1,032 research outputs found
Langevin dynamics in crossed magnetic and electric fields: Hall and diamagnetic fluctuations
Based on the classical Langevin equation, we have re-visited the problem of
orbital motion of a charged particle in two dimensions for a normal magnetic
field crossed with or without an in-plane electric bias. We are led to two
interesting fluctuation effects: First, we obtain not only a longitudinal
"work-fluctuation" relation as expected for a barotropic type system, but also
a transverse work-fluctuation relation perpendicular to the electric bias. This
"Hall fluctuation" involves the product of the electric and the magnetic
fields. And second, for the case of harmonic confinement without bias, the
calculated probability density for the orbital magnetic moment gives non-zero
even moments, not derivable as field derivatives of the classical free energy.Comment: 4 pages, 2 figures, revised versio
Negative Diffusion and Traveling Waves in High Dimensional Lattice Systems
This is the publisher's version, also available electronically from http://epubs.siam.org/doi/abs/10.1137/120880628We consider bistable reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. The discrete diffusion term is allowed to have positive spatially periodic coefficients, and the two spatially periodic equilibria are required to be well ordered. We establish the existence of traveling wave solutions to such pure lattice systems that connect the two stable equilibria. In addition, we show that these waves can be approximated by traveling wave solutions to systems that incorporate both local and nonlocal diffusion. In certain special situations our results can also be applied to reaction diffusion systems that include (potentially large) negative coefficients. Indeed, upon splitting the lattice suitably and applying separate coordinate transformations to each sublattice, such systems can sometimes be transformed into a periodic diffusion problem that fits within our framework. In such cases, the resulting traveling structure for the original system has a separate wave profile for each sublattice and connects spatially periodic patterns that need not be well ordered. There is no direct analogue of this procedure that can be applied to reaction diffusion systems with continuous spatial variables
Interdimensional degeneracies for a quantum -body system in dimensions
Complete spectrum of exact interdimensional degeneracies for a quantum
-body system in -dimensions is presented by the method of generalized
spherical harmonic polynomials. In an -body system all the states with
angular momentum in dimensions are degenerate where
and are given and is an arbitrary integer if the representation
exists for the SO() group and . There is an
exceptional interdimensional degeneracy for an -body system between the
state with zero angular momentum in dimensions and the state with zero
angular momentum in dimensions.Comment: 8 pages, no figure, RevTex, Accepted by EuroPhys.Let
Yet another surprise in the problem of classical diamagnetism
The well known Bohr-van Leeuwen Theorem states that the orbital diamagnetism
of classical charged particles is identically zero in equilibrium. However,
results based on real space-time approach using the classical Langevin equation
predicts non-zero diamagnetism for classical unbounded (finite or infinite)
systems. Here we show that the recently discovered Fluctuation Theorems,
namely, the Jarzynski Equality or the Crooks Fluctuation Theorem surprisingly
predict a free energy that depends on magnetic field as well as on the friction
coefficient, in outright contradiction to the canonical equilibrium results.
However, in the cases where the Langevin approach is consistent with the
equilibrium results, the Fluctuation Theorems lead to results in conformity
with equilibrium statistical mechanics. The latter is demonstrated analytically
through a simple example that has been discussed recently.Comment: 6 pages, 6 figure
Lande-like formula for the g factors of hole-nanowire subband edges
We have analyzed theoretically the Zeeman splitting of hole-quantum-wire
subband edges. As is typical for any bound state, their g factor depends on
both an intrinsic g factor of the material and an additional contribution
arising from a finite bound-state orbital angular momentum. We discuss the
quantum-confinement-induced interplay between bulk-material and orbital
effects, which is nontrivial due to the presence of strong spin-orbit coupling.
A compact analytical formula is provided that elucidates this interplay and can
be useful for predicting Zeeman splitting in generic hole-wire geometries.Comment: 4 pages, 2 figure
Quantum Electrical Dipole in Triangular Systems: a Model for Spontaneous Polarity in Metal Clusters
Triangular symmetric molecules with mirror symmetry perpendicular to the
3-fold axis are forbidden to have a fixed electrical dipole moment. However, if
the ground state is orbitally degenerate and lacks inversion symmetry, then a
``quantum'' dipole moment does exist. The system of 3 electrons in D_3h
symmetry is our example. This system is realized in triatomic molecules like
Na_3. Unlike the fixed dipole of a molecule like water, the quantum moment does
not point in a fixed direction, but lies in the plane of the molecule and takes
quantized values +/- mu_0 along any direction of measurement in the plane. An
electric field F in the plane leads to a linear Stark splitting +/- mu_0 F}. We
introduce a toy model to study the effect of Jahn-Teller distortions on the
quantum dipole moment. We find that the quantum dipole property survives when
the dynamic Jahn-Teller effect is included, if the distortion of the molecule
is small. Linear Stark splittings are suppressed in low fields by molecular
rotation, just as the linear Stark shift of water is suppressed, but will be
revealed in moderately large applied fields and low temperatures. Coulomb
correlations also give a partial suppression.Comment: 10 pages with 7 figures included; thoroughly revised with a new
coauthor; final minor change
Bohr-van Leeuwen theorem and the thermal Casimir effect for conductors
The problem of estimating the thermal corrections to Casimir and
Casimir-Polder interactions in systems involving conducting plates has
attracted considerable attention in the recent literature on dispersion forces.
Alternative theoretical models, based on distinct low-frequency extrapolations
of the plates reflection coefficient for transverse electric (TE) modes,
provide widely different predictions for the magnitude of this correction. In
this paper we examine the most widely used prescriptions for this reflection
coefficient from the point of view of their consistency with the Bohr-van
Leeuwen theorem of classical statistical physics, stating that at thermal
equilibrium transverse electromagnetic fields decouple from matter in the
classical limit. We find that the theorem is satisfied if and only if the TE
reflection coefficient vanishes at zero frequency in the classical limit. This
criterion appears to rule out some of the models that have been considered
recently for describing the thermal correction to the Casimir pressure with
non-magnetic metallic plates.Comment: 12 pages, no figures. Presentation has been significantly improved,
more references included. The new version matches the one accepted for
publication in Phys. Rev.
Self-magnetic compensation and Exchange Bias in ferromagnetic Samarium systems
For Sm(3+) ions in a vast majority of metallic systems, the following
interesting scenario has been conjured up for long, namely, a magnetic lattice
of tiny self (spin-orbital) compensated 4f-moments exchange coupled (and phase
reversed) to the polarization in the conduction band. We report here the
identification of a self-compensation behavior in a variety of ferromagnetic Sm
intermetallics via the fingerprint of a shift in the magnetic hysteresis (M-H)
loop from the origin. Such an attribute, designated as exchange bias in the
context of ferromagnetic/antiferromagnetic multilayers, accords these compounds
a potential for niche applications in spintronics. We also present results on
magnetic compensation behavior on small Gd doping (2.5 atomic percent) in one
of the Sm ferromagnets (viz. SmCu(4)Pd). The doped system responds like a
pseudo-ferrimagnet and it displays a characteristic left-shifted linear M-H
plot for an antiferromagnet.Comment: 7 pages and 7 figure
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