The absorption edges of GeS and Urbach's rule

The low-energy absorption tail of the E∥a exciton in GeS obeys Urbach's rule over at least three orders of magnitude in absorption coefficient for 4.2 ? T ? 240 K. The E∥b polarization (for which no exciton is observed) does not obey Urbach's rule. The E∥a Urbach edge is caused by interactions between the excitons and a 8.7 meV rigid-layer vibrational mode. Our results are consistent with Sumi and Toyazawa's theory of the Urbach edge, and inconsistent with the models of Dow, Redfield and Skettrup. The absorption edge of GeS is confirmed as a direct edge.     

Nonlinear superposition rule for Abel's equation

A nonlinear superposition rule for Abel's cubic differential equation involving four particular solutions can be replaced by a superposition rule involving only two particular solutions. Chiellini's restrictions on the particular solutions are found to be satisfied.     

Hume-Rothery's 15% rule and the pseudo-alloy-atom model

The total binding energies of Na, K, Rb, Cs and their mutual binary alloys were calculated by the pseudo alloy atom model. From the calculated values of heat of solution, Hume-Rothery's so-called 15% rule on the atomic size factors of primary solid solutions was justified.     

On the physical sense of Planck's quantum and the problem of divergencies

Starting from the hypothesis of a material carrier of the EMF, the Planck formula E = hv is generalized, statistical sense is ascribed to the Planck action quantum, and a general scheme is proposed for removing the divergencies in QFT.     

A computation of Adler's β sum rule

We try to check Adler's β sum rule for q² = μ². The integral of β can be divided into two parts: a first part which, if q² = μ², involves only an integral of the experimental πN cross section, and a second one which is a priori of order μ² compared to the first. This second term can be approximated by an explicit calculation of the $\text{N}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext><mtext>3</mtext><mtext>2</mtext>}}{}^1$ contribution in the framework of Adler's model for the $\text{ν}\text{N}\text{→ μ}\text{N}{}^1$ reactions. The sum rule is not too well balanced and different hypotheses are presented to explain the defect.     

Self-consistent many-body theory for the standard basis operator Green's functions

We propose a self-consistent many-body theory for the standard basis operator Green's functions and obtain an exact Dyson-type matrix equation for the interacting many-level systems. A zeroth order approximation, which neglects all the damping effects, is investigated in detail for the anisotropic Heisenberg model, the isotropic quadrupolar system and the Hubbard model. In the case of the anisotropic Heisenberg ferromagnet with both exchange and single-ion anisotropy the low-temperature renormalization of the spin-waves for the uniaxial ordering agrees with the Bloch-Dyson theory. For the spin-1 easy-plane ferromagnet, the critical parameters for the phase transition at zero temperature are determined and compared with other theories. The elementary excitation spectrum of the spin-1 isotropic quadrupolar system is calculated and compared with the random phase approximation and Callen-like decoupling schemes. Finally, the theory is applied to the study of the single-particle excitation spectrum of the Hubbard model.     

A computation of Adler's β sum rule II

We improve our previous calculation of Adler's β sum rule by including the Born contributions to the πN states. The result is that the sum rule is only balanced if the weak axial nucleon form factor g_A(q²) and the strong pion-nucleon form factor have roughly the same q² dependance.     

Deviations of Matthiessen's rule in some PdAu alloys

The low temperature electrical resistivity of Pd_1?cAu_c alloys (c = 0.1, 0.22, 0.38, 0.69, 0.82 and 1.1 at.%) have been studied in detail between 1.5 and 300 K. Deviations from Matthiessen's rule (DMR) have been analysed on the basis of a two-band model, and the agreement is found to be reasonably good. The parameter λ was found to decrease monotonically with temperature, and no anomalous maximum was observed as with earlier studies of $\text{Pd}$Ti. The variation of β shows a weak temperature dependence. The limitations of the model are also discussed.     

Electron-dislocation scattering and negative deviations from matthiessen's rule

It is shown that the negative deviations from Matthiessen's rule observed recently for the electrical resistivity of Al and of Ag can be explained quantitatively by including the effect of anisotropic electron-dislocation scattering.     

Breakdown of Kohler's rule in Indium at low temperatures

Precise measurements of the transverse magnetoresistivity of pure samples of Indium between 3.4° and 7.8°K show that Kohler's rule is not strictly valid. Deviations from Kohler's rule occur even when the analysis is restricted to data obtained for a single sample in small magnetic fields.     

Itô's formula is the chain rule with wick ordering

Non-commutative stochastic integrals are defined using exponential vectors in Fock space. It is shown that the generalisation of Itô's formula is essentially the ordinary chain rule, combined with Wick ordering.     

Breakdown of Matthiessen's rule in high purity aluminum based alloys

Deviations from Matthiessen's rule were measured for dilute alloys of Al with Mg. The concentration of the alloyed elements varied from 0.03 to 1.0 at.%. The results were compared with other experimental results and discussed with respect to the relevant theoretical models.     

On Milne's quantum number function

The quantum number function N(E) introduced by Milne is studied in detail. It is shown that N(E) is not uniquely defined for energies different from the bound state values. The density of states $\text{d}\text{N}\text{d}\text{E}$ is nowhere unique and not necessarily positive.     

On converse to Koopman's Lemma

Koopman's Lemma states that if a flow T_t is measure preserving for a measure μ on a constant energy surface Ω, then the flow generates a one parameter family of unitary operators U_t on L² (Ω, μ). We show here a converse, namely that under certain (physically motivated) conditions a unitary operator family U_t can be made to generate a corresponding underlying family T_t of point transformations. This result comes out of questions of independent interest in the study of relationships between reversibility and irreversibility, and has application to the foundations of statistical mechanics. In particular, it establishes the principle often used intuitively in chemistry that a forward moving (e.g., Markov) process that loses information cannot be reversed. In a different setting, it provides the answer to a question in the representation theory of isometries on L^p spaces a Banach-Lamperti theorem). These results also allow an interesting reformulation of Ornstein's isomorphism theorem on Bernoulli systems.     

On Synge's covariant conservation laws for general relativity

Following Synge, the covariant formulas for the total four-momentum and angular momentum of an isolated physical system in general relativity are derived. These formulas are first obtained in the weak-field approximation, for which they are shown to be expressible in surface integral form, to be unique, and to represent covariantly conserved quantities. The covariant expressions for the general case are then shown to be identical to those for the weak-field case. The uniquely determined and covariantly conserved quantities so obtained are found to agree with the corresponding canonical, noncovariant surface integral expressions.     

On the semiclassical green's function in the energy-representation

We present a detailed discussion of the semiclassical approximation for the Green's function in the energy representation, G(qⁱ,q^j; E). In particular, we describe the way in which classical catastrophes influence the semiclassical approximation, and present a practical scheme to determine the phases with which the contributions due to the various classical trajectories enter the semiclassical result.     

Gribov's Reggeon calculus: Its physical basis and implications

The equations of Gribov's Reggeon calculus and the cutting rules of Abramovskii, Gribov and Kancheli are derived from the assumption that processes involving large virtual masses are damped. The discussion is carried out entirely in the s channel and no use is made of the details of any particular field theory. Both the mathematical development and the physical picture which evolves rest on the assumed multiperipheral origin of Regge behavior.     

Matthiessen's rule and its variation for cyclotron resonance width in two and three dimensions

Based on the proper connected diagram expansion, we calculated cyclotron resonance widths Γ_n associated with neighboring Landau states (n, n +1) for free electrons in interaction with more than one kind of impurities. In 3D usual Matthiessen's rule Γ_n=Γ⁽¹⁾_n+Γ⁽²⁾_n+…where Γ⁽ⁱ⁾_n represent widths calculated separately for each kind, is obtained. In 2D a new rule: is obtained.