Rate equations in the hopping transport

The rate equation formulation of the hopping transport problem is analyzed in detail. It is shown that the usual form of the rate equations for the system of electrons in localized states interacting with phonons is incorrect in the dc limit. A generalized form of the rate equations is derived. Both usual solution and that one corresponding to the result ofKasuya andKoide for the dc conductivity are shown to solve these equations. However, the former one is shown to be improper from the physical point of view as well as from the point of view of a (for a given model) exact asymptotic identity derived. For high frequencies, both forms of the rate equations are shown to be indistinguishable.     

Bihamiltonian structures and Stäckel separability

It is shown that a class of Stäckel separable systems is characterized in terms of a Gel’fand–Zakharevich bihamiltonian structure. This structure arises as an extension of a Poisson–Nijenhuis structure on phase space. It is also shown that the Casimir of the Gel’fand–Zakharevich bihamiltonian structure provides the family of commuting Killing tensors found by Benenti and that, because of Eisenhart’s theorem, characterize orthogonal separability. It is also shown that recently found properties of quasi-bihamiltonian systems are natural consequences of the geometry of the extension of the Poisson–Nijenhuis structure.     

Deformations of 2k-Einstein structures

It is shown that the space of infinitesimal deformations of 2k-Einstein structures is finite dimensional on compact non-flat space forms. Moreover, spherical space forms are shown to be rigid in the sense that they are isolated in the corresponding moduli space.     

Solution of the Dirac Equation on the Bertotti–Robinson Metric

It is shown that each component of the Dirac field satisfies a decoupled equation, which admits separable solutions, when the background spacetime is the Bertotti–Robinson metric, which is a solution of the Einstein vacuum field equations with a cosmological constant. Furthermore, the seperated functions appearing in the solutions are shown to obey identities of the Teukolsky–Starobinsky type and the separable solutions are shown to be eigenfunctions of a certain differential operator.     

The Lewis metric and flat space-time

It is shown that the stationary solution of the Einstein equationsin vacuo, with the cylindrical symmetry obtained by Lewis, does not contain a space-time that is globally Minkowskian. It is shown that the inclusion of a certain constant of integration excludes this flat space-time metric.     

Models of the axiomatic theory associated with the lattice of subspaces of a finite-dimensional Hilbert space

It is shown that we can associate with the latticeL of subspaces of a separable Hilbert space an axiomatic theory in sentential logic that reflects some of the basic properties of the simplest types of experimental reports in quantum mechanics. It is also shown that every collection of mutually nonorthogonal elements ofL determines a model of the axioms and that, if the Hilbert space is finite dimensional, every model is determined this way.     

Direct processes in heavy ion collisions at E ⩽ 20 MeV/u

Elastic and inelastic scattering at projectile energies of E ? 20 MeV/u have been studied using a magnetic spectrometer. It is shown that nuclear rainbow scattering for ¹²C + ¹²C allows to extract information from small inter nuclear distances. The role of the collective inelastic excitations is studied and it is shown that they lead to a decomposition of the projectile (or target)if the threshold for particle emission is close to the excitation energy of low lying collective states. The origin of the continuous background in the study of high lying excitations in nuclei is studied and it is shown that it can be analysed quantitatively.     

Gravitational radiation,radiation damping,and the fast-motion approximation

The sign of the gravitational energy radiated by a material system, as calculated by one or another appropriate stress-energy pseudotensor, is shown always to be positive. A fastmotion approximation that finds this quantity to be negative is shown to violate one of the conditions that ensure its positivity. As a consequence the calculation based on this approximation is shown to neglect terms of the same order (G ²) as it retains.     

Loss reduction of dielectric-coated metallic hollow waveguides for CO2 laser light transmission

A condition for reducing transmission loss of a dielectric-coated metallic hollow waveguide is shown theoretically when the inner metallic surface is not perfect. It is also shown that the transmission loss for CO₂ laser light is 10.6 μm wavelength is able to be estimated from an attenuation spectrum of a short waveguide. By fabricating a ZnSe coated Ag hollow waveguide of short length, we have shown that it has a lower loss than a Ge coated waveguide for CO₂ laser light.     

Dynamical Breaking of Supersymmetry and Its Restoration at High Temperatures

The dynamical breaking of the supersymmetric Higgs model is discussed without adding the Fayet—Iliopoulos term to the Lagrangian. It is shown, in terms of the Nambu—Jona-Lasinio mechanism, that the supersymmetry breaking can be realized dynamically in the supersymmetric Higgs model. The supersymmetry behavior at finite temperatures is also investigated and it is shown that the supersymmetry broken dynamically at zero temperature can be restored at finite temperatures.     

The topology of geodesically complete space-times

Two theorems are given on the topology of geodesically complete space-times which satisfy the energy condition. Firstly, the condition that a compact embedded 3-manifold in space-time be dentless is defined in terms of causal structure. Then it is shown that a dentless 3-manifold must separate space-time, and that it must enclose a compact portion of space-time. Further, it is shown that if the dentless 3-manifold is homeomorphic toS ³ then the part of space-time that it encloses must be simply connected.     

Moufang plane and octonionic Quantum Mechanics

It is shown that the usual axioms of one-particle Quantum Mechanics can be implemented with projection operators belonging to the exceptional Jordan algebraJ ₈ ³ over real octonions. Certain lemmas on these projection operators are proved by elementary means. Use is made of the Moufang projective plane. It is shown that this plane can be orthocomplemented and that there exists a unique probability function. The result of successive, compatible experiments is shown not to depend on the order in which they are performed, in spite of the non-associativity of octonion multiplication. The algebra of observables and the action of the exceptional groupF ₄ is studied, as well as a possible relation with the color group SU(3) and quark confinement.Work supported by the Swiss National Science Foundation     

Conditions for the existence of double resonance effects in Raman scattering

The condition for the existence of Double Resonance effects in Raman scattering are analyzed. It is shown that the existence of points in the electronic momentum space for which both denominators in the expression for Raman scattering vanish is not sufficient. Based on this analysis, it is shown that double resonance effects cannot show up in Resonant Raman scattering in the vicinity of the E₁ point in InSb.     

The use of the CNDO method in spectroscopy : Naphthalene and the breakdown of the pairing theorems

It is shown that CNDO/S calculations provide 6 significant figures of accuracy in the energies of configurations, and 4 significant figures after configuration interaction. The pairing theorem is shown not to hold in the CNDO/S method since all F_μν are calculated and since the F_μμ are not constant. It is further shown that the degeneracies required by the pairing theorem are not even approximated in naphthalene. Finally, using absorption and emission spectroscopic measurements, including triplet-triplet and excited singlet-singlet absorptions, the spectroscopic states of naphthalene are discussed in detail.     

No effect of Majorana phases in neutrino oscillations

It is shown that the Majorana phases of the neutrino mixing matrix cannot have any effect in neutrino oscillations, contrary to the argument presented in arXiv:0912.5266. It is also shown that in a charged–current weak interaction process it is not possible to create a coherent superposition of different flavor neutrinos which is independent of the associated charged leptons.     

The spontaneous coherent state transition in the ϕ4-field model with an image mass

It is shown, that in the ?⁴-field model with an image mass (μ²<0) the phase transition is a spontaneous coherent state (SCS) phase transition. The connection between the spontaneous symmetry breaking, the coherent state and the phenomenological Ginzburg-Landau theory is shown.     

Universal Character of Stochastic Resonance and a Constructive Role of White Noise

It is shown that, in spite of claims put forward in the literature, the stochastic resonance (SR) appears even in linear systems—both overdamped and inertial—driven by Gaussian white noise, and even after averaging the asymptotics over the initial phase of the input signal. This supports recent suggestions that SR is a universal effect present in every stochastic process modulated by external signals. It is also shown that the noise may sustain the output signal which otherwise would vanish exponentially in the course of time.     

Penetration of a low-pressure reflex-discharge plasma into a hollow electrode

It is shown experimentally that the plasma of a hollow-cathode reflex discharge is characterized by a nonequilibrium electron velocity distribution. The parameters of the electron distribution, which is approximated by a superposition of two Maxwellian distributions with different temperatures, are estimated. The penetration of the discharge plasma into the hollow cathode at various cathode potentials and a gas pressure of ∼10^{\t− 2} Pa is studied. It is shown that the plasma parameters in the hollow electrode depend not only on the parameters of the reflex-discharge plasma, but also on the magnitude and configuration of the magnetic and electric fields in the plasma expansion region. It is shown that the plasma penetration can be accompanied by quasineutrality violation and the formation of space-charge double layers. Experiments confirm that the ion current from the nonequilibrium plasma exceeds the Bohm current.     

Degenerate Integrability of the Spin Calogero–Moser Systems and the Duality with the Spin Ruijsenaars Systems

It is shown that spin Calogero–Moser systems are completely integrable in a sense of degenerate integrability. Their Liouville tori have dimension less than half of the dimension of the phase space. It is also shown that rational spin Ruijsenaars systems are degenerately integrable and dual to spin Calogero–Moser systems in a sense that action-angle variables of one are angle-action variables of the other.     

Undamped self-oscillations and dynamical chaos under conditions of impurity breakdown of a semiconductor in the fixed-current regime

It is shown theoretically that chaotic oscillations of the Hall field, the Hall constant, and the magnetoresistance appear in a compensated semiconductor under impurity breakdown conditions. It is shown that the transition to chaos occurs via the Feigenbaum scenario. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 340–343 (10 March 1998)