Uniform WKB approximation of Coulomb wave functions for arbitrary partial wave

Coulomb wave functions are difficult to compute numerically for extremely low energies, even with direct numerical integration. Hence, it is more convenient to use asymptotic formulas in this region. It is the object of this paper to derive analytical asymptotic formulas valid for arbitrary energies and partial waves. Moreover, it is possible to extend these formulas for complex values of parameters.Comment: 5 pages, 2 figure

Spectral fluctuations and 1/f noise in the order-chaos transition regime

Level fluctuations in quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate level fluctuations to the classical dynamics in the regular and chaotic limit. In this we show that the spectrum of the system undergoing order to chaos transition displays a characteristic $f^{-\gamma}$ noise and $\gamma$ is correlated with the classical chaos in the system. We demonstrate this using a smooth potential and a time-dependent system modeled by Gaussian and circular ensembles respectively of random matrix theory. We show the effect of short periodic orbits on these fluctuation measures.Comment: 4 pages, 5 figures. Modified version. To appear in Phys. Rev. Let

Correlations in Chaotic Eigenfunctions at Large Separation

An energy eigenfunction in a classically chaotic system is known to have spatial correlations which (in the limit of small $\hbar$) are governed by a microcanonical distribution in the classical phase space. This result is valid, however, only over coordinate distances which are small compared to any relevant classical distance scales (such as the cyclotron radius for a charged particle in a magnetic field). We derive a modified formula for the correlation function in the regime of large separation. This then permits a complete description, over all length scales, of the statistical properties of chaotic eigenfunctions in the $\hbar\to 0$ limit. Applications to quantum dots are briefly discussed.Comment: 8 pages, 1 figure, RevTeX, eps

METABOLIC PROPERTIES OF CELLS ISOLATED FROM ADULT MOUSE LIVER

Suspensions of isolated cells were prepared from mouse livers that had been perfused via the portal vein with a buffered medium containing sucrose. The demonstration of metabolic activities in these cells was found to be critically dependent on the composition of the suspending medium. The cells showed considerable metabolic activity in a simple medium containing 0.06 to 0.20 M sucrose, but did not respire in 0.30 M sucrose medium. Endogenous respiration was greatest when the sucrose concentration of the medium was 0.10 M or lower and was associated with the formation of acetoacetate. The cells oxidized citric acid cycle intermediates, glutamate, lactate, pyruvate, β-hydroxybutyrate, α-glycerophosphate, and fatty acids and synthesized urea from ammonium chloride, but carbohydrate substrates did not stimulate oxygen uptake. Cells incubated in Krebs' phosphate-saline did not respire. The lack of respiration in this medium is thought to be related to increased permeability of the cell membrane with penetration of calcium ions and orthophosphate into the cells causing mitochondrial swelling and destruction. Further evidence for the loss of cellular permeability barriers is provided by the demonstration of leakage of certain soluble enzymes into the preparative media

Nonclassical Degrees of Freedom in the Riemann Hamiltonian

The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum hamiltonian. If so, conjectures by Katz and Sarnak put this hamiltonian in Altland and Zirnbauer's universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.Comment: 4 pages, no figures; v3-6 have minor corrections to v2, v2 has a more complete solution of the sign problem than v

Geometric phase for a dimerized disordered continuum: Topological shot noise

Geometric phase shift associated with an electron propagating through a dimerized-disordered continuum is shown to be 0, or $\pm \pi$ (modulo 2$\pi$), according as the associated circuit traversed in the two-dimensional parameter space excludes, or encircles a certain singularity. This phase-shift is a topological invariant. Its discontinuous dependence on the electron energy and disorder implies a statistical spectral and conductance fluctuation in a corresponding mesoscopic system. Inasmuch as the fluctuation derives from the discreteness of the phase shift, it may aptly be called a topological shot-noise.Comment: 10 pages(LATEX) + 1 figure, (revised version). Will appear in Europhys. Let

Geometric gauge potentials and forces in low-dimensional scattering systems

We introduce and analyze several low-dimensional scattering systems that exhibit geometric phase phenomena. The systems are fully solvable and we compare exact solutions of them with those obtained in a Born-Oppenheimer projection approximation. We illustrate how geometric magnetism manifests in them, and explore the relationship between solutions obtained in the diabatic and adiabatic pictures. We provide an example, involving a neutral atom dressed by an external field, in which the system mimics the behavior of a charged particle that interacts with, and is scattered by, a ferromagnetic material. We also introduce a similar system that exhibits Aharonov-Bohm scattering. We propose some practical applications. We provide a theoretical approach that underscores universality in the appearance of geometric gauge forces. We do not insist on degeneracies in the adiabatic Hamiltonian, and we posit that the emergence of geometric gauge forces is a consequence of symmetry breaking in the latter.Comment: (Final version, published in Phy. Rev. A. 86, 042704 (2012

Topological properties of Berry's phase

By using a second quantized formulation of level crossing, which does not assume adiabatic approximation, a convenient formula for geometric terms including off-diagonal terms is derived. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian in the present formulation. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial for any finite time interval $T$. The topological interpretation of Berry's phase such as the topological proof of phase-change rule thus fails in the practical Born-Oppenheimer approximation, where a large but finite ratio of two time scales is involved.Comment: 9 pages. A new reference was added, and the abstract and the presentation in the body of the paper have been expanded and made more precis

Can apparent superluminal neutrino speeds be explained as a quantum weak measurement?

Probably not.Comment: 10 pages, 1 figur

Collisions with ice-volatile objects: Geological implications

The collision of the Earth with extra-terrestrial ice-volatile bodies is proposed as a mechanism to produce rapid changes in the geologic record. These bodies would be analogs of the ice satellites found for the Jovian planets and suspected for comets and certain low density bodies in the Asteroid belt. Five generic end-members are postulated: (1) water ice; (2) dry ice: carbon-carbon dioxide rich, (3) oceanic (chloride) ice; (4) sulfur-rich ice; (5) ammonia hydrate-rich ice; and (6) clathrate: methane-rich ice. Due to the volatile nature of these bodies, evidence for their impact with the Earth would be subtle and probably best reflected geochemically or in the fossil record. Actual boloids impacting the Earth may have a variable composition, generally some admixture with water ice. However for discussion purposes, only the effects of a dominant component will be treated. The general geological effects of such collisions, as a function of the dominant component would be: (1) rapid sea level rise unrelated to deglaciation, (2) decreased oceanic pH and rapid climatic warming or deglaciation; (3) increased paleosalinities; (4) increased acid rain; (5) increased oceanic pH and rapid carbonate deposition; and (6) rapid climatic warming or deglaciation