Hamiltonian formulation of the modified Hasegawa–Mima equation

We derive the Hamiltonian structure of the modified Hasegawa–Mima equation from the ion fluid equations applying Dirac's theory of constraints. We discuss the Casimirs obtained from the corresponding Poisson structure.     

Cosmologies with variable Newton's “constant”

We discuss cosmologies where the Planck length is not a fundamental constant but rather evolves with time. The dynamics which should be responsible for today's tiny value of this length scale are governed by the effective potential of a Brans-Dicke type theory. Qualitative properties of this potential depend on the short distance behaviour of the unifying fundamental theory. We discuss criteria for the asymptotic behaviour of realistic cosmologies and show that the role of a possible cosmological constant is quite different from the case of standard cosmology.     

Spontaneous Symmetry Breaking and Higgs' Mechanism in the Nonsymmetric Jordan-Thiry Theory

In the paper we construct the nonsymmetric Jordan-Thiry theory unifying Moffat's theory of gravitation, the Yang-Mills' field, the Higgs' fields and scalar forces in a geometric manner. We discuss spontaneous symmetry breaking, the Higgs' mechanism and mass generation in the theory. The scalar field Ψ (as in classical Jordan-Thiry theory) is connected to the effective gravitational constant. This field is massive and has Yukawa-type behavior. We discuss the relation between R₊ invariance and U(1)_F from G. U. T. within Einstein λ-transformation, and fermion number conservation. In this way we connect W _μ-field from nonsymmetric theory of gravitation with a gauge field A from G. U. T. We derive the equation of motion for a test particle from conservation laws in the hydrodynamic limit.     

Irreversibility and nonlocality

We discuss and illustrate the fact that the second law of thermodynamics, when formulated as a dynamical principle, implies a departure from locality. This discussion involves an extension of our theory to singular distribution functions. Certain analogies between our considerations and the conclusion of Gödel's theorem are briefly mentioned.     

Supersymmetric instantons and topological quantum field theory

We present an action which generates the supersymmetric self-dual equations corresponding to euclidean super Yang-Mills theory in four dimensions. By adding additional constraint fields with new local symmetries, the classical equations of this system are the usual super self-dual equations when a gauge is chosen for the constraint fields. This construction is a supersymmetric generalization of the Labastida-Pernici action which corresponds to a gauge unfixed version of Witten's topological quantum field theory. We discuss some topological prospects for this model, and the role of supersymmetric instantons in Donaldson theory.     

Deviations from Matthiessen's Rule

We present a comprehensive review of the subject of Deviations from Matthiessens's Rule, including a historical survey and detailed critical evaluations of both theory and experimental data. We discuss deviations occurring: in substitutional alloys (both magnetic and non-magnetic); after quenching; after radiation damage; after plastic deformation; and in thin samples. The only topic omitted is that of anomalous negative deviations occurring at low temperatures (e.g. the Kondo effect).     

Bubble-nucleation rates for radiatively induced first-order phase transitions

We present a consistent calculation of bubble-nucleation rates in theories of two scalar fields. Our approach is based on the notion of a coarse-grained free energy that incorporates the effects of fluctuations with momenta above a given scale k. We establish the reliability of the method for a variety of two-scalar models and confirm the conclusions of previous studies in one-field theories: Langer's theory of homogeneous nucleation is applicable as long as the expansion around the semi-classical saddle point associated with tunnelling is convergent. This expansion breaks down when the exponential suppression of the rate by the saddle-point action becomes comparable to the pre-exponential factor associated with fluctuations around the saddle point. We reconfirm that Langer's theory is not applicable to the case of weakly first-order phase transitions. We also find that the same is true in general for radiatively induced first-order phase transitions. We discuss the relevance of our results for the electroweak phase transition and the metastability bound on the Higgs-boson mass.     

Associating fluids with four bonding sites against a hard wall: density functional theory

We present two new perturbation density functional theories to investigate non-uniform fluids of associating molecules. Each fluid molecule is modelled as a spherical hard core with four highly anisotropic square well sites placed in tetrahedral symmetry on the hard core surface. In one theory we apply the weighting from Tarazona's hard sphere density functional theory to Wertheim's bulk first-order perturbation theory. The other theory uses the inhomogeneous form of Wertheim's theory as a perturbation to Tarazona's hard-sphere density functional theory. Each theory approaches Tarazona's theory in the limit of zero association. We compare results from theory and simulation for density profiles, fraction of monomers, and adsorption of an associating fluid against a hard, smooth wall over a range of temperatures and densities. The non-uniform fluid theory which uses Tarazona's weighting of Wertheim's theory in the bulk is in good agreement with computer simulation results.     

Quantum Computing without Magic,by Zdzislaw Meglicki

We will discuss the key concepts in density functional theory (DFT), how it can be used to model experimental data, and consider how the synergy between DFT and experiment can give significant insights. The discussion will centre on the scanning tunnelling microscope (STM) and surface problems, tracking the author's personal interest, though the general principles are widely applicable.     

Path integral over reparametrizations: Lévy flights versus random walks

We investigate the properties of the path integral over reparametrizations (or the boundary value of the Liouville field in string theory). Discretizing the path integral, we apply the Metropolis–Hastings algorithm to numerical simulations of a proper (subordinator) stochastic process and find that typical trajectories are not Brownian but rather have discontinuities of the type of Lévy's flights. We study a fractal structure of these trajectories and show that their Hausdorff dimension is zero. We confirm thereby previous results on QCD scattering amplitudes by analytical and numerical calculations. We also perform Monte Carlo simulations of the path integral over reparametrization in the effective string ansatz for a circular Wilson loop and discuss their subtleties associated with the discretization of Douglas' functional.     

Global cosmic strings,Nambu-Goldstone bosons and their constraints on unification

We show how the existence of a Nambu-Goldstone boson of the type recently argued for by Sikivie powerfully constrains possible models for grand unification. In particular, we show that the only models consistent with Sikivie's arguments are those in which at least part of the electric charge operator lies outside the group containing color. This rules out most known grand unification schemes including many of those inspired by superstring theory. We discuss the implications of this fact and construct a toy omion model.     

Thermodynamic properties of the one-dimensional Hubbard model

We discuss the thermodynamic behaviour of the one-dimensional Hubbard model in the narrow-band regime, where the intra-atomic Coulomb-repulsion is large compared to the bandwidth. An approximation scheme on a perturbative basis is developed which applies for all temperatures. First order perturbation theory is performed for arbitrary electron densities; second order perturbation theory is discussed in the case of the half-filled band. Also the one-particle Green's function is calculated. Our approximation agrees excellently with numerical calculations. By comparison with exact results, which are available for some special limits, the range of validity of our approximation is estimated.     

Is physics at the threshold of a new stage of evolution?

Starting from Planck's thesis concerning the aims and methods of theoretical physics as stated in his famous lecture (Leiden, 1908) onDie Einheit des physikalischen Weltbildes and his lectures in the next year at Columbia University, we discuss some aspects of physics and mathematics in our time. We compare relativity theory, quantum mechanics, and atomic physics at their inception with the situation today in field theories, elementary particle physics, and mathematical physics.     

Virtual photons in chiral perturbation theory

In the framework of chiral perturbation theory virtual photons are included. We calculate the divergences of the generating functional to one loop and determine the structure of the local action that incorporates the counterterms which cancel the divergences. As an application we discuss the corrections to Dashen's theorem at order e²M_q.     

Modification of black‐body radiance at low temperatures and frequencies

In contrast to earlier reports, where the spectrum of the energy density of photonic black‐body radiation modified by SU(2) effects was discussed, we discuss the low‐frequency spectrum of the radiance at temperatures ranging between 5 and 20 Kelvin. We conclude that compared to the conventional theory the only observable effect is associated with the spectral gap (total screening) which for T≥ 4.3 K scales with temperature T as ν^*(T)}/GHz = 42.70 (T/K)^‐0.53 + 0.21. We also discuss how a low‐temperature black body cavity under the influence of a sufficiently strong static electric field is forced to emit according to Planck's radiation law (pure U(1) theory) even at low frequencies and how this effect can be utilized to measure SU(2) induced deviations.     

Residual resistivity dipoles in electromigration

In the presence of an electric field a driving force is exerted by the surrounding electron gas on the impurity atoms. The contribution from this term is usually referred to as the Bosvieux-Friedel term who related it to the residual resistivity of the impurity. It has been suggested that the residual resistivity of the impurity causes a dipolar buildup around the impurity resulting in the so-called residual resistivity dipoles (RRD's) which in turn contribute a term to the driving force, in addition to the Boxvieux-Friedel term. We discuss the nature of this term for an impurity in a jellium matrix using nonlinear screening theory. It is found to vanish if it is identified with the third order terms in the impurity potential representing contribution from the RRD's.