1,174 research outputs found
Kondo-Anderson Transitions
Dilute magnetic impurities in a disordered Fermi liquid are considered close
to the Anderson metal-insulator transition (AMIT). Critical Power law
correlations between electron wave functions at different energies in the
vicinity of the AMIT result in the formation of pseudogaps of the local density
of states. Magnetic impurities can remain unscreened at such sites. We
determine the density of the resulting free magnetic moments in the zero
temperature limit. While it is finite on the insulating side of the AMIT, it
vanishes at the AMIT, and decays with a power law as function of the distance
to the AMIT. Since the fluctuating spins of these free magnetic moments break
the time reversal symmetry of the conduction electrons, we find a shift of the
AMIT, and the appearance of a semimetal phase. The distribution function of the
Kondo temperature is derived at the AMIT, in the metallic phase and in
the insulator phase. This allows us to find the quantum phase diagram in an
external magnetic field and at finite temperature . We calculate the
resulting magnetic susceptibility, the specific heat, and the spin relaxation
rate as function of temperature. We find a phase diagram with finite
temperature transitions between insulator, critical semimetal, and metal
phases. These new types of phase transitions are caused by the interplay
between Kondo screening and Anderson localization, with the latter being
shifted by the appearance of the temperature-dependent spin-flip scattering
rate. Accordingly, we name them Kondo-Anderson transitions (KATs).Comment: 18 pages, 9 figure
Two remarks on generalized entropy power inequalities
This note contributes to the understanding of generalized entropy power
inequalities. Our main goal is to construct a counter-example regarding
monotonicity and entropy comparison of weighted sums of independent identically
distributed log-concave random variables. We also present a complex analogue of
a recent dependent entropy power inequality of Hao and Jog, and give a very
simple proof.Comment: arXiv:1811.00345 is split into 2 papers, with this being on
Strong suppression of weak (anti)localization in graphene
Low-field magnetoresistance is ubiquitous in low-dimensional metallic systems
with high resistivity and well understood as arising due to quantum
interference on self-intersecting diffusive trajectories. We have found that in
graphene this weak-localization magnetoresistance is strongly suppressed and,
in some cases, completely absent. This unexpected observation is attributed to
mesoscopic corrugations of graphene sheets which cause a dephasing effect
similar to that of a random magnetic field.Comment: improved presentation of the theory part after referees comments;
important experimental info added (see "note added in proof"
Influence of high-energy electron irradiation on the transport properties of La_{1-x}Ca_{x}MnO_{3} films (x \approx 1/3)
The effect of crystal lattice disorder on the conductivity and colossal
magnetoresistance in La_{1-x}Ca_{x}MnO_{3} (x \approx 0.33) films has been
examined. The lattice defects are introduced by irradiating the film with
high-energy (\simeq 6 MeV) electrons with a maximal fluence of about 2\times
10^{17} cm^{-2}. This comparatively low dose of irradiation produces rather
small radiation damage in the films. The number of displacements per atom (dpa)
in the irradiated sample is about 10^{-5}. Nethertheless, this results in an
appreciable increase in the film resistivity. The percentage of resistivity
increase in the ferromagnetic metallic state (below the Curie tempetature
T_{c}) was much greater than that observed in the insulating state (above
T_{c}). At the same time irradiation has much less effect on T_{c} or on the
magnitude of the colossal magnetoresistance. A possible explanation of such
behavior is proposed.Comment: RevTex, 22 pages, 3 Postscript figures, submitted to Eur. Phys. J.
The central limit problem for random vectors with symmetries
Motivated by the central limit problem for convex bodies, we study normal
approximation of linear functionals of high-dimensional random vectors with
various types of symmetries. In particular, we obtain results for distributions
which are coordinatewise symmetric, uniform in a regular simplex, or
spherically symmetric. Our proofs are based on Stein's method of exchangeable
pairs; as far as we know, this approach has not previously been used in convex
geometry and we give a brief introduction to the classical method. The
spherically symmetric case is treated by a variation of Stein's method which is
adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem
Graviton-Scalar Interaction in the PP-Wave Background
We compute the graviton two scalar off-shell interaction vertex at tree level
in Type IIB superstring theory on the pp-wave background using the light-cone
string field theory formalism. We then show that the tree level vertex vanishes
when all particles are on-shell and conservation of p_{+} and p_{-} are
imposed. We reinforce our claim by calculating the same vertex starting from
the corresponding SUGRA action expanded around the pp-wave background in the
light-cone gauge.Comment: 26 pages, harvmac One reference added. A few comments changed in the
introduction. The "cyclic perms." term removed from some equations as
unnecessary and equations (2.38) and (3.19) are corrected accordingl
Systematics of Moduli Stabilization, Inflationary Dynamics and Power Spectrum
We study the scalar sector of type IIB superstring theory compactified on
Calabi-Yau orientifolds as a place to find a mechanism of inflation in the
early universe. In the large volume limit, one can stabilize the moduli in
stages using perturbative method. We relate the systematics of moduli
stabilization with methods to reduce the number of possible inflatons, which in
turn lead to a simpler inflation analysis. Calculating the order-of-magnitude
of terms in the equation of motion, we show that the methods are in fact valid.
We then give the examples where these methods are used in the literature. We
also show that there are effects of non-inflaton scalar fields on the scalar
power spectrum. For one of the two methods, these effects can be observed with
the current precision in experiments, while for the other method, the effects
might never be observable.Comment: 20 pages, JHEP style; v.2 and v.3: typos fixed, discussion and
references adde
Disorder-quenched Kondo effect in mesosocopic electronic systems
Nonmagnetic disorder is shown to quench the screening of magnetic moments in
metals, the Kondo effect. The probability that a magnetic moment remains free
down to zero temperature is found to increase with disorder strength.
Experimental consequences for disordered metals are studied. In particular, it
is shown that the presence of magnetic impurities with a small Kondo
temperature enhances the electron's dephasing rate at low temperatures in
comparison to the clean metal case. It is furthermore proven that the width of
the distribution of Kondo temperatures remains finite in the thermodynamic
(infinite volume) limit due to wave function correlations within an energy
interval of order , where is the elastic scattering time. When
time-reversal symmetry is broken either by applying a magnetic field or by
increasing the concentration of magnetic impurities, the distribution of Kondo
temperatures becomes narrower.Comment: 17 pages, 7 figures, new results on Kondo effect in quasi-1D wires
added, 6 Refs. adde
Isoperimetry and stability of hyperplanes for product probability measures
International audienceWe investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results can be applied, with a particular emphasis on the logistic measure
Concentration inequalities for random fields via coupling
We present a new and simple approach to concentration inequalities for
functions around their expectation with respect to non-product measures, i.e.,
for dependent random variables. Our method is based on coupling ideas and does
not use information inequalities. When one has a uniform control on the
coupling, this leads to exponential concentration inequalities. When such a
uniform control is no more possible, this leads to polynomial or
stretched-exponential concentration inequalities. Our abstract results apply to
Gibbs random fields, in particular to the low-temperature Ising model which is
a concrete example of non-uniformity of the coupling.Comment: New corrected version; 22 pages; 1 figure; New result added:
stretched-exponential inequalit
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