3,646 research outputs found
Peierls Mechanism of the Metal-Insulator Transition in Ferromagnetic Hollandite K2Cr8O16
Synchrotron X-ray diffraction experiment shows that the metal-insulator
transition occurring in a ferromagnetic state of a hollandite
KCrO is accompanied by a structural distortion from the
tetragonal to monoclinic phase with a
supercell. Detailed electronic structure
calculations demonstrate that the metal-insulator transition is caused by a
Peierls instability in the quasi-one-dimensional column structure made of four
coupled Cr-O chains running in the -direction, leading to the formation of
tetramers of Cr ions below the transition temperature. This furnishes a rare
example of the Peierls transition of fully spin-polarized electron systems.Comment: Phys. Rev. Lett., in press, 5 pages, 3 figure
Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials
The object of the present study is the integrated density of states of a
quantum particle in multi-dimensional Euclidean space which is characterized by
a Schr\"odinger operator with a constant magnetic field and a random potential
which may be unbounded from above and from below. For an ergodic random
potential satisfying a simple moment condition, we give a detailed proof that
the infinite-volume limits of spatial eigenvalue concentrations of
finite-volume operators with different boundary conditions exist almost surely.
Since all these limits are shown to coincide with the expectation of the trace
of the spatially localized spectral family of the infinite-volume operator, the
integrated density of states is almost surely non-random and independent of the
chosen boundary condition. Our proof of the independence of the boundary
condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and
T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal.
{\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first
version of math-ph/0010013. For a revised version of the second part, see
math-ph/0105046. To appear in Reviews in Mathematical Physic
Independent Component Analysis of Spatiotemporal Chaos
Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear
oscillators are analyzed using independent component analysis (ICA). For
diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth
amplitude patterns, ICA extracts localized one-humped basis vectors that
reflect the characteristic hole structures of the system, and for nonlocally
coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns,
ICA extracts localized basis vectors with characteristic gap structures.
Statistics of the decomposed signals also provide insight into the complex
dynamics of the spatiotemporal chaos.Comment: 5 pages, 6 figures, JPSJ Vol 74, No.
Gravitational Collapse with a Cosmological Constant
We consider the effect of a positive cosmological constant on spherical
gravitational collapse to a black hole for a few simple, analytic cases. We
construct the complete Oppenheimer-Snyder-deSitter (OSdS) spacetime, the
generalization of the Oppenheimer-Snyder solution for collapse from rest of a
homogeneous dust ball in an exterior vacuum. In OSdS collapse, the cosmological
constant may affect the onset of collapse and decelerate the implosion
initially, but it plays a diminishing role as the collapse proceeds. We also
construct spacetimes in which a collapsing dust ball can bounce, or hover in
unstable equilibrium, due to the repulsive force of the cosmological constant.
We explore the causal structure of the different spacetimes and identify any
cosmological and black hole event horizons which may be present.Comment: 7 pages, 10 figures; To appear in Phys. Rev.
Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses
Populations of uncoupled limit-cycle oscillators receiving common random
impulses show various types of phase-coherent states, which are characterized
by the distribution of phase differences between pairs of oscillators. We
develop a theory to predict the stationary distribution of pairwise phase
difference from the phase response curve, which quantitatively encapsulates the
oscillator dynamics, via averaging of the Frobenius-Perron equation describing
the impulse-driven oscillators. The validity of our theory is confirmed by
direct numerical simulations using the FitzHugh-Nagumo neural oscillator
receiving common Poisson impulses as an example
The Density of States and the Spectral Shift Density of Random Schroedinger Operators
In this article we continue our analysis of Schroedinger operators with a
random potential using scattering theory. In particular the theory of Krein's
spectral shift function leads to an alternative construction of the density of
states in arbitrary dimensions. For arbitrary dimension we show existence of
the spectral shift density, which is defined as the bulk limit of the spectral
shift function per unit interaction volume. This density equals the difference
of the density of states for the free and the interaction theory. This extends
the results previously obtained by the authors in one dimension. Also we
consider the case where the interaction is concentrated near a hyperplane.Comment: 1 figur
Dynamical renormalization group methods in theory of eternal inflation
Dynamics of eternal inflation on the landscape admits description in terms of
the Martin-Siggia-Rose (MSR) effective field theory that is in one-to-one
correspondence with vacuum dynamics equations. On those sectors of the
landscape, where transport properties of the probability measure for eternal
inflation are important, renormalization group fixed points of the MSR
effective action determine late time behavior of the probability measure. I
argue that these RG fixed points may be relevant for the solution of the gauge
invariance problem for eternal inflation.Comment: 11 pages; invited mini-review for Grav.Cos
Dynamic scaling regimes of collective decision making
We investigate a social system of agents faced with a binary choice. We
assume there is a correct, or beneficial, outcome of this choice. Furthermore,
we assume agents are influenced by others in making their decision, and that
the agents can obtain information that may guide them towards making a correct
decision. The dynamic model we propose is of nonequilibrium type, converging to
a final decision. We run it on random graphs and scale-free networks. On random
graphs, we find two distinct regions in terms of the "finalizing time" -- the
time until all agents have finalized their decisions. On scale-free networks on
the other hand, there does not seem to be any such distinct scaling regions
Non-linear inflationary perturbations
We present a method by which cosmological perturbations can be quantitatively
studied in single and multi-field inflationary models beyond linear
perturbation theory. A non-linear generalization of the gauge-invariant
Sasaki-Mukhanov variables is used in a long-wavelength approximation. These
generalized variables remain invariant under time slicing changes on long
wavelengths. The equations they obey are relatively simple and can be
formulated for a number of time slicing choices. Initial conditions are set
after horizon crossing and the subsequent evolution is fully non-linear. We
briefly discuss how these methods can be implemented numerically in the study
of non-Gaussian signatures from specific inflationary models.Comment: 10 pages, replaced to match JCAP versio
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