Collision of Polymers in a Vacuum

In a number of experimental situations, single polymer molecules can be suspended in a vacuum. Here collisions between such molecules are considered. The limit of high collision velocity is investigated numerically for a variety of conditions. The distribution of contact times, scattering angles, and final velocities are analyzed. In this limit, self avoiding chains are found to become highly stretched as they collide with each other, and have a distribution of scattering times that depends on the scattering angle. The velocity of the molecules after the collisions is similar to predictions of a model assuming thermal equilibration of molecules during the collision. The most important difference is a significant subset of molecules that inelastically scatter but do not substantially change direction.Comment: 7 pages, 6 figure

H\"older Regularity of Geometric Subdivision Schemes

We present a framework for analyzing non-linear $\mathbb{R}^d$-valued subdivision schemes which are geometric in the sense that they commute with similarities in $\mathbb{R}^d$. It admits to establish $C^{1,\alpha}$-regularity for arbitrary schemes of this type, and $C^{2,\alpha}$-regularity for an important subset thereof, which includes all real-valued schemes. Our results are constructive in the sense that they can be verified explicitly for any scheme and any given set of initial data by a universal procedure. This procedure can be executed automatically and rigorously by a computer when using interval arithmetics.Comment: 31 pages, 1 figur

Distribution of occupation numbers in finite Fermi-systems and role of interaction in chaos and thermalization

New method is developed for calculation of single-particle occupation numbers in finite Fermi systems of interacting particles. It is more accurate than the canonical distribution method and gives the Fermi-Dirac distribution in the limit of large number of particles. It is shown that statistical effects of the interaction are absorbed by an increase of the effective temperature. Criteria for quantum chaos and statistical equilibrium are considered. All results are confirmed by numerical experiments in the two-body random interaction model.Comment: 4 pages, Latex, 4 figures in the form of PS-file

Almost Certain Escape from Black Holes

This paper examines how black holes might compute in light of recent models of the black-hole final state. These models suggest that quantum information can escape from the black hole by a process akin to teleportation. They require a specific final state and restrictions on the interaction between the collapsing matter and the incoming Hawking radiation for quantum information to escape. This paper shows that for an arbitrary final state and for generic interactions between matter and Hawking radiation, the quantum information about how the hole was formed and the results of any computation performed by the matter inside the hole escapes with fidelity exponentially close to 1.Comment: 9 Pages, Te

A Model for Phase Transition based on Statistical Disassembly of Nuclei at Intermediate Energies

Consider a model of particles (nucleons) which has a two-body interaction which leads to bound composites with saturation properties. These properties are : all composites have the same density and the ground state energies of composites with k nucleons are given by -kW+\sigma k^{2/3} where W and \sigma are positive constants. W represents a volume term and \sigma a surface tension term. These values are taken from nuclear physics. We show that in the large N limit where N is the number of particles such an assembly in a large enclosure at finite temperature shows properties of liquid-gas phase transition. We do not use the two-body interaction but the gross properties of the composites only. We show that (a) the p-\rho isotherms show a region where pressure does not change as $\rho$ changes just as in Maxwell construction of a Van der Waals gas, (b) in this region the chemical potential does not change and (c) the model obeys the celebrated Clausius-Clapeyron relations. A scaling law for the yields of composites emerges. For a finite number of particles N (upto some thousands) the problem can be easily solved on a computer. This allows us to study finite particle number effects which modify phase transition effects. The model is calculationally simple. Monte-Carlo simulations are not needed.Comment: RevTex file, 21 pages, 5 figure

Radial Spin Helix in Two-Dimensional Electron Systems with Rashba Spin-Orbit Coupling

We suggest a long-lived spin polarization structure, a radial spin helix, and study its relaxation dynamics. For this purpose, starting with a simple and physically clear consideration of spin transport, we derive a system of equations for spin polarization density and find its general solution in the axially symmetric case. It is demonstrated that the radial spin helix of a certain period relaxes slower than homogeneous spin polarization and plain spin helix. Importantly, the spin polarization at the center of the radial spin helix stays almost unchanged at short times. At longer times, when the initial non-exponential relaxation region ends, the relaxation of the radial spin helix occurs with the same time constant as that describing the relaxation of the plain spin helix.Comment: 9 pages, 7 figure