5,557 research outputs found
Quantum fluctuations and glassy behavior: The case of a quantum particle in a random potential
In this paper we expand our previous investigation of a quantum particle
subject to the action of a random potential plus a fixed harmonic potential at
a finite temperature T. In the classical limit the system reduces to a
well-known ``toy'' model for an interface in a random medium. It also applies
to a single quantum particle like an an electron subject to random
interactions, where the harmonic potential can be tuned to mimic the effect of
a finite box. Using the variational approximation, or alternatively, the limit
of large spatial dimensions, together with the use the replica method, and are
able to solve the model and obtain its phase diagram in the
plane, where is the particle's mass. The phase diagram is similar to that
of a quantum spin-glass in a transverse field, where the variable
plays the role of the transverse field. The glassy phase is characterized by
replica-symmetry-breaking. The quantum transition at zero temperature is also
discussed.Comment: revised version, 23 pages, revtex, 5 postscript figures in a separate
file figures.u
Quantum Monte Carlo simulations of a particle in a random potential
In this paper we carry out Quantum Monte Carlo simulations of a quantum
particle in a one-dimensional random potential (plus a fixed harmonic
potential) at a finite temperature. This is the simplest model of an interface
in a disordered medium and may also pertain to an electron in a dirty metal. We
compare with previous analytical results, and also derive an expression for the
sample to sample fluctuations of the mean square displacement from the origin
which is a measure of the glassiness of the system. This quantity as well as
the mean square displacement of the particle are measured in the simulation.
The similarity to the quantum spin glass in a transverse field is noted. The
effect of quantum fluctuations on the glassy behavior is discussed.Comment: 23 pages, 7 figures included as eps files, uses RevTeX. Accepted for
publication in J. of Physics A: Mathematical and Genera
The importance of radio sources in accounting for the highest mass black holes
The most massive black holes lie in the most massive elliptical galaxies, and
at low-z all radio-loud AGNs lie in giant ellipticals. This strongly suggests a
link between radio-loudness and black hole mass. We argue that the increase in
the radio-loud fraction with AGN luminosity in optically-selected quasar
samples is consistent with this picture. We also use the ratio of black holes
today to quasars at z~2 to conclude that the most bolometrically-luminous AGN,
either radio-loud or radio quiet, are constrained to have lifetimes <~10^8 yr.
If radio sources are associated with black holes of >~10^9 M_sun at all
redshifts, then the same lifetime constraint applies to all radio sources with
luminosities above L_5GHz ~ 10^24 W/Hz/sr.Comment: 6 pages, 2 figures. To appear in "Lifecycles of Radio Galaxies", ed
J. Biretta et al., New Astronomy Review
Interpolation of the Josephson interaction in highly anisotropic superconductors from a solution of the two dimensional sine-Gordon equation
In this paper we solve numerically the two dimensional elliptic sine-Gordon
equation with appropriate boundary conditions. These boundary conditions are
chosen to correspond to the Josephson interaction between two adjacent pancakes
belonging to the same flux-line in a highly anisotropic superconductor. An
extrapolation is obtained between the regimes of low and high separation of the
pancakes. The resulting formula is a better candidate for use in numerical
simulations than previously derived formulas.Comment: 18 pages, 9 figure
Replica field theory for a polymer in random media
In this paper we revisit the problem of a (non self-avoiding) polymer chain
in a random medium which was previously investigated by Edwards and Muthukumar
(EM). As noticed by Cates and Ball (CB) there is a discrepancy between the
predictions of the replica calculation of EM and the expectation that in an
infinite medium the quenched and annealed results should coincide (for a chain
that is free to move) and a long polymer should always collapse. CB argued that
only in a finite volume one might see a ``localization transition'' (or
crossover) from a stretched to a collapsed chain in three spatial dimensions.
Here we carry out the replica calculation in the presence of an additional
confining harmonic potential that mimics the effect of a finite volume. Using a
variational scheme with five variational parameters we derive analytically for
d<4 the result R~(g |ln \mu|)^{-1/(4-d)} ~(g lnV)^{-1/(4-d)}, where R is the
radius of gyration, g is the strength of the disorder, \mu is the spring
constant associated with the confining potential and V is the associated
effective volume of the system. Thus the EM result is recovered with their
constant replaced by ln(V) as argued by CB. We see that in the strict infinite
volume limit the polymer always collapses, but for finite volume a transition
from a stretched to a collapsed form might be observed as a function of the
strength of the disorder. For d<2 and for large
V>V'~exp[g^(2/(2-d))L^((4-d)/(2-d))] the annealed results are recovered and
R~(Lg)^(1/(d-2)), where L is the length of the polymer. Hence the polymer also
collapses in the large L limit. The 1-step replica symmetry breaking solution
is crucial for obtaining the above results.Comment: Revtex, 32 page
Disorder effects in the quantum Heisenberg model: An Extended Dynamical mean-field theory analysis
We investigate a quantum Heisenberg model with both antiferromagnetic and
disordered nearest-neighbor couplings. We use an extended dynamical mean-field
approach, which reduces the lattice problem to a self-consistent local impurity
problem that we solve by using a quantum Monte Carlo algorithm. We consider
both two- and three-dimensional antiferromagnetic spin fluctuations and
systematically analyze the effect of disorder. We find that in three dimensions
for any small amount of disorder a spin-glass phase is realized. In two
dimensions, while clean systems display the properties of a highly correlated
spin-liquid (where the local spin susceptibility has a non-integer power-low
frequency and/or temperature dependence), in the present case this behavior is
more elusive unless disorder is very small. This is because the spin-glass
transition temperature leaves only an intermediate temperature regime where the
system can display the spin-liquid behavior, which turns out to be more
apparent in the static than in the dynamical susceptibility.Comment: 15 pages, 7 figure
Molecular Dynamics of pancake vortices with realistic interactions: Observing the vortex lattice melting transition
In this paper we describe a version of London Langevin molecular dynamics
simulations that allows for investigations of the vortex lattice melting
transition in the highly anisotropic high-temperature superconductor material
BiSrCaCuO. We include the full electromagnetic
interaction as well as the Josephson interaction among pancake vortices. We
also implement periodic boundary conditions in all directions, including the
z-axis along which the magnetic field is applied. We show how to implement flux
cutting and reconnection as an analog to permutations in the multilevel Monte
Carlo scheme and demonstrate that this process leads to flux entanglement that
proliferates in the vortex liquid phase. The first-order melting transition of
the vortex lattice is observed to be in excellent agreement with previous
multilevel Monte Carlo simulations.Comment: 4 figure
The dusty environment of Quasars. Far-IR properties of Optical Quasars
We present the ISO far-IR photometry of a complete sub-sample of optically
selected bright quasars belonging to two complete surveys selected through
multicolour (U,B,V,R,I) techniques. The ISOPHOT camera on board of the ISO
Satellite was used to target these quasars at wavelengths of 7.3, 11.5, 60, 100
and 160 micron. Almost two thirds of the objects were detected at least in one
ISOPHOT band. The detection rate is independent of the source redshift, very
likely due to the negative K-correction of the far-IR thermal emission. More
than a half of the optically selected QSOs show significant emission between 4
and 100 micron in the quasar rest-frame. These fluxes have a very likely
thermal origin, although in a few objects an additional contribution from a
non-thermal component is plausible in the long wavelength bands. In a
colour-colour diagram these objects span a wide range of properties from
AGN-dominated to ULIRG-like. The far-IR composite spectrum of the quasar
population presents a broad far-IR bump between 10 and 30 micron and a sharp
drop at wavelengths greater than 100 micron in the quasar restframe. The amount
of energy emitted in the far-IR, is on average a few times larger than that
emitted in the blue and the ratio L(FIR)/L(B) increases with the bolometric
luminosity. Objects with fainter blue magnitudes have larger ratios between the
far-IR (wavelengths > 60 micron) fluxes and the blue band flux, which is
attributed to extinction by dust around the central source. No relation between
the blue absolute magnitude and the dust colour temperature is seen, suggesting
that the dominant source of FIR energy could be linked to a concurrent
starburst rather than to gravitational energy produced by the central engine.Comment: Astronomical Journal, in pres
Langevin Dynamics of the vortex matter two-stage melting transition in Bi_2Sr_2CaCu_2O in the presence of straight and of tilted columnar defects
In this paper we use London Langevin molecular dynamics simulations to
investigate the vortex matter melting transition in the highly anisotropic
high-temperature superconductor material Bi_2Sr_2CaCu_2O in the
presence of low concentration of columnar defects (CDs). We reproduce with
further details our previous results obtained by using Multilevel Monte Carlo
simulations that showed that the melting of the nanocrystalline vortex matter
occurs in two stages: a first stage melting into nanoliquid vortex matter and a
second stage delocalization transition into a homogeneous liquid. Furthermore,
we report on new dynamical measurements in the presence of a current that
identifies clearly the irreversibility line and the second stage delocalization
transition. In addition to CDs aligned along the c-axis we also simulate the
case of tilted CDs which are aligned at an angle with respect to the applied
magnetic field. Results for CDs tilted by with respect to c-axis
show that the locations of the melting and delocalization transitions are not
affected by the tilt when the ratio of flux lines to CDs remains constant. On
the other hand we argue that some dynamical properties and in particular the
position of the irreversibility line should be affected.Comment: 13 pages, 11 figure
Localization of a polymer in random media: Relation to the localization of a quantum particle
In this paper we consider in detail the connection between the problem of a
polymer in a random medium and that of a quantum particle in a random
potential. We are interested in a system of finite volume where the polymer is
known to be {\it localized} inside a low minimum of the potential. We show how
the end-to-end distance of a polymer which is free to move can be obtained from
the density of states of the quantum particle using extreme value statistics.
We give a physical interpretation to the recently discovered one-step
replica-symmetry-breaking solution for the polymer (Phys. Rev. E{\bf 61}, 1729
(2000)) in terms of the statistics of localized tail states. Numerical
solutions of the variational equations for chains of different length are
performed and compared with quenched averages computed directly by using the
eigenfunctions and eigenenergies of the Schr\"odinger equation for a particle
in a one-dimensional random potential. The quantities investigated are the
radius of gyration of a free gaussian chain, its mean square distance from the
origin and the end-to-end distance of a tethered chain. The probability
distribution for the position of the chain is also investigated. The glassiness
of the system is explained and is estimated from the variance of the measured
quantities.Comment: RevTex, 44 pages, 13 figure
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