the basis of random-matrix theory, even after removal of bouncing-ball states and visible scars. A major point of the paper is that symmetry considerations, including parity and time-reversal symmetries, enter to influence the total amount of localization. The properties of the local density of states spectrum are also investigated, as a function of phase space location. Aside from the bouncing-ball region of phase space, excess localization of the spectrum is found on short periodic orbits and along certain symmetry-related lines; the origin of all these sources of localization is discussed quantitatively and comparison is made with analytical predictions. Scarring is observed to be present in all the energy ranges considered. In light of these results the excess localization in individual eigenstates is interpreted as being primarily due to symmetry effects; another source of excess localization, scarring by multiple unstable periodic orbits, is smaller by a factor of $\sqrt{\hbar}$.Comment: 31 pages, including 10 figure

Focusing in Multiwell Potentials: Applications to Ion Channels

We investigate out of equilibrium stationary distributions induced by a stochastic dichotomous noise on double and multi-well models for ion channels. Ion-channel dynamics is analyzed both through over-damped Langevin equations and master equations. As a consequence of the external stochastic noise, we prove a non trivial focusing effect, namely the probability distribution is concentrated only on one state of the multi-well model. We also show that this focusing effect, which occurs at physiological conditions, cannot be predicted by a simple master equation approach.Comment: 8 pages, 7 figure

Depletion forces near curved surfaces

Based on density functional theory the influence of curvature on the depletion potential of a single big hard sphere immersed in a fluid of small hard spheres with packing fraction \eta_s either inside or outside of a hard spherical cavity of radius R_c is calculated. The relevant features of this potential are analyzed as function of \eta_s and R_c. There is a very slow convergence towards the flat wall limit R_c \to \infty. Our results allow us to discuss the strength of depletion forces acting near membranes both in normal and lateral directions and to make contact with recent experimental results