23,596 research outputs found
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 noise and 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 ) 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 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 (modulo 2),
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 . 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
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