On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Thermodynamic scaling theory for impurities in metals

A perturbative scaling theory for calculating static thermodynamic properties of arbitrary local impurity degrees of freedom interacting with the conduction electrons of a metal is presented. The basic features are developments of the ideas of Anderson and Wilson, but the precise formulation is new and is capable of taking into account band-edge effects which cannot be neglected in certain problems. Recursion relations are derived for arbitrary interaction Hamiltonians up to third order in perturbation theory. A generalized impurity Hamiltonian is defined and its scaling equations are derived up to third order. The strategy of using such perturbative scaling equations is delineated and the renormalization-group aspects are discussed. The method is illustrated by applying it to the single-impurity Kondo problem whose static properties are well understood.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Fluctuation Theory Of The Specific-Heat Of Normal Liquid-3He

The measured specific heat of normal liquid 3He shows a plateau for 0.15<1 K; below 0.15 K and above 1 K, it rises linearly with temperature. However, the slope on the high-temperature side is very much reduced compared with the free-Fermi-gas value. We explain these features through a microscopic, thermal spin- and density-fluctuation model. The plateau is due to spin fluctuations which have a low characteristic energy in 3He. Because of the low compressibility, the density fluctuations are highly suppressed; this leads to a reduced slope for CV(T) for high temperatures.

Information theory and resistance fluctuations in one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a distribution of maximum information entropy, constrained by the following physical requirements: (1) flux conservation, (2) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of ω, where R=exp(iω→⋅Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

Theory of freezing in simple systems

The transition parameters for the freezing of two one-component liquids into crystalline solids are evaluated by two theoretical approaches. The first system considered is liquid sodium which crystallizes into a body-centered-cubic (bcc) lattice; the second system is the freezing of adhesive hard spheres into a face-centered-cubic (fcc) lattice. Two related theoretical techniques are used in this evaluation: One is based upon a recently developed bifurcation analysis; the other is based upon the theory of freezing developed by Ramakrishnan and Yussouff. For liquid sodium, where experimental information is available, the predictions of the two theories agree well with experiment and each other. The adhesive-hard-sphere system, which displays a triple point and can be used to fit some liquids accurately, shows a temperature dependence of the freezing parameters which is similar to Lennard-Jones systems. At very low temperature, the fractional density change on freezing shows a dramatic increase as a function of temperature indicating the importance of all the contributions due to the triplet direction correlation function. Also, we consider the freezing of a one-component liquid into a simple-cubic (sc) lattice by bifurcation analysis and show that this transition is highly unfavorable, independent of interatomic potential choice. The bifurcation diagrams for the three lattices considered are compared and found to be strikingly different. Finally, a new stability analysis of the bifurcation diagrams is presented.

Sensing Shape Recovery Using Conductivity Noise in Thin Films of NiTi Shape Memory Alloys

Low frequency fluctuations in the electrical resistivity, or noise, have been used as a sensitive tool to probe into the temperature driven martensite transition in dc magnetron sputtered thin films of nickel titanium shape-memory alloys. Even in the equilibrium or static case, the noise magnitude was more than nine orders of magnitude larger than conventional metallic thin films and had a characteristic dependence on temperature. We observe that the noise while the temperature is being ramped is far larger as compared to the equilibrium noise indicating the sensitivity of electrical resistivity to the nucleation and propagation of domains during the shape recovery. Further, the higher order statistics suggests the existence of long range correlations during the transition. This new characterization is based on the kinetics of disorder in the system and separate from existing techniques and can be integrated to many device applications of shape memory alloys for in-situ shape recovery sensing.

Thermodynamic scaling theory for the two-impurity Anderson model

We present results of a study of the two-impurity Anderson model using a thermodynamic scaling theory developed recently. The model is characterized by the Coulomb energy U, the orbital energy epsilond, the d-level width Gamma, and the separation between impurities R. If Gamma<<−epsilond<cs maps onto that of the two-impurity Kondo problem, discussed by us elsewhere; the main difference is that the RKKY interaction can acquire an antiferromagnetic contribution with a (kFR)−2 envelope over a restricted range of kFR. In this case impurity-impurity interactions can be substantial. The other interesting case is when the impurities have a ''fluctuating valence'' with the singlet lying lower in energy, i.e., epsilond>~Gamma. Here we find that the single-impurity physics dominates the low-temperature behavior, and impurity-impurity interactions are perturbative. The qualitative features of the temperature-dependent susceptibility are discussed. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Critical-point Properties of Liquids and the Born-Green Theory

Recent work of Jones et al. giving the long-range behaviour of the pair correlation function is used to confirm that the critical ratio Pc/nckBTc = 1/2 in the Born-Green theory. This deviates from experimental results on simple insulating liquids by more than the predictions of the van der Waals equation of state. A brief discussion of conditions for thermodynamic consistency, which the Born-Green theory violates, is then given. Finally, the approach of the Ornstein-Zernike correlation function to its critical point behaviour is discussed within the Born-Green theory.

Gel growth and dielectric studies of K. Rb and Cs perchlorates

Single crystals of K, Rb and Cs perchlorates have been grown by the counter diffusion of the respective ions and CIO4 through the gel medium. Studies on nucleation, growth kinetics, morphological aspects and purity are discussed in this paper. The dielectric constant, ~b, as well as loss measured along the longest axis, exhibits an anomaly at the transition temperature, Tt, in all the three crystals. It is found that the peak values of Tt are approximately 800, 100 and 53 in K, Rb and Cs perchlorates, respectively. The dielectric anomaly and the large value of c b in the cubic phase are discussed in terms of the degree of disorder of the CIO~ group and the possible contribution from defects.

Coupled amplitude theory of nonlinear surface acoustic waves

The nonlinear propagation characteristics of surface acoustic waves on an isotropic elastic solid have been studied in this paper. The solution of the harmonic boundary value problem for Rayleigh waves is obtained as a generalized Fourier series whose coefficients are proportional to the slowly varying amplitudes of the various harmonics. The infinite set of coupled equations for the amplitudes when solved exhibit an oscillatory slow variation signifying a continuous transfer of energy back and forth among the various harmonics. A conservation relation is derived among all the harmonic amplitudes.

On the propagation of a weak shock front: Theory and application

In this paper the kinematics of a weak shock front governed by a hyperbolic system of conservation laws is studied. This is used to develop a method for solving problems, involving the propagation of nonlinear unimodal waves. It consists of first solving the nonlinear wave problem by moving along the bicharacteristics of the system and then fitting the shock into this solution field, so that it satisfies the necessary jump conditions. The kinematics of the shock leads in a natural way to the definition of ldquoshock-raysrdquo, which play the same role as the ldquoraysrdquo in a continuous flow. A special case of a circular cylinder introduced suddenly in a constant streaming flow is studied in detail. The shock fitted in the upstream region propagates with a velocity which is the mean of the velocities of the linear and the nonlinear wave fronts. In the downstream the solution is given by an expansion wave.

Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.