1,543 research outputs found
On dominant contractions and a generalization of the zero-two law
Zaharopol proved the following result: let T,S:L^1(X,{\cf},\m)\to
L^1(X,{\cf},\m) be two positive contractions such that . If
then for all n\in\bn. In the present paper we
generalize this result to multi-parameter contractions acting on . As an
application of that result we prove a generalization of the "zero-two" law.Comment: 10 page
How quantum bound states bounce and the structure it reveals
We investigate how quantum bound states bounce from a hard surface. Our
analysis has applications to ab initio calculations of nuclear structure and
elastic deformation, energy levels of excitons in semiconductor quantum dots
and wells, and cold atomic few-body systems on optical lattices with sharp
boundaries. We develop the general theory of elastic reflection for a composite
body from a hard wall. On the numerical side we present ab initio calculations
for the compression of alpha particles and universal results for two-body
states. On the analytical side we derive a universal effective potential that
gives the reflection scattering length for shallow two-body states.Comment: final publication version, new lattice results on alpha particle
compression, 5 pages, 2 figure
Stabilization of Hydrodynamic Flows by Small Viscosity Variations
Motivated by the large effect of turbulent drag reduction by minute
concentrations of polymers we study the effects of a weakly space-dependent
viscosity on the stability of hydrodynamic flows. In a recent Letter [Phys.
Rev. Lett. {\bf 87}, 174501, (2001)] we exposed the crucial role played by a
localized region where the energy of fluctuations is produced by interactions
with the mean flow (the "critical layer"). We showed that a layer of weakly
space-dependent viscosity placed near the critical layer can have a very large
stabilizing effect on hydrodynamic fluctuations, retarding significantly the
onset of turbulence. In this paper we extend these observation in two
directions: first we show that the strong stabilization of the primary
instability is also obtained when the viscosity profile is realistic (inferred
from simulations of turbulent flows with a small concentration of polymers).
Second, we analyze the secondary instability (around the time-dependent primary
instability) and find similar strong stabilization. Since the secondary
instability develops around a time-dependent solution and is three-dimensional,
this brings us closer to the turbulent case. We reiterate that the large effect
is {\em not} due to a modified dissipation (as is assumed in some theories of
drag reduction), but due to reduced energy intake from the mean flow to the
fluctuations. We propose that similar physics act in turbulent drag reduction.Comment: 10 pages, 17 figs., REVTeX4, PRE, submitte
Spectral functions of the Falicov-Kimball model with electronic ferroelectricity
We calculate the angular resolved photoemission spectrum of the
Falicov-Kimball model with electronic ferroelectricity where - and
-electrons have different hoppings. In mix-valence regimes, the presence of
strong scattering processes between - excitons and a hole, created by
emission of an electron, leads to the formation of pseudospin polarons and
novel electronic structures with bandwidth scaling with that of -
excitons. Especially, in the two-dimensional case, we find that flat regions
exist near the bottom of the quasiparticle band in a wide range of the - and
-level energy difference.Comment: 5 pages, 5 figure
Alternative Fourier Expansions for Inverse Square Law Forces
Few-body problems involving Coulomb or gravitational interactions between
pairs of particles, whether in classical or quantum physics, are generally
handled through a standard multipole expansion of the two-body potentials. We
discuss an alternative based on a compact, cylindrical Green's function
expansion that should have wide applicability throughout physics. Two-electron
"direct" and "exchange" integrals in many-electron quantum systems are
evaluated to illustrate the procedure which is more compact than the standard
one using Wigner coefficients and Slater integrals.Comment: 10 pages, latex/Revtex4, 1 figure
Relativistic Mass Ejecta from Phase-transition-induced Collapse of Neutron Stars
We study the dynamical evolution of a phase-transition-induced collapse
neutron star to a hybrid star, which consists of a mixture of hadronic matter
and strange quark matter. The collapse is triggered by a sudden change of
equation of state, which result in a large amplitude stellar oscillation. The
evolution of the system is simulated by using a 3D Newtonian hydrodynamic code
with a high resolution shock capture scheme. We find that both the temperature
and the density at the neutrinosphere are oscillating with acoustic frequency.
However, they are nearly 180 out of phase. Consequently, extremely
intense, pulsating neutrino/antineutrino fluxes will be emitted periodically.
Since the energy and density of neutrinos at the peaks of the pulsating fluxes
are much higher than the non-oscillating case, the electron/positron pair
creation rate can be enhanced dramatically. Some mass layers on the stellar
surface can be ejected by absorbing energy of neutrinos and pairs. These mass
ejecta can be further accelerated to relativistic speeds by absorbing
electron/positron pairs, created by the neutrino and antineutrino annihilation
outside the stellar surface. The possible connection between this process and
the cosmological Gamma-ray Bursts is discussed.Comment: 40 pages, 11 figures, accepted for publication in JCA
Independent Eigenstates of Angular Momentum in a Quantum N-body System
The global rotational degrees of freedom in the Schr\"{o}dinger equation for
an -body system are completely separated from the internal ones. After
removing the motion of center of mass, we find a complete set of
independent base functions with the angular momentum . These are
homogeneous polynomials in the components of the coordinate vectors and the
solutions of the Laplace equation, where the Euler angles do not appear
explicitly. Any function with given angular momentum and given parity in the
system can be expanded with respect to the base functions, where the
coefficients are the functions of the internal variables. With the right choice
of the base functions and the internal variables, we explicitly establish the
equations for those functions. Only (3N-6) internal variables are involved both
in the functions and in the equations. The permutation symmetry of the wave
functions for identical particles is discussed.Comment: 24 pages, no figure, one Table, RevTex, Will be published in Phys.
Rev. A 64, 0421xx (Oct. 2001
Percolation in three-dimensional random field Ising magnets
The structure of the three-dimensional random field Ising magnet is studied
by ground state calculations. We investigate the percolation of the minority
spin orientation in the paramagnetic phase above the bulk phase transition,
located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the
Gaussian random fields (J=1). With an external field H there is a disorder
strength dependent critical field +/- H_c(Delta) for the down (or up) spin
spanning. The percolation transition is in the standard percolation
universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/-
0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <=
Delta_p. When, with zero external field, Delta is decreased from a large value
there is a transition from the simultaneous up and down spin spanning, with
probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This
is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster
has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta).
We provide evidence that this is asymptotically true even at H=0 for Delta_c <
Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is
approached from above. Percolation implies extra finite size effects in the
ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review
Recent developments in planet migration theory
Planetary migration is the process by which a forming planet undergoes a
drift of its semi-major axis caused by the tidal interaction with its parent
protoplanetary disc. One of the key quantities to assess the migration of
embedded planets is the tidal torque between the disc and planet, which has two
components: the Lindblad torque and the corotation torque. We review the latest
results on both torque components for planets on circular orbits, with a
special emphasis on the various processes that give rise to additional, large
components of the corotation torque, and those contributing to the saturation
of this torque. These additional components of the corotation torque could help
address the shortcomings that have recently been exposed by models of planet
population syntheses. We also review recent results concerning the migration of
giant planets that carve gaps in the disc (type II migration) and the migration
of sub-giant planets that open partial gaps in massive discs (type III
migration).Comment: 52 pages, 18 figures. Review article to be published in "Tidal
effects in Astronomy and Astrophysics", Lecture Notes in Physic
Ferromagnetism without flat bands in thin armchair nanoribbons
Describing by a Hubbard type of model a thin armchair graphene ribbon in the
armchair hexagon chain limit, one shows in exact terms, that even if the system
does not have flat bands at all, at low concentration a mesoscopic sample can
have ferromagnetic ground state, being metallic in the same time. The mechanism
is connected to a common effect of correlations and confinement.Comment: 37 pages, 12 figures, in press at Eur. Phys. Jour.
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