132 research outputs found
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
Influence of radiative damping on the optical-frequency susceptibility
Motivated by recent discussions concerning the manner in which damping
appears in the electric polarizability, we show that (a) there is a dependence
of the nonresonant contribution on the damping and that (b) the damping enters
according to the "opposite sign prescription." We also discuss the related
question of how the damping rates in the polarizability are related to
energy-level decay rates
Canonical Transformations and Path Integral Measures
This paper is a generalization of previous work on the use of classical
canonical transformations to evaluate Hamiltonian path integrals for quantum
mechanical systems. Relevant aspects of the Hamiltonian path integral and its
measure are discussed and used to show that the quantum mechanical version of
the classical transformation does not leave the measure of the path integral
invariant, instead inducing an anomaly. The relation to operator techniques and
ordering problems is discussed, and special attention is paid to incorporation
of the initial and final states of the transition element into the boundary
conditions of the problem. Classical canonical transformations are developed to
render an arbitrary power potential cyclic. The resulting Hamiltonian is
analyzed as a quantum system to show its relation to known quantum mechanical
results. A perturbative argument is used to suppress ordering related terms in
the transformed Hamiltonian in the event that the classical canonical
transformation leads to a nonquadratic cyclic Hamiltonian. The associated
anomalies are analyzed to yield general methods to evaluate the path integral's
prefactor for such systems. The methods are applied to several systems,
including linear and quadratic potentials, the velocity-dependent potential,
and the time-dependent harmonic oscillator.Comment: 28 pages, LaTe
Phonon Hall effect in ionic crystals in the presence of static magnetic field
We study phonon Hall effect (PHE) for ionic crystals in the presence of
static magnetic field. Using Green-Kubo formula, we present an exact
calculation of thermal conductivity tensor by considering both positive and
negative frequency phonons. Numerical results are shown for some lattices such
as hexagonal lattices, triangular lattices, and square lattices. We find that
the PHE occurs on the nonmagnetic ionic crystal NaCl, although the magnitude is
very small which is due to the tiny charge-to-mass ratio of the ions. The
off-diagonal thermal conductivity is finite for nonzero magnetic field and
changes sign for high value of magnetic field at high temperature. We also
found that the off-diagonal thermal conductivity diverges as at low
temperature
The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics
The analysis of this article is entirely within classical physics. Any
attempt to describe nature within classical physics requires the presence of
Lorentz-invariant classical electromagnetic zero-point radiation so as to
account for the Casimir forces between parallel conducting plates at low
temperatures. Furthermore, conformal symmetry carries solutions of Maxwell's
equations into solutions. In an inertial frame, conformal symmetry leaves
zero-point radiation invariant and does not connect it to non-zero-temperature;
time-dilating conformal transformations carry the Lorentz-invariant zero-point
radiation spectrum into zero-point radiation and carry the thermal radiation
spectrum at non-zero temperature into thermal radiation at a different
non-zero-temperature. However, in a non-inertial frame, a time-dilating
conformal transformation carries classical zero-point radiation into thermal
radiation at a finite non-zero-temperature. By taking the no-acceleration
limit, one can obtain the Planck radiation spectrum for blackbody radiation in
an inertial frame from the thermal radiation spectrum in an accelerating frame.
Here this connection between zero-point radiation and thermal radiation is
illustrated for a scalar radiation field in a Rindler frame undergoing
relativistic uniform proper acceleration through flat spacetime in two
spacetime dimensions. The analysis indicates that the Planck radiation spectrum
for thermal radiation follows from zero-point radiation and the structure of
relativistic spacetime in classical physics.Comment: 21 page
Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation
It is pointed out that relativistic classical electron theory with classical
electromagnetic zero-point radiation has a scaling symmetry which is suitable
for understanding the equilibrium behavior of classical thermal radiation at a
spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical
electron theory, the masses of the particles are the only scale-giving
parameters associated with mechanics while the action-angle variables are scale
invariant. The theory thus separates the interaction of the action variables of
matter and radiation from the scale-giving parameters. Classical zero-point
radiation is invariant under scattering by the charged particles of
relativistic classical electron theory. The basic ideas of the matter
-radiation interaction are illustrated in a simple relativistic classical
electromagnetic example.Comment: 18 page
Tunneling with dissipation and decoherence for a large spin
We present rigorous solution of problems of tunneling with dissipation and
decoherence for a spin of an atom or a molecule in an isotropic solid matrix.
Our approach is based upon switching to a rotating coordinate system coupled to
the local crystal field. We show that the spin of a molecule can be used in a
qubit only if the molecule is strongly coupled with its atomic environment.
This condition is a consequence of the conservation of the total angular
momentum (spin + matrix), that has been largely ignored in previous studies of
spin tunneling.Comment: 4 page
Spin-Lattice Relaxation in Si Quantum Dots
We consider spin-lattice relaxation processes for electrons trapped in
lateral Si quantum dots in a inversion layer. Such dots are
characterized by strong confinement in the direction perpendicular to the
surface and much weaker confinement in the lateral direction. The spin
relaxation is assumed to be due to the modulation of electron -factor by the
phonon-induced strain, as was shown previously for the shallow donors. The
results clearly indicate that the specific valley structure of the ground
electron state in Si quantum dots causes strong anisotropy for both the
one-phonon and two-phonon spin relaxation rates. In addition, it gives rise to
a partial suppression of the two-phonon relaxation in comparison to the spin
relaxation of donor electrons.Comment: RevTex file, 3 PS figure
Electronic Structure of Transition-Metal Dicyanamides Me[N(CN)] (Me = Mn, Fe, Co, Ni, Cu)
The electronic structure of Me[N(CN)] (Me=Mn, Fe, Co, Ni, Cu)
molecular magnets has been investigated using x-ray emission spectroscopy (XES)
and x-ray photoelectron spectroscopy (XPS) as well as theoretical
density-functional-based methods. Both theory and experiments show that the top
of the valence band is dominated by Me 3d bands, while a strong hybridization
between C 2p and N 2p states determines the valence band electronic structure
away from the top. The 2p contributions from non-equivalent nitrogen sites have
been identified using resonant inelastic x-ray scattering spectroscopy with the
excitation energy tuned near the N 1s threshold. The binding energy of the Me
3d bands and the hybridization between N 2p and Me 3d states both increase in
going across the row from Me = Mn to Me = Cu. Localization of the Cu 3d states
also leads to weak screening of Cu 2p and 3s states, which accounts for shifts
in the core 2p and 3s spectra of the transition metal atoms. Calculations
indicate that the ground-state magnetic ordering, which varies across the
series is largely dependent on the occupation of the metal 3d shell and that
structural differences in the superexchange pathways for different compounds
play a secondary role.Comment: 20 pages, 11 figures, 2 table
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