First-order phase transitions in large entropy lattice models

We show the existence of a first-order phase transition in thev-dimensional Potts model forv≧2, when the number of states of a single spin is big enough. Low-temperature pure phases are proved to survive up to the critical temperature. Also the existence of a first-order transition in thev-dimensional Potts gauge model,v≧3, is obtained if the underlying gauge group is finite but large.     

Dust-acoustic solitons in quantum plasma with kappa-distributed ions

Arbitrary amplitude dust-acoustic (DA) solitary waves in an unmagnetized and collisionless quantum dusty plasma comprising cold dust particles, kappa (κ)-distributed ions and degenerate electrons are investigated. The influence of suprathermality and quantum effects on the linear dispersion relation of DA waves is investigated. Then, the effect of κ-distributed ions and degenerate electrons on the existence domain of solitons is discussed in the space of (M, f). The comparison of the existence domain for higher and lower values of κ shows that suprathermality results in propagation of solitons with lower Mach number, and the quantum effects, lead to a higher values of Mach number. The existence domain of solitons for nondegenerate κ-distributed electrons is considered for comparison with effect of degenerate electrons. Also, we found that the Sagdeev potential well becomes deeper and wider as ε _F???i decreases, as for lower κ values, the influence of quantum effects on the Sagdeev pseudopotential profile is smaller.     

Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories

We study the existence of monopole bound states saturating the BPS bound in N = 2 supersymmetric Yang-Mills theories. We describe how the existence of such bound states relates to the topology of index bundles over the moduli space of BPS solutions. Using an L² index theorem, we prove the existence of certain BPS states predicted by Seiberg and Witten based on their study of the vacuum structure of N = 2 Yang-Mills theories.     

Analytic approximations to Hamiltonian lattice field theories (II). The weak-coupling behavior of U(1) theories

It is shown that at weak coupling physical quantities in hamiltonian U(1) lattive gauge (or global symmetric) theories of arbitrary dimension are provided as expectation values in a d ? 1 dimensional lagrangian Z(2) gauge (or spin) theory with calculable long-range interactions.Confinement and the existence of a magnetic mass gap are equivalent to the existence of infinite-range plaquette-plaquette (or link-link) correlations in the spin field. The existence of infinite range correlations is simply related to the dimension of the lattice and the transformation property of the order parameter. As expected, only the d = 2+1 U(1) gauge theory confines electric charges at all non-vanishing coupling.     

Magnetic monopoles and tachyons in special relativity

The mere special relativity does not explicitly predict existence of (sub-luminal) monopoles, but on the contrary explicitly predicts existence of super-luminal (tachyon) monopoles, with magnetic charge about 100 times less than usually assumed. This fact is relevant also at the light of current experiments looking for magnetic poles.     

The existence of periodic motions in rub-impact rotor systems

The existence of rub-impact periodic motions in an eccentric rotor system is considered. A criterion for the periodicity condition of n-periodic impacts is derived and other conditions for real rub-impacts are also discussed. A method consisting of analytical and numerical techniques is presented to solve the existence problem of rub-impact periodic motions. Some special results are obtained by theoretical analyses for rub-impact rotor systems, including the existence of grazing circle motions and that of single-impact periodic motions.     

Zur spezifischen Wärme amorpher Metalle

The specific Heat of amorphous and polycrystalline Bi+10 at % Sb has been measured between 0.5 and 2.2 K. In the superconducting, amorphous Bi no sign of aT proportional term was found. In contrast, such aT term is observed on the polycrystalline Bi. This behaviour is compared with the specific heat anomaly previously found in disordered glasses. The present experiments suggest, that for the existence of an anomalousT proportional term in the lattice specific heat, not only structural disorder is important but also the existence of covalent bonds.     

On wormhole throats in f (R) gravity theory

We study the existence and properties of wormhole throats in modified f (R) gravity theory. Specifically, we concentrate on the cases where the lapse is not necessarily constant, and hence are not limited to the zero tidal force scenarios. In the class of theories whose actions are generated by Lagrangians of the form f (R)?=?∑ α _n ?R ⁿ we find parameters which allow for the existence of energy condition respecting throats, which do not exist in Einstein gravity. We also consider the effect of the modified action on the anisotropy of the models, and find that modified gravity can minimize the amount of anisotropy required to support the existence of a throat. In both these respects, the sector containing theories with positive n is more promising than the negative n sector in comparison to Einstein gravity alone, with large n being most favorable.     

Existence theorem for solitary waves on lattices

In this article we give an existence theorem for localized travelling wave solutions on one-dimensional lattices with Hamiltonian $$H = \sum\limits_{n \in \mathbb{Z}} {\left( {\tfrac{1}{2}p_n^2 + V(q_{n + 1} - q_n )} \right)} ,$$ whereV(·) is the potential energy due to nearest-neighbour interactions. Until now, apart from rare integrable lattices like the Toda latticeV(φ)=ab ^?1(e ^?bφ+bφ?1), the only evidence for existence of such solutions has been numerical. Our result in particular recovers existence of solitary waves in the Toda lattice, establishes for the first time existence of solitary waves in the (nonintegrable) cubic and quartic latticesV(φ)= 1/2φ ² + 1/3aφ ³,V(φ) = 1/2φ ² + 1/4bφ ⁴, thereby confirming the numerical findings in [1] and shedding new light on the recurrence phenomena in these systems observed first by Fermi, Pasta and Ulam [2], and shows that contrary to widespread belief, the presence of exact solitary waves is not a peculiarity of integrable systems, but “generic” in this class of nonlinear lattices. The approach presented here is new and quite general, and should also be applicable to other forms of lattice equations: the travelling waves are sought as minimisers of a naturally associated variational problem (obtained via Hamilton's principle), and existence of minimisers is then established using modern methods in the calculus of variations (the concentration-compactness principle of P.-L. Lions [3]).     

On supersymmetry breaking in superstrings

We prove that the existence of a slightly massive or gravitino or gaugino in a class of gaussian string compactifications, implies the existence of an entire tower of such states below M_Planck, signaling the approach to a limit of decompactification.     

Self-replication of mesa patterns in reaction-diffusion systems

Certain two-component reaction-diffusion systems on a finite interval are known to possess mesa (box-like) steady-state patterns in the singularly perturbed limit of small diffusivity for one of the two solution components. As the diffusivity D of the second component is decreased below some critical value D_c, with D_c=O(1), the existence of a steady-state mesa pattern is lost, triggering the onset of a mesa self-replication event that ultimately leads to the creation of additional mesas. The initiation of this phenomena is studied in detail for a particular scaling limit of the Brusselator model. Near the existence threshold D_c of a single steady-state mesa, it is shown that an internal layer forms in the centre of the mesa. The structure of the solution within this internal layer is shown to be governed by a certain core problem, comprised of a single nonautonomous second-order ODE. By analysing this core problem using rigorous and formal asymptotic methods, and by using the Singular Limit Eigenvalue Problem (SLEP) method to asymptotically calculate small eigenvalues, an analytical verification of the conditions of Nishiura and Ueyama [Y. Nishiura, D. Ueyama, A skeleton structure of self-replicating dynamics, Physica D 130 (1) (1999) 73-104], believed to be responsible for self-replication, is given. These conditions include: (1) The existence of a saddle-node threshold at which the steady-state mesa pattern disappears; (2) the dimple-shaped eigenfunction at the threshold, believed to be responsible for the initiation of the replication process; and (3) the stability of the mesa pattern above the existence threshold. Finally, we show that the core problem is universal in the sense that it pertains to a class of reaction-diffusion systems, including the Gierer-Meinhardt model with saturation, where mesa self-replication also occurs.     

On the existence of non-one-dimensional soliton-like solutions for some field theories

Some general conditions of the existence of non-dimensional spherically symmetric solitons are discussed. As a particular case, the condition of the existence of instanton-like solutions is obtained which coincides in an amasing way with the well-known formula $\text{p =}\text{2D}\text{(D?2)}$ the condition for theory to be renormalizable. (D is the space time dimension, p is the degree of nonlinearity.)     

Global existence of coupled Yang-Mills and scalar fields in 2 + 1 dimensional space-time

We present results on the Cauchy problem for coupled classical Yang-Mills and scalar fields in n + 1 dimensional space-time both in the temporal and in the Lorentz gauge. We prove the existence of local solutions for any n, and the existence of global solutions for n = 1, 2 in the temporal gauge and for n = 1 in the Lorentz gauge. The last result also holds for massive Yang-Mill fields.     

Dynamical R-matrices for Calogero models

We present a systematic study of the integrability of the Calogero models, degenerate as well as elliptic, associated with arbitrary (semi-)simple Lie algebras and with symmetric pairs of Lie algebras, where “integrability” is understood to encompass not only the existence of a Lax representation for the equations of motion but also the—more far-reaching—existence of a (dynamical) R-matrix. Using the standard group-theoretical machinery available in this context, we show that integrability of these models, in this sense, can be reduced to the existence of a certain function, denoted here by F, defined on the relevant root system and taking values in the respective Cartan subalgebra, subject to a rather simple set of algebraic constraints: these ensure, in one stroke, the existence of a Lax representation and of a dynamical R-matrix, all given by explicit formulas. We also show that among the simple Lie algebras, only those belonging to the A-series admit a solution of these constraints, whereas the AIII-series of symmetric pairs of Lie algebras, corresponding to the complex Grassmannians SU(p,q)/S(U(p)×U(q)), allows non-trivial solutions when |p−q|⩽1. Apart from reproducing all presently known dynamical R-matrices for Calogero models, our method provides new ones, namely for the degenerate models when |p−q|=1 and for the elliptic models when |p−q|=1 or p=q.     

On the s-type superconductivity in heavy-fermion compounds

The amplitude of scattering of f electrons has been calculated for the periodic Anderson model in the strong-correlation limit (U = ∞) in the Cooper channel. From the condition of the existence of a pole of this amplitude, an equation is derived for determining the critical temperature (T _c) of the transition to the superconducting phase with the s symmetry of the order parameter. The temperature T _c as a function of the electron density and hybridization parameter has been calculated by self-consistently solving the system of equations. The region of the existence of the superconducting phase is found to adjoin the region of the existence of the unsaturated ferromagnetic state and does not overlap it. The results can be used to describe the transition to the superconducting phase with the s symmetry of the order parameter in heavy-fermion skutterudite LaFe₄P₁₂. In this case, the inclusion of the scattering of fermions by spin fluctuations turns out to be substantial enough to obtain T _c values close to the experimental data.     

Cohomological extension of Spin(7)-invariant super-Yang–Mills theory in eight dimensions

It is shown that the Spin(7)-invariant super-Yang–Mills theory in eight dimensions, which relies on the existence of the Cayley invariant, permits the construction of a cohomological extension, which relies on the existence of the eight-dimensional analogue of the Pontryagin invariant arising from a quartic chiral primary operator.     

Phase transitions in polarized samples of multicomponent solid solutions based on lead zirconate titanate

The physical properties of multicomponent solid solutions that are based on lead zirconate titanate and belong to the rhombohedral part of the phase diagram are investigated. The conditions for the existence of the R3c, R3m, and P4mm phases in polarized samples are determined. The region of existence of the relaxor phase is revealed.     

Molecules in nuclei

The possible existence of analogues of atomic molecules within nuclei is considered in the context of the neutron-rich beryllium and carbon isotopes, where the underlying α cluster structure is believed to produce a multi-centred potential in which valence neutrons move. The generation of molecular wave-functions is examined and the link with the deformed harmonic oscillator and the Nilsson single-particle level scheme traced. Experimental evidence for the existence of molecular exotic cluster structures is reviewed particularly the nature of spectroscopic information provided by break-up reaction measurements. To cite this article: M. Freer, C. R. Physique 4 (2003).     

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.