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 $\pm{1/T}$ 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 $[001]$ 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 $g$-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)2_2]2_2 (Me = Mn, Fe, Co, Ni, Cu)

The electronic structure of Me[N(CN)$_2$]$_2$ (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