Computing the KAC determinant using dual model techniques and more about the no-ghost theorem

We relate some mathematical results concerning the Virasoro algebra to properties of dual models. Specifically, we show how to compute the Kac determinant using well known techniques from dual models. Then we use the Kac formula to discuss the validity of the no-ghost theorem of dual models in a more general setting than the original proofs of that theorem.     

Prediction of the acoustic form function by neural network techniques for immersed tubes

A new approach is used to predict the acoustic form function (FF) for an infinite length cylindrical shell excited perpendicularly to its axis using the artificial neural network (ANN) techniques. The Wigner-Ville distribution is used like a comparison tool between the FF calculated by the analytical method and that predicted by the ANN techniques for a stainless steel tube. During the development of the network, several configurations are evaluated for various radius ratios ba (a: outer radius: b: inner radius of the tube). The optimal model is a network with one hidden layer. It is able to predict the FF with a mean relative error about 1.61% for the cases studied in this paper.     

Brillouin's theorem and the Hellmann-Feynman theorem for Hartree-Fock wave functions

It is shown that there is an intimate relation between the Hellmann-Feynman theorem and Brillouin's theorem. A more general form of Brillouin's theorem is provided, which applies to excited states of arbitrary symmetry and multiplicity. This new form leads to a simple proof of the Hellmann-Feynman theorem. This theorem is valid when all the orbitals that occur in the wave function are determined by a complete, and not a partial, variational procedure. Arguing in the opposite direction it is shown that the complete satisfaction of the generalized Brillouin's theorem provides an alternative scheme for obtaining the Hartree-Fock orbitals.     

Hydrodynamics and the fluctuation theorem

The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the probabilities of observing entropy-producing and entropy-consuming fluctuations measured over a finite volume and time span in terms of the rate of entropy production in the system, the measurement volume, and time. We study the fluctuation theorem in computer simulations of planar shear flow. The simulations are performed by employing the method of multiparticle collision dynamics, which captures both thermal fluctuations and hydrodynamic interactions. The main outcome of our analysis is that the fluctuation theorem is verified at any averaging time provided that the measurement volume exhibits a specific dependence on a hydrodynamic time scale.     

An application of boson second quantization techniques to the calculation of electron scattering form factors

It is suggested that boson second quantization, in terms of harmonic oscillator bosons, may be much more useful than its fermion counterpart for shell-model calculations in an LS coupled basis. The bosons carry the fundamental representation of SU(3). The combined set of boson creation and annihilation operators also carry the fundamental representation of Sp(3, R). Boson second quantization therefore provides a mechanism for expressing operators in terms of SU(3) and Sp(3, R) irreducible tensors. This is of major importance for shell-model calculations in an SU(3) basis and for the development of the symplectic shell model. Applications are made to the calculation of electron scattering form factors and it is shown how major simplifications arise when the space is restricted to a single major shell. For example, longitudinal form factors for 0 → 2 transitions in the sd-shell are shown to depend on just three parameters while the corresponding transverse form factors are uniquely determined up to an overall multiplicative constant. Further simplifications result on restriction to a single SU(3) irreducible representation.     

Quadratic Lagrangians and massive gravitons

An expansion of a quadratic Lagrangian in a series in small corrections to a flat metric yields the Lagrangian of the free gravitational field (first term of the expansion); by a substitution of the field variables this is reduced to a sum of standard Lagrangians that define massless and massive scalar and tensor fields. Independent variation of the corresponding Lagrangian with respect to the massive scalar and tensor gravitational fields is possible only if the coupling constants in the quadratic Langrangian satisfy a certain relation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 15–20, June, 1975.I thank Professor D. D. Ivanenko for his constant interest.     

Quadratic spin-orbit forces and the deuteron magnetic moment

The contribution to the deuteron magnetic moment due to L-dependent components of the two-nucleon force is discussed and evaluated for several potential models. The Reid soft core potential is expressed as a sum of central, tensor, spin-orbit, L² and Q₁₂ forces and it is argued that this choice of components has a number of advantages.     

Kinesin and the Crooks fluctuation theorem

The thermal efficiency of the kinesin cycle at stalling is presently a matter of some debate, with published predictions ranging from 0 [Phys. Rev. Lett. 99, 158102 (2007); Phys. Rev. E 78, 011915 (2008)] to 100% [in Molecular Motors, edited by M. Schliwa (Wiley-VCH Verlag GmbH, Weinheim (2003), p. 207]. In this note we attemp to clarify the issues involved. We also find an upper bound on the kinesin efficiency by constructing an ideal kinesin cycle to which the real cycle may be compared. The ideal cycle has a thermal efficiency of less than one, and the real one is less efficient than the ideal one always, in compliance with Carnot’s theorem.     

Supersymmetry and the Atiyah-Singer index theorem

Using a recently introduced index for supersymmetric theories, we present a simple derivation of the Atiyah-Singer index theorem for classical complexes and itsG-index generalization using elementary properties of quantum mechanical supersymmetric systems.     

Wavefunction collapse and the optical theorem

The optical theorem is examined and shown to be compatible with the possibility of wavefunction collapse at the level of particle-particle interactions.     

Quadratic spatial solitons

Quadratic spatial solitons, beams that propagate unchanged in shape and magnitude, are supported by second order optical nonlinearities and can occur in all wave mixing processes under appropriate conditions. They are multi-component, consisting of all the frequency components that are coupled by a second order nonlinear interaction near a phase-matching condition. They have been observed in a number of bulk crystalline media, in LiNbO₃ slab waveguides and in arrays of parallel, weakly coupled, LiNbO₃ channel waveguides. The properties of the solitons and their excitation will be reviewed. To cite this article: G.I. Stegeman, C. R. Physique 8 (2007).     

Compact space-times and the no-return theorem

It is shown that, as a consequence of the no-return theorem of Tipler, a generic non-spacelike convergent compact space-time cannot admit a closed embedded edgeless spacelike hypersurface. Such a space-time cannot therefore be spatially isotropic and so cannot provide a satisfactory model of the universe.     

Exchange algebra and the Drinfeld-Sokolov theorem

We analyse the relation between the exchange algebra and the separation of the chiralities in classical Toda field theory. We show that there exists a conformally covariant Bloch wave basis such that the two chiralities commute. In terms of this basis we then reconstruct the periodic and local solution of Toda field theory.Work supported by Fondazione Angelo Della Riccia     

Intermittency and the central limit theorem

Central limit theorem estimates of anomalous fractal dimensions of self-similar random cascades are studied. It is found that, in general, the normal approximation fails badly. A systematic series of approximations which converges to the exact result (both for the fractal dimensions and for the distribution itself) is derived for the -model. Consequences for the empty bin effect are indicated.Supported by the World Laboratory/HED and the CERN/LAA Projects     

Nonextensive thermostatistics and the H theorem

The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the "molecular chaos hypothesis." For q>0, the q-transport equation satisfies an H theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' q-nonextensive velocity distribution.