An exact magnetic-moment invariant of charged-particle gyromotion

For the motion of a charged particle in a uniform, time-dependent axial magnetic field B(t)e(z), it is shown that there is an exact magnetic-moment invariant of the particle dynamics M, to which the adiabatic magnetic-moment invariant mu = mv2 perpendicular/2B is asymptotic when the time scale of the magnetic field variation is much slower than the gyroperiod. The connection between the exact invariant M and the adiabatic invariant mu enables us to characterize in detail the robustness of the adiabatic magnetic-moment invariant mu.     

Local observables and particle statistics I

We consider the family of those states which become asymptotically indistinguishable from the vacuum for observations in far away regions of space. The pure states of this family may be subdivided into superselection sectors labelled by generalized charge quantum numbers. The principle of locality implies that within this family one may define a natural product composition (leading for instance from single particle states ton-particle states). Intrinsically associated with then-fold product of states of one sector there is a unitary representation ofP ⁽ⁿ⁾, the permutation group ofn elements, analogous in its role to that arising in wave mechanics from the permutations of the arguments of ann-particle wave function. We show that each sector possesses a statistics parameter which determines the nature of the representation ofP ⁽ⁿ⁾ for alln and whose possible values are 0, ±d ^–1 (d a positive integer). A sector with 0 has a unique charge conjugate (antiparticle states); if =d ^–1 the states of the sector obey para-Bose statistics of orderd, if =–d ^–1 they obey para-Fermi statistics of orderd. Some conditions which restrict to ± 1 (ordinary Bose or Fermi statistics) are given.     

Wormholes, Classical Limit and Dynamical Vacuum in Quantum Cosmology

First a Friedmann-Robertson-Walker (FRW)universe filled with dust and a conformally invariantscalar field is quantized. For the closed model we finda discrete set of wormhole quantum states. In the case of flat spacelike sections we find states withclassical behaviour at small values of the scale factorand quantum behaviour for large values of the scalefactor. Next we study a FRW model with a conformally invariant scalar field and a nonvanishingcosmological constant dynamically introduced byregarding the vacuum as a perfect fluid with equation ofstate p = –. The ensuing Wheeler-DeWittequation turns out to be a bona fide Schrodinger equation, andwe find that there are realizable states with a definitevalue of the cosmological constant. Once again we findfinite-norm solutions to the Wheeler-DeWitt equation with definite values of thecosmological constant that represent wormholes,suggesting that in quantum cosmological models with asimple matter content wormhole states are a commonoccurrence.     

Incompatibility of Bianchi Type III Space Time in Scale Invariant Theory

It is shown here that the development of scale invariant theory of gravitation is not possible when (a) the space time is governed by diagonal Bianchi type III metric (b) the gauge function depends on the time coordinate only (Dirac gauge) and (c) the energy momentum tensor is that of a perfect fluid.     

Study of the neutron quantum states in the gravity field

We have studied neutron quantum states in the potential well formed by the earths gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in the two lowest quantum states correspond to expectations with an experimental accuracy. A position-sensitive neutron detector with an extra-high spatial resolution of m was developed and tested for this particular experiment, to be used to measure the spatial density distribution in a standing neutron wave above a mirror for a set of some of the lowest quantum states. The present experiment can be used to set an upper limit for an additional short-range fundamental force. We studied methodological uncertainties as well as the feasibility of improving further the accuracy of this experiment.Received: 31 July 2004, Published online: 7 March 2005PACS: 03.65, 28.20 Correspondence to: V. Nesvizhevsky     

Direct and Inverse Cascades in Two-DimensionalTurbulence with a Generalized Enstrophy Invariant

Direct and reverse cascades are shown to be generic to two-dimensional turbulencewith a generalized enstrophy invariant Ü = 1/2|^2q|² dx = const, q 1/2. Theclassical hydrodynamical situation is a special case (q = 1) of thegeneral result.     

Neutral currents in deep inelastic νN scattering and γ emission

This paper analyzes the bremsstrahlung which occurs in the deep inelastic scattering of neutrinos by nucleons which is caused by an interaction of the neutral weak currents of neutrinos and quarks. The cross section for the reaction + q + + q (q is a quark) is calculated in lowest order in the constants of the electromagnetic and weak interactions. A detailed study is made of the behavior of the contributions to the bremsstrahlung cross section from various kinematic regions. An integration over the final states of the (q + @#@) system is carried out in an invariant manner. There is a violation of scaling in the deep inelastic scattering of neutrinos by nucleons because of radiation corrections.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 78–82, May, 1981.     

Metastable states and T=0 hysteresis in the random-field Ising model on random graphs

We study the ferromagnetic random-field Ising model on random graphs of fixed connectivity z (Bethe lattice) in the presence of an external magnetic field H. We compute the number of single-spin-flip stable configurations with a given magnetization m and study the connection between the distribution of these metastable states in the H-m plane (focusing on the region where the number is exponentially large) and the shape of the saturation hysteresis loop obtained by cycling the field between - and + at T=0. The annealed complexity A(m,H) is calculated for z=2,3,4 and the quenched complexity Q(m,H) for z=2. We prove explicitly for z=2 that the contour Q(m,H)=0 coincides with the saturation loop. On the other hand, we show that A(m,H) is irrelevant for describing, even qualitatively, the observable hysteresis properties of the system.     

Continuous spectrum in the ground state of two spin-1/2 models in the infinite-volume limit

We show that in the ground states of the infinite-volume limits of both the spin-1/2 anisotropic antiferromagnetic Heisenberg model (in dimensions d2), and the ferromagnetic Ising model in a strong transverse field (in dimensions d1) there is an interval in the spectrum above the mass gap which contains a continuous band of energy levels. We use the methods of Bricmont and Fröhlich to develop our expansions, as well as a method of Kennedy and Tasaki to do the expansions in the quantum mechanical limit. Where the expansions converge, they are then shown to have spectral measures which have absolutely continuous parts on intervals above the mass gaps.     

Conformal Transformations as Observables

C denotes either the conformal group in 3+1 dimensions, PSO(4, 2), or in one chiral dimension, PSL(2, ). Let U be a unitary, strongly continuous representation of C satisfying the spectrum condition and inducing, by its adjoint action, automorphisms of a von Neumann algebra . We construct the unique inner representation of the universal covering group of C implementing these automorphisms. satisfies the spectrum condition and acts trivially on any U-invariant vector. This means in particular: Conformal transformations of a field theory having positive energy are weak limit points of local observables. Some immediate implications for chiral subnets are given. We propose the name Borchers–Sugawara construction.     

Kinetics of positron annihilation in ionic crystals

A kinetic scheme of decay of positron and positronium states for the general case — a real ionic crystal with point lattice defects and a developed surface — is examined. The properties of positron and positronium states in the volume of the crystal, positron and positronium color centers, and surface positron and positronium states, are analyzed. It is shown that all the available experimental data qualitatively confirm the conclusion of an annihilation mechanism based on the postulated kinetic scheme of positron annihilation in real ionic crystals.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 50–55, September, 1977.     

Waves in nonlinear lattices: ultrashort optical pulses and Bose-Einstein condensates

The nonlinear Schr?dinger equation i (partial differential)(z)A(z,x,t)+(inverted Delta)(2)(x,t)A+[1+m(kappax)]|A|2A=0 models the propagation of ultrashort laser pulses in a planar waveguide for which the Kerr nonlinearity varies along the transverse coordinate x, and also the evolution of 2D Bose-Einstein condensates in which the scattering length varies in one dimension. Stability of bound states depends on the value of kappa=beamwidth/lattice period. Wide (kappa>1) and kappa=O(1) bound states centered at a maximum of m(x) are unstable, as they violate the slope condition. Bound states centered at a minimum of m(x) violate the spectral condition, resulting in a drift instability. Thus, a nonlinear lattice can only stabilize narrow bound states centered at a maximum of m(x). Even in that case, the stability region is so small that these bound states are "mathematically stable" but "physically unstable."     

Shell sources of stationary axisymmetric gravitational fields

A number of solutions for material shell sources of stationary axisymmetric gravitational fields are presented. Explicit solutions are found for shells lying on equipotential hypersurfaces (g _tt = const) and generating static monopole fields in prolate and oblate spheroidal coordinates (Zipoy-Voorhees fields). Numerical solutions are found for shells lying on hypersurfaces of constantg /g and generating Kerr- and Tomimatsu-Sato ( = 2) fields. The shells have minimum areas allowed by the energy conditions of Hawking and Ellis.     

Conformally Invariant Quantization at Order Three

Let (M, g) be a pseudo-Riemannian manifold and the space of densities of degree on M. Denote the space of differential operators from to of order k and S _k with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map . This result generalizes that of Duval and Ovsienko.     

Absence of long-range order in one-dimensional spin systems

For a one-dimensional Ising model with interaction energy $$E\left\{ \mu \right\} = - \sum\limits_{1 \leqslant i< j \leqslant N} {J(j - i)} \mu _\iota \mu _j \left[ {J(k) \geqslant 0,\mu _\iota = \pm 1} \right]$$ it is proved that there is no long-range order at any temperature when $$S_N = \sum\limits_{k = 1}^N {kJ\left( k \right) = o} \left( {[\log N]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } \right)$$ The same result is shown to hold for the corresponding plane rotator model when $$S_N = o\left( {\left[ {{{\log N} \mathord{\left/ {\vphantom {{\log N} {\log \log N}}} \right. \kern-\nulldelimiterspace} {\log \log N}}} \right]} \right)$$      

Abundance of translation invariant pure states on quantum spin chains

We construct a set of translation invariant pure states of a quantum spin chain, which is w -dense in the set of all translation invariant states of the chain. Each of the approximating states has exponential decay of correlations, and is the unique ground state of a finite range Hamiltonian with a spectral gap above the ground state energy.     

Boundary conditions for quantum mechanics on cones and fields around cosmic strings

We study the options for boundary conditions at the conical singularity for quantum mechanics on a two-dimensional cone with deficit angle 2 and for classical and quantum scalar fields propagating with a translationally invariant dynamics in the 1+3 dimensional spacetime around an idealized straight infinitely long, infinitesimally thin cosmic string. The key to our analysis is the observation that minus-the-Laplacian on a cone possesses a one-parameter family of selfadjoint extensions. These may be labeled by a parameterR with the dimensions of length—taking values in [0, ). ForR=0, the extension is positive. WhenR0 there is a bound state. Each of our problems has a range of possible dynamical evolutions corresponding to a range of allowedR-values. They correspond to either finite, forR=0, or logarithmically divergent, forR0, boundary conditions at zero radius. Non-zeroR-values are a satisfactory replacement for the (mathematically ill-defined) notion of -function potentials at the cone's apex.We discuss the relevance of the various idealized dynamics to quantum mechanics on a cone with a rounded-off centre and field theory around a true string of finite thickness. Provided one is interested in effects at sufficiently large length scales, the true dynamics will depend on the details of the interaction of the wave function with the cone's centre (/field with the string etc.) only through a single parameterR (its scattering length) and will be well-approximated by the dynamics for the corresponding idealized problem with the sameR-value. This turns out to be zero if the interaction with the centre is purely gravitational and minimally coupled, but non-zero values can be important to model nongravitational (or non-minimally coupled) interactions. Especially, we point out the relevance of non-zeroR-values to electromagnetic waves around superconducting strings. We also briefly speculate on the relevance of theR-parameter in the application of quantum mechanics on cones to 1+2 dimensional quantum gravity with massive scalars.     

Exact time correlation function for a nonlinearly coupled vibrational system

The time correlation function (t)=Re<[c(t), c (0)]>, which is related to the dipole spectrum and is the main focus of quantum molecular time scale generalized Langevin equation theory, is calculated for the Hamiltonian system in which a single oscillator is coupled by a nonlinear Davydov term to a chain of oscillators comprising a phonon heat bath. An exact expression for (t) is obtained. At long times we find that the time correlation function decays as a small power law atT=0K, but switches to exponential decay at higher temperature. This is a new result and bears on the long-standing issue of the existence of long-time tails.     

Chaotic Eigenfunctions in Phase Space

We study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann–Husimi representations for quantum states as well as their stellar parametrization, which encodes states through a minimal set of points in phase space (the constellation of zeros of the Husimi density). We rigorously prove that a semiclassical uniform distribution of Husimi densities on the torus entails a similar equidistribution for the corresponding constellations. We deduce from this property a universal behavior for the phase patterns of chaotic Bargmann eigenfunctions which is reminiscent of the WKB approximation for eigenstates of integrable systems (though in a weaker sense). In order to obtain more precise information on chaotic eigenconstellations, we then model their properties by ensembles of random states, generalizing former results on the 2-sphere to the torus geometry. This approach yields statistical predictions for the constellations which fit quite well the chaotic data. We finally observe that specific dynamical information, e.g., the presence of high peaks (like scars) in Husimi densities, can be recovered from the knowledge of a few long-wavelength Fourier coefficients, which therefore appear as valuable order parameters at the level of individual chaotic eigenfunctions.     

Enhanced Sensitivity to Variation of m(e)/m(p) in molecular spectra

We propose new experiments with high sensitivity to a possible variation of the electron-to-proton mass ratio mu identical with m(e)/m(p). We consider a nearly degenerate pair of molecular vibrational levels, each associated with a different electronic potential. With respect to a change in mu, the change in the splitting between such levels can be large both on an absolute scale and relative to the splitting. We demonstrate the existence of such pairs of states in Cs2, where the narrow spectral lines achievable with ultracold molecules make the system promising for future searches for small variations in mu.