479 research outputs found
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.
Magnetic Coupling Between Non-Magnetic Ions: Eu3+ in EuN and EuP
We consider the electronic structure of, and magnetic exchange (spin)
interactions between, nominally nonmagnetic Eu^3+ ions (4f^6, S=3, L=3, J=0)
within the context of the rocksalt structure compounds EuN and EuP. Both
compounds are ionic [Eu^3+; N^3- and P^3-] semimetals similar to isovalent GdN.
Treating the spin polarization within the 4f shell, and then averaging
consistent with the J=0 configuration, we estimate semimetallic band overlaps
(Eu 5d with pnictide 2p or 3p) of ~0.1 eV (EuN) and ~1.0 eV (EuP) that increase
(become more metallic) with pressure. The calculated bulk modulus is 130 (86)
GPa for EuN (EuP). Exchange (spin-spin) coupling calculated from correlated
band theory is small and ferromagnetic in sign for EuN, increasing in magnitude
with pressure. Conversely, the exchange coupling is antiferromagnetic in sign
for EuP and is larger in magnitude, but decreases with compression. Study of a
two-site model with S_1*S_2 coupling within the J=0,1 spaces of each ion
illustrates the dependence of the magnetic correlation functions on the model
parameters, and indicates that the spin coupling is sufficient to alter the Van
Vleck susceptibility. We outline a scenario of a spin-correlation transition in
a lattice of S=3, L=3, J=0 nonmagnetic ions
Heisenberg models and a particular isotropic model
The Heisenberg model, a quantum mechanical analogue of the Ising model, has a
large ground state degeneracy, due to the symmetry generated by the total spin.
This symmetry is also responsible for degeneracies in the rest of the spectrum.
We discuss the global structure of the spectrum of Heisenberg models with
arbitrary couplings, using group theoretical methods. The Hilbert space breaks
up in blocks characterized by the quantum numbers of the total spin, and
, and each block is shown to constitute the representation space of an
explicitly given irreducible representation of the symmetric group ,
consisting of permutations of the spins in the system.
In the second part of the paper we consider, as a concrete application, the
model where each spin is coupled to all the other spins with equal strength.
Its partition function is written as a single integral, elucidating its
-dependence. This provides a useful framework for studying finite size
effects. We give explicit results for the heat capacity, revealing interesting
behavior just around the phase transition.Comment: 16 pages LaTeX, one of the 2 figures included as a postscript file.
Oxford preprint OUTP-93-18S, to be published in Phys. Rev.
Thermal Casimir Force between Magnetic Materials
We investigate the Casimir pressure between two parallel plates made of
magnetic materials at nonzero temperature. It is shown that for real
magnetodielectric materials only the magnetic properties of ferromagnets can
influence the Casimir pressure. This influence is accomplished through the
contribution of the zero-frequency term of the Lifshitz formula. The
possibility of the Casimir repulsion through the vacuum gap is analyzed
depending on the model used for the description of the dielectric properties of
the metal plates.Comment: 9 pages, 3 figures. Contribution to the Proceedings of QFEXT09,
Norman, OK, September 21-25, 200
A generalization of the Heine--Stieltjes theorem
We extend the Heine-Stieltjes Theorem to concern all (non-degenerate)
differential operators preserving the property of having only real zeros. This
solves a conjecture of B. Shapiro. The new methods developed are used to
describe intricate interlacing relations between the zeros of different pairs
of solutions. This extends recent results of Bourget, McMillen and Vargas for
the Heun equation and answers their question on how to generalize their results
to higher degrees. Many of the results are new even for the classical case.Comment: 12 pages, typos corrected and refined the interlacing theorem
The Inhibition of Mixing in Chaotic Quantum Dynamics
We study the quantum chaotic dynamics of an initially well-localized wave
packet in a cosine potential perturbed by an external time-dependent force. For
our choice of initial condition and with small but finite, we find that
the wave packet behaves classically (meaning that the quantum behavior is
indistinguishable from that of the analogous classical system) as long as the
motion is confined to the interior of the remnant separatrix of the cosine
potential. Once the classical motion becomes unbounded, however, we find that
quantum interference effects dominate. This interference leads to a long-lived
accumulation of quantum amplitude on top of the cosine barrier. This pinning of
the amplitude on the barrier is a dynamic mechanism for the quantum inhibition
of classical mixing.Comment: 20 pages, RevTeX format with 6 Postscript figures appended in
uuencoded tar.Z forma
Quantum Dot Version of Berry's Phase: Half-Integer Orbital Angular Momenta
We show that Berry's geometrical (topological) phase for circular quantum
dots with an odd number of electrons is equal to \pi and that eigenvalues of
the orbital angular momentum run over half-integer values. The non-zero value
of the Berry's phase is provided by axial symmetry and two-dimensionality of
the system. Its particular value (\pi) is fixed by the Pauli exclusion
principle. Our conclusions agree with the experimental results of T. Schmidt
{\it at el}, \PR B {\bf 51}, 5570 (1995), which can be considered as the first
experimental evidence for the existence of a new realization of Berry's phase
and half-integer values of the orbital angular momentum in a system of an odd
number of electrons in circular quantum dots.Comment: 4 pages, 2 figure
On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)
In October 1924, the Physical Review, a relatively minor journal at the time,
published a remarkable two-part paper by John H. Van Vleck, working in virtual
isolation at the University of Minnesota. Van Vleck combined advanced
techniques of classical mechanics with Bohr's correspondence principle and
Einstein's quantum theory of radiation to find quantum analogues of classical
expressions for the emission, absorption, and dispersion of radiation. For
modern readers Van Vleck's paper is much easier to follow than the famous paper
by Kramers and Heisenberg on dispersion theory, which covers similar terrain
and is widely credited to have led directly to Heisenberg's "Umdeutung" paper.
This makes Van Vleck's paper extremely valuable for the reconstruction of the
genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did
not take the next step and develop matrix mechanics himself.Comment: 82 page
Thermodynamic perturbation theory for dipolar superparamagnets
Thermodynamic perturbation theory is employed to derive analytical
expressions for the equilibrium linear susceptibility and specific heat of
lattices of anisotropic classical spins weakly coupled by the dipole-dipole
interaction. The calculation is carried out to the second order in the coupling
constant over the temperature, while the single-spin anisotropy is treated
exactly. The temperature range of applicability of the results is, for weak
anisotropy (A/kT << 1), similar to that of ordinary high-temperature
expansions, but for moderately and strongly anisotropic spins (A/kT > 1) it can
extend down to the temperatures where the superparamagnetic blocking takes
place (A/kT \sim 25), provided only the interaction strength is weak enough.
Besides, taking exactly the anisotropy into account, the results describe as
particular cases the effects of the interactions on isotropic (A = 0) as well
as strongly anisotropic (A \to \infty) systems (discrete orientation model and
plane rotators).Comment: 15 pages, 3 figure
Spin versus Lattice Polaron: Prediction for Electron-Doped CaMnO3
CaMnO3 is a simple bi-partite antiferromagnet(AF) which can be continuously
electron-doped up to LaMnO3. Electrons enter the doubly degenerate E_g subshell
with spins aligned to the S=3/2 core of Mn^4+ (T_2g^3)$. We take the Hubbard
and Hund energies to be effectively infinite. Our model Hamiltonian has two E_g
orbitals per Mn atom, nearest neighbor hopping, nearest neighbor exchange
coupling of the S=3/2 cores, and electron-phonon coupling of Mn orbitals to
adjacent oxygen atoms. We solve this model for light doping. Electrons are
confined in local ferromagnetic (FM) regions (spin polarons) where there
proceeds an interesting competition between spin polarization (spin polarons)
which enlarges the polaron, and lattice polarization (Jahn-Teller polarons)
which makes it smaller. A symmetric 7-atom ferromagnetic cluster (Mn_7^27+) is
the stable result, with net spin S=2 relative to the undoped AF. The distorted
oxygen positions around the electron are predicted. The model also predicts a
critical doping x_c=0.045 where the polaronic insulator becomes unstable
relative to a FM metal.Comment: 9 pages with 7 embedded postscript figures and 2 table
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