Symmetry Breaking Process Research Articles

Loose ends

Loose ends

The possibility that the optical second-harmonic generation in lead phosphate, Pb3(PO4)2, is related to structural imperfections

The second-harmonic generation (SHG) of nominally pure lead phosphate Pb3(PO4)2, was reinvestigated. SHG is confirmed at room temperature albeit with a large spatial variation within each sample. The signal did not disappear when the crystal was heated well above the ferroelastic transition temperature of 453 K. Chemical analysis using X-ray microprobe techniques showed a weak oxygen deficit for all samples. It is suggested that SHG is not necessarily indicative of an intrinsic symmetry breaking process in Pb3(PO4)2 but may be related to structural imperfections.

Intramolecular energy transfer and vibrational redistribution in chiral molecules: experiment and theory

The quantum vibrational dynamics of the CH-chromophore in a chiral environment are studied with the examples CHDTMu, CHDTF and CHFClBr. For the chiral methane isotopomer we use a recently established nine-dimensional potential hypersurface to extract the three-dimensional short-time quantum dynamics and the related CH-overtone spectra. We have carried out ab initio(MP2) calculations in the appropriate normal coordinate subspace for CHDTF, a chiral isotopomer of methylfluoride for which we have previously carried out extensive related calculations, and also experimental investigations on other isotopomers. For CHFClBr we report the first experimental and theoretical study of the CH-chromophore overtone spectra. The results are systematically analysed in terms of anharmonic coupling constants of the effective hamiltonian as well as the potential hypersurfaces in the appropriate three-dimensional subspaces. We show that the chiral, symmetry-breaking coupling constant ksab is of appreciable absolute magnitude for all three cases (ca. 25 cm–1 for CHFClBr). The resulting fast intramolecular vibrational redistribution in the highly excited CH-chromophore, on the femtosecond timescale, leads to appreciable population transfer between states of dynamical a′ and a″ symmetry for the electronically, ‘chemically’ chiral CHFClBr and for CHDTF, which is chiral only by isotope substitution. The symmetry-breaking intra-molecular redistribution processes in chiral molecules are briefly discussed in relation to dynamical chirality, time-dependent optical activity and fundamental symmetry violations of parity, and even of charge conjugation, parity and time-reversal symmetry and their combinations.

Hadronic transitions among quarkonium states in a soft-exchange-approximation. Chiral breaking and spin symmetry breaking processes

Although no asymptotic heavy quark spin symmetry, and even more no flavor symmetry, are expected for systems such as quarkonium, a numerical discussion shows that for some processes and in a preasymptotic region which may roughly include charmonium and bottomonium, the use of the spin-symmetry may be useful in conjunction with chiral symmetry for light hadrons (soft-exchange-approximation regime, SEA). We continue our discussion of hadronic transitions in the SEA-regime by studying in particular chiral breaking transitions such as 3P′ → 3Pπ 0, 3Pη , level splittings and transitions which break both chiral and spin symmery, such as ψ′ → J/ ψπ 0, J/ ψη and 1 P 1 → J/ ψπ 0.

Optical vortex solitons and the stability of dark soliton stripes

Dark soliton stripes are robust but can decay into optical vortex solitons when subjected to a persistent, long-period, transverse modulation. We explore the nonlinear dynamics of this symmetry-breaking process and determine growth rates, vortex densities, and other characteristics by conducting a nonlinear stability analysis that uses numerical techniques for several cases of special interest.

A ‘morphogenetic’ model of learning

The continuous mathematical model of morphogenesis within the area of self-organizing systems is taken into account. The learning process is identified with the creation of a dissipative structure. The relationship between dissipative structure and whole system operation is displayed by the associated symmetry-breaking process.

Spatiotemporal dynamics of lasers in the presence of an imperfect O(2) symmetry.

We show theoretically and experimentally that an infinitesimal imperfection in the symmetry of a system has a macroscopic influence on the stability of spatiotemporal patterns originated in a symmetry breaking process. This result makes it possible to discuss differences between experiments and models in which such corrections have not been taken into account. We show that the stability of the solutions arising from the first symmetry breaking transition in the Maxwell-Bloch equations is valid for every laser with radial symmetry.

Affine CS theories and WZNW models

We review the general properties of affine Chern-Simons theories and ensuing WZNW models. We quantize the former in the Schrödinger representation. We solve the Gauss constraint equations and construct holonomies in the punctured R 2 plane. We then study the reduction of affine WZNW models to affine Toda field theories both classically and from the point of view of the partition function. We analyze as well a different reduction to a previously introduced conformal invariant integrable model. Finally we pass from the latter to a generalization of the sinh-Gordon model through a process of hamiltonian reduction and spontaneous symmetry breaking of the conformal symmetry.

Sinh-Gordon model as a spontaneously broken conformal theory

We continue the study of the s1 2 affine Toda field theory introduced in a previous paper. We carry out the classical analysis of the theory, we exhibit in particular the chiral exchange algebra. We then recover from this theory the sinh-Gordon model through a process of hamiltonian reduction and spontaneous symmetry breaking of the conformal symmetry. We identify the sinh-Gordon vacuum solution.

Control of a symmetry-breaking process in the course of the morphogenesis of plantlets of Bidens pilosa L.

A mechanism involving transport, storage and retrieval of a symmetry-breaking message controls the relative growth rate of the cotyledonary buds of plantlets of Bidens pilosa L. The asymmetry was induced by administering a few needle pricks to one cotyledon of each plant. The storage of the symmetry-breaking message was independent of the number of pricks ("all or nothing" process) and irreversible. However, various treatments could render the plants either able to retrieve the stored symmetry-breaking message (in which case, the bud opposite to the pricked cotyledon began to elongate statistically sooner than the one associated with the stimulated cotyledon) or not (both buds then had an equal chance to be the first to start to grow). The retrieval process was also associated with a temporal oscillation. At the level of the whole plants, bud growth was observed only after the removal of apical dominance, and its degree of asymmetry was expressed by use of a parameter g ranging from zero (symmetrical case) to ± 1 (full asymmetry in favor of one of the cotyledonary buds). The highest g-values observed in the present contribution were of the order of 0.5. At the cellular level, the pricking of one cotyledon caused a number of cells, which were within the meristem of the bud associated with the pricked cotyledon and were in cell-cycle phases S or G2, to undergo cellular division and then be blocked in phase G1, whereas the cells of the opposite bud were practically unchanged.

Coleman-Weinberg symmetry breaking in the early Universe with an inhomogeneity

The 1-loop renormalized effective potential for a phi 4 theory in the early Universe with a small inhomogeneity is evaluated under the adiabatic approximation. It is used to investigate the Coleman-Weinberg symmetry breaking processes usually leading to inflationary cosmologies in the presence of an inhomogeneity. The result shows that whether the symmetry is radiatively broken or not will crucially depend upon the scalar-gravitational coupling xi and the magnitude of the scalar curvature R. In particular, the author shows how the mode-mixing behaviour resulting from the inhomogeneity of spacetime is naturally replaced by introducing the non-local term into the field equation. This property allows the analysis of other quantum field effects in the inhomogenous spacetime, which will be presented in later papers.

Unified prescription for the generation of electroweak and gravitational gauge field Lagrangian on a principal fiber bundle

It is essentially known that useful gauge field Lagrangians arise as Weil polynomials of the curvature of the gauge connection. The deeper implications and details of this fact are worked out in two widely differing cases. The Glashow–Weinberg–Salam gauge field Lagrangian for electroweak theory and the Townsend–Zardecki action for gravitation are obtained from the same type of ‘‘Yang–Mills’’ Weil form on a principal fiber bundle over space-time, with symmetry group U(2) and SO(2,3), respectively. The unified geometrical approach given here shows that fiber bundle reduction and symmetry breaking are essential not only in electroweak theory but also in the SO(2,3) gauge theory for gravitation. In fact, the process of symmetry breaking in electroweak theory and the soldering of the anti-de Sitter bundle, essential in the interpretation of SO(2,3) gauge theory as a theory for gravitation, are corresponding geometrical concepts.

Pattern formation dynamics resulting from a reaction-diffusion instability

The transient evolution associated to the Turing instability of the brusselator is studied. This enables us to examine genuine dynamical features of spatial pattern forming mechanisms in reaction-diffusion equations. By including thermal noise effects, we are able to calculate the onset time for this symmetry breaking process, as well as the behaviour of the concentration fluctuations accompanying it. Interesting effects related to anomalous fluctuations and symmetry restoring mechanisms are qualitatively and quantitatively discussed.

On the origin of compactification in the superstring theory

The D -dimensional superstring theory is considered in the anisotropic space-time d s 2 = d t 2 −exp[2α( t )]d x 2 − exp[2β( t )]d y 2 , where exp[α( t )] is the radius function of the M -dimensional physical space, whose curvature is K , exp[β( t )] is the radius function of the N -dimensional internal space, whose curvature is , and D = M + N + 1. To lowest order in the slope parameter α′, the classical equations of motion are known to admit the solution α= −β, when K =0, provided that ( M−N) 2 = M+N , a condition which includes most cases of physical interest. Here it is pointed out, applying recent results and conjectures in superstring theory, that this solution may be dual to the isotropic solution α = β. This suggests that the anisotropic solution is favoured as the consequence of a symmetry-breaking process, which yields some understanding of how the compactification mechanism occurs, and of why the Universe does not expand in a completely isotropic fashion.

Alkali feldspars: ordering rates, phase transformations and behaviour diagrams for igneous rocks

AbstractHomogeneous and heterogeneous phase relationships in the alkali feldspars are reviewed, and behaviour diagrams developed. Al,Si ordering is almost certainly continuous and higher order in both albite and potassium feldspar and has been established reversibly or nearly so down to below 500°C in albite and possibly to ∼ 200°C in potassium feldspar. The degree of order in intermediate albite changes strongly over a range of ∼ 75–150°C depending on pressure, low albite being stable up to about 620–650°C and high albite above about 725°C at low pressure. Symmetry is broken at ∼ 980°C mainly by a cooperative shearing of the whole framework and not by Al,Si ordering alone; there is a thermal crossover near 700°C shearing being dominant above (high albite) and ordering dominant below (intermediate albite).In potassium feldspar symmetry is broken by Al,Si ordering at a temperature of about 500°C The change in degree of order with respect to temperature has been followed easily and reversibly in sanidine from ∼ 1075 to ∼ 550°C and to a lesser extent in microcline from 450 to 200°C. Ordering rates in sanidine down to 500°C and ordering rates in microcline between 450 and 200°C are almostas fast as in albite. Ordering in sanidine at 500°C and below slows and then stops with the development of the tweed orthoclase domain texture. The tweed texture acts as a barrier to further order because the strain energy associated with the (incipient) twin domain texture balances or nearly balances the free energy decrease resulting from ordering. Ordering stops not because of the kinetics of Al,Si diffusion, but because the totaldriving forceis very small or nil. Ordering can readily proceed to completion, with the formation of low microcline, only if the domain-texture barrier is overcome by processes involving fluids or strong external stresses. There is no barrier in albite.The symmetry-breaking process in alkali feldspar changes with composition from mainly shearing in albite to ordering in potassium feldspar. Symmetry is broken equally at a compositional crossover (metastable with respect to exsolution) near Ab80-75at low pressure and progressively displaced towards Or at higher pressures. Ordering in pure albite occurs by a (nearly) one-step path which progressively becomes two-step with substitution of Or. Diagrams showing the near-equilibrium variation of the order parameters at low pressure with composition andTare given, as well as two extreme phase andbehaviourdiagrams for complete coherent and complete incoherent (strain-free) relationships. These diagrams can be used to understand feldspar relationships and microtextures in hypersolvus and subsolvus rocks, the occurrence of orthoclase, and of intermediate and low microcline.

Three generation SU(3)× SU(2)× U(1) Y models from orbifolds

Explicit SU(3) × SU(2) × U(1) Y four-dimensional string models are obtained from compactification of the heterotic string on the Z 3 orbifold. The presence of a Fayet-Iliopoulos term, associated with an “anomalous” U(1), plays a crucial role in the symmetry breaking process. In the example presented here the spectrum of light particles is remarkably close to that of the standard model. It contains three generations of the standard particles, with the correct representations under SU(3) × SU(2) × U(1) Y , and all the extra colour triplets, which could mediate fast proton decay, become naturally massive. Finally, there is a true (not mixed) hidden sector. Despite these attractive facts the model still has some problems (related to renormalization group equations and fermion masses), which may be cured in other examples.

Replica symmetry breaking in weak connectivity systems

The authors propose a generalisation of Parisi's replica symmetry breaking scheme (1979) to spin glasses (or optimisation problems) described by a set of order parameters Q(r)alpha 1. . . alpha r, or equivalently by a global order parameter G( sigma alpha ), rather than by Q(r)alpha 1 alpha 2 alone. They study the particular case of Derrida's p-spin model (1981) in the very dilute limit. The model is solved exactly in the large p limit and a freezing transition occurs. Using replicas and a single step of their replica symmetry breaking ansatz they recover the exact result. They discuss the implications for the global order parameter G( sigma alpha ) when more than one step in the replica symmetry breaking process is taken.

The structure of Jahn–Teller surfaces

In chemical applications of the Jahn–Teller effect, the shape of the adiabatic potential near the instability point is of primary importance. The present article examines this shape, both in the usual representation in the space of the nuclear configurations and in the less current projective representation in the space of the electronic functions. The general structural aspects of these representations are viewed as the results of a symmetry breaking process, starting at the continuous invariance group of the degenerate coupling limit, and ending with the finite point group of the representation space. The various vibronic coupling mechanisms involved in this process are characterized by irreducible tensor functions of the full orthogonal groups. The leading tensorial rank of the unequal linear coupling mechanism is shown to be four, while the bilinear coupling mechanism also involves an irreducible component of the sixth rank. This tensorial analysis provides a grouptheoretical foundation for the recently formulated epikernel principle, which predicts the location of extremal points on a Jahn–Teller surface.

Magnetoresistance and growth of the coherent state in CeCu6

The magnetoresistance is studied in the heavy fermion compound CeCu6 over the temperature range in which the coherent state forms. At high temperatures it is negative and agrees with the theory for a single Kondo impurity. At low temperatures, in the coherent state, it is dominated by a linear positive magnetoresistance which is attributed to the field-induced symmetry breaking process discussed by Mahan (1983, 1984). From the growth of the linear magnetoresistance and deviations from single impurity Kondo behaviour it is concluded that formation of the coherent state is accompanied by an anisotropic reconstruction of the Fermi surface.

Low-energy supergravity and superstring-inspired models

We study the process of gauge symmetry breaking in superstring-inspired models with two, one and no extra Z 0' gauge bosons. We present analytic expressions for the solutions of the renormalization group equations for the masses and couplings of an arbitrary extra U(1) model. A specific model with an extra Z 0' (the only one consistent with a heavy v R) is studied numerically and results for the sparticle spectrum, as well as for the constraints amongst parameters, are given. We also consider a minimal “stringy” model with no extra Z 0's. Consistent gauge symmetry breaking in this model requires the t-quark mass m t ≳ 70 GeV, the sneutrino (or a higgsino) being very often the lightest SUSY particle. We argue that the models with an extra Z 0, (although viable), are rather artificial and emphasize the importance of obtaining compactification schemes leading to rank = 4 low-energy groups.