249 research outputs found
Spectra of Cayley graphs of the lamplighter group and random Schrödinger operators
We show that the lamplighter group L has a system of generators for which the spectrum of the discrete Laplacian on the Cayley graph is a union of an interval and a countable set of isolated points accumulating to a point outside this interval. This is the first example of a group with infinitely many gaps in the spectrum of its Cayley graph. The result is obtained by a careful study of spectral properties of a one-parametric family of convolution operators on L. Our results show that the spectrum is a pure point spectrum for each value of the parameter, the eigenvalues are solutions of algebraic equations involving Chebyshev polynomials of the second kind, and the topological structure of the spectrum makes a bifurcation when the parameter passes the points 1 and -1
A longitudinal study of the association between persistent pathogens and incident depression among older U.S. Latinos
Depression is estimated to affect more than 6.5 million Americans 65 years of age and older and compared with non-Latino whites older U.S. Latinos have a greater incidence and severity of depression, warranting further investigation of novel risk factors for depression onset among this population. We used data on 771/1,789 individuals ≥60 years of age from the Sacramento Area Latino Study on Aging (1998-2008) who were tested for cytomegalovirus (CMV), herpes simplex virus, varicella zoster, Helicobacter pylori, Toxoplasma gondii, and C-reactive protein (CRP) and interleukin-6 (IL-6) level. Among those without elevated depressive symptoms at baseline, we examined the association between each pathogen, inflammatory markers and incident depression over up to nearly 10 years of follow-up using discrete-time logistic regression. We found that only CMV seropositivity was statistically significantly associated with increased odds of incident depression (odds ratio [OR]: 1.38, 95% confidence interval [CI]: 1.00-1.90) in the total sample as well as among women only (OR: 1.70, 95% CI: 1.01-2.86). These associations were not mediated by CRP or IL-6 levels. Our findings suggest that CMV seropositivity may serve as an important risk factor for the onset of depression among older U.S. Latinos, but act outside of inflammatory pathways
Bose-Einstein Condensation on inhomogeneous complex networks
The thermodynamic properties of non interacting bosons on a complex network
can be strongly affected by topological inhomogeneities. The latter give rise
to anomalies in the density of states that can induce Bose-Einstein
condensation in low dimensional systems also in absence of external confining
potentials. The anomalies consist in energy regions composed of an infinite
number of states with vanishing weight in the thermodynamic limit. We present a
rigorous result providing the general conditions for the occurrence of
Bose-Einstein condensation on complex networks in presence of anomalous
spectral regions in the density of states. We present results on spectral
properties for a wide class of graphs where the theorem applies. We study in
detail an explicit geometrical realization, the comb lattice, which embodies
all the relevant features of this effect and which can be experimentally
implemented as an array of Josephson Junctions.Comment: 11 pages, 9 figure
Quantum effects in a superconducting glass model
We study disordered Josephson junctions arrays with long-range interaction
and charging effects. The model consists of two orthogonal sets of positionally
disordered parallel filaments (or wires) Josephson coupled at each crossing
and in the presence of a homogeneous and transverse magnetic field. The large
charging energy (resulting from small self-capacitance of the ultrathin wires)
introduces important quantum fluctuations of the superconducting phase within
each filament. Positional disorder and magnetic field frustration induce
spin-glass like ground state, characterized by not having long-range order of
the phases. The stability of this phase is destroyed for sufficiently large
charging energy. We have evaluated the temperature vs charging energy phase
diagram by extending the methods developed in the theory of infinite-range spin
glasses, in the limit of large magnetic field. The phase diagram in the
different temperature regimes is evaluated by using variety of methods, to wit:
semiclassical WKB and variational methods, Rayleigh-Schr\"{o}dinger
perturbation theory and pseudospin effective Hamiltonians. Possible
experimental consequences of these results are briefly discussed.Comment: 17 pages REVTEX. Two Postscript figures can be obtained from the
authors. To appear in PR
Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions
We have studied a quantum Hamiltonian that models an array of ultrasmall
Josephson junctions with short range Josephson couplings, , and charging
energies, , due to the small capacitance of the junctions. We derive a new
effective quantum spherical model for the array Hamiltonian. As an application
we start by approximating the capacitance matrix by its self-capacitive limit
and in the presence of an external uniform background of charges, . In
this limit we obtain the zero-temperature superconductor-insulator phase
diagram, , that improves upon previous theoretical
results that used a mean field theory approximation. Next we obtain a
closed-form expression for the conductivity of a square array, and derive a
universal scaling relation valid about the zero--temperature quantum critical
point. In the latter regime the energy scale is determined by temperature and
we establish universal scaling forms for the frequency dependence of the
conductivity.Comment: 18 pages, four Postscript figures, REVTEX style, Physical Review B
1999. We have added one important reference to this version of the pape
Mean Field Theory of Josephson Junction Arrays with Charge Frustration
Using the path integral approach, we provide an explicit derivation of the
equation for the phase boundary for quantum Josephson junction arrays with
offset charges and non-diagonal capacitance matrix. For the model with nearest
neighbor capacitance matrix and uniform offset charge , we determine,
in the low critical temperature expansion, the most relevant contributions to
the equation for the phase boundary. We explicitly construct the charge
distributions on the lattice corresponding to the lowest energies. We find a
reentrant behavior even with a short ranged interaction. A merit of the path
integral approach is that it allows to provide an elegant derivation of the
Ginzburg-Landau free energy for a general model with charge frustration and
non-diagonal capacitance matrix. The partition function factorizes as a product
of a topological term, depending only on a set of integers, and a
non-topological one, which is explicitly evaluated.Comment: LaTex, 24 pages, 8 figure
Inertial Mass of a Vortex in Cuprate Superconductors
We present here a calculation of the inertial mass of a moving vortex in
cuprate superconductors. This is a poorly known basic quantity of obvious
interest in vortex dynamics. The motion of a vortex causes a dipolar density
distortion and an associated electric field which is screened. The energy cost
of the density distortion as well as the related screened electric field
contribute to the vortex mass, which is small because of efficient screening.
As a preliminary, we present a discussion and calculation of the vortex mass
using a microscopically derivable phase-only action functional for the far
region which shows that the contribution from the far region is negligible, and
that most of it arises from the (small) core region of the vortex. A
calculation based on a phenomenological Ginzburg-Landau functional is performed
in the core region. Unfortunately such a calculation is unreliable, the reasons
for it are discussed. A credible calculation of the vortex mass thus requires a
fully microscopic, non-coarse grained theory. This is developed, and results
are presented for a s-wave BCS like gap, with parameters appropriate to the
cuprates. The mass, about 0.5 per layer, for magnetic field along the
axis, arises from deformation of quasiparticle states bound in the core, and
screening effects mentioned above. We discuss earlier results, possible
extensions to d-wave symmetry, and observability of effects dependent on the
inertial mass.Comment: 27 pages, Latex, 3 figures available on request, to appear in
Physical Review
Resistance of a domain wall in the quasiclassical approach
Starting from a simple microscopic model, we have derived a kinetic equation
for the matrix distribution function. We employed this equation to calculate
the conductance in a mesoscopic F'/F/F' structure with a domain wall (DW).
In the limit of a small exchange energy and an abrupt DW, the conductance
of the structure is equal to . Assuming that the scattering times
for electrons with up and down spins are close to each other we show that the
account for a finite width of the DW leads to an increase in this conductance.
We have also calculated the spatial distribution of the electric field in the F
wire. In the opposite limit of large (adiabatic variation of the
magnetization in the DW) the conductance coincides in the main approximation
with the conductance of a single domain structure . The account for rotation of
the magnetization in the DW leads to a negative correction to this conductance.
Our results differ from the results in papers published earlier.Comment: 11 pages; replaced with revised versio
Angular dependence of domain wall resistivity in SrRuO films
is a 4d itinerant ferromagnet (T 150 K) with
stripe domain structure. Using high-quality thin films of SrRuO we study
the resistivity induced by its very narrow ( nm) Bloch domain walls,
(DWR), at temperatures between 2 K and T as a function of the
angle, , between the electric current and the ferromagnetic domains
walls. We find that which provides the first experimental
indication that the angular dependence of spin accumulation contribution to DWR
is . We expect magnetic multilayers to exhibit a similar
behavior.Comment: 5 pages, 5 figure
Landau theory of bi-criticality in a random quantum rotor system
We consider here a generalization of the random quantum rotor model in which
each rotor is characterized by an M-component vector spin. We focus entirely on
the case not considered previously, namely when the distribution of exchange
interactions has non-zero mean. Inclusion of non-zero mean permits
ferromagnetic and superconducting phases for M=1 and M=2, respectively. We find
that quite generally, the Landau theory for this system can be recast as a
zero-mean problem in the presence of a magnetic field. Naturally then, we find
that a Gabay-Toulouse line exists for when the distribution of exchange
interactions has non-zero mean. The solution to the saddle point equations is
presented in the vicinity of the bi-critical point characterized by the
intersection of the ferromagnetic (M=1) or superconducting (M=2) phase with the
paramagnetic and spin glass phases. All transitions are observed to be second
order. At zero temperature, we find that the ferromagnetic order parameter is
non-analytic in the parameter that controls the paramagnet/ferromagnet
transition in the absence of disorder. Also for M=1, we find that replica
symmetry breaking is present but vanishes at low temperatures. In addition, at
finite temperature, we find that the qualitative features of the phase diagram,
for M=1, are {\it identical} to what is observed experimentally in the random
magnetic alloy .Comment: 20 pages, 5 figure
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