Showing papers on "Explicit symmetry breaking published in 1992"

Continuous symmetry measures

Abstract: We advance the notion that for many realistic issues involving symmetry in chemistry, it is more natural to analyze symmetry properties in terms of a continuous scale rather than in terms of "yes or no". Justification of that approach is dealt with in some detail using examples such as: symmetry distortions due to vibrations; changes in the "allowedness" of electronic transitions due to deviations from an ideal symmetry; continuous changes in environmental symmetry with reference to crystal and ligand field effects; non-ideal symmetry in concerted reactions; symmetry issues of polymers and large random objects. A versatile, simple tool is developed as a continuous symmetry measure. Its main property is the ability to quantify the distance of a given (distorted molecular) shape from any chosen element of symmetry. The generality of this symmetry measure allows one to compare the symmetry distance of several objects relative to a single symmetry element and to compare the symmetry distance of a single object relative to various symmetry elements. The continuous symmetry approach is presented in detail for the case of cyclic molecules, first in a practical way and then with a rigorous mathematical analysis. The versatility of the approah is then further demonstrated with alkane conformations, with a vibrating ABA water-like molecule, and with a three-dimensional analysis of the symmetry of a (2 3 21 reaction in which the double bonds are not ideally aligned.

Hidden symmetry breaking and the Haldane phase in S=1 quantum spin chains

Abstract: We study the phase diagram ofS=1 antiferromagnetic chains with particular emphasis on the Haldane phase. The hidden symmetry breaking measured by the string order parameter of den Nijs and Rommelse can be transformed into an explicit breaking of aZ2×Z2 symmetry by a nonlocal unitary transformation of the chain. For a particular class of Hamiltonians which includes the usual Heisenberg Hamiltonian, we prove that the usual Neel order parameter is always less than or equal to the string order parameter. We give a general treatment of rigorous perturbation theory for the ground state of quantum spin systems which are small perturbations of diagonal Hamiltonians. We then extend this rigorous perturbation theory to a class of “diagonally dominant” Hamiltonians. Using this theory we prove the existence of the Haldane phase in an open subset of the parameter space of a particular class of Hamiltonians by showing that the string order parameter does not vanish and the hiddenZ2×Z2 symmetry is completely broken. While this open subset does not include the usual Heisenberg Hamiltonian, it does include models other than VBS models.

Hidden Z2*Z2 symmetry in quantum spin chains with arbitrary integer spin

Abstract: The author studies integer S>1 spin chains. He extends the Kennedy-Tasaki nonlocal unitary transformation for S=1 to arbitrary integer S. He shows the main results of Kennedy and Tasaki (1992) are maintained for S>1: Heisenberg-type Hamiltonians are transformed to Hamiltonians of nearest-neighbour interactions with Z2*Z2 symmetry, and the den Nijs-Rommelse string observables are transformed to the ferromagnetic correlation observables. He asserts that in general values of integer S there exist several phases with the hidden Z2*Z2 symmetry breaking. The den Nijs-Rommelse string order parameters, which measure the hidden Z2*Z2 symmetry breaking, are calculated explicitly for several variants of the VBS-type states. In the standard VBS state, the hidden Z2*Z2 symmetry breaks down when S is odd but remains unbroken when S is even. His results for partially dimerized VBS states suggest that the hidden Z2*Z2 symmetry breaking can be used to detect the successive dimerization transitions predicted by Affleck and Haldane (1987). Some new anisotropic VBS-type states are investigated. The result suggests that there are successive phase transitions when he increases the uniaxial anisotropy in a Heisenberg-type model. Other new VBS-type states with long-range order are considered, and their relevance to the phase diagram of the Heisenberg XXZ model and the magnetization process of antiferromagnets is investigated. He introduces an extended string order parameter which possesses a characteristic behavior in the partially dimerized VBS states.

Replica Symmetry Breaking in the Random Field Ising Model

Abstract: We discuss the critical behavior of the random field Ising model, using techniques of replica symmetry breaking familiar from the theory of spin glasses and random manifolds. Using an approximation that is valid in the limit of a large number of spin components, m, we find that the replica symmetric solution is unstable and obtain equations for solutions which break replica symmetry according to a natural scaling ansatz. Although we are unable to solve these equations exactly, we show that they lead to exponents which are different to order 1/m from the replica symmetric solution.

Sympletic quantization of constrained systems

Abstract: In this paper it is shown that the symplectic two-form, which defines the geometrical structure of a constrained theory in the Faddeev-Jackiw approach, may be brought into a non-degenerated form, by an iterative implementation of the existing constraints. The resulting generalized brackets coincide with those obtained by the Dirac bracket approach, if the constrained system under investigation presents only second-class constraints. For gauge theories, a symmetry breaking term must be supplemented to bring the symplectic form into a non-singular configuration. At present, the singular symplectic two-form provides directly the generators of the time independent gauge transformations.

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

Abstract: 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.

Partial dynamical symmetry

Abstract: A novel type of symmetry structure, which the authors call 'partial dynamical symmetry', is discussed. A general algorithm is presented to construct Hamiltonians with such symmetry, for any semisimple group. These Hamiltonians are not invariant under that group, and various irreducible representations are mixed in their eigenstates. However, they possess a subset of eigenstates which do have good symmetry and can therefore be labelled by the irreducible representations of that group. The eigenvalues and wavefunctions of these states are given in closed form. An example of a Hamiltonian with a partial SU(3) symmetry is provided.

Finite Unified Models

Abstract: We present phenomenologically viable $SU(5)$ unified models which are finite to all orders before the spontaneous symmetry breaking. In the case of two models with three families the top quark mass is predicted to be 178.8 GeV.

Symmetry breaking and localization in quantum chaotic systems.

Abstract: Using semiclassical arguments substantiated by numerical results for the quantum kicked rotor, we establish that breaking an antiunitary symmetry in a system with dynamical localization increases the localization length by a factor of 2. The transition between the symmetric and the symmetry broken case is smooth. The semiclassical theory provides an approximate expression for the transition function as well as the critical strength of the symmetry-breaking interaction necessary to achieve the full factor of 2 increase of the localization length.

Instability induced by symmetry reduction

Abstract: We demonstrate that instabilities in a Hamiltonian system can occur via deformations that reduce the symmetry of the system. The movement of eigenvalues at an equilibrium point of a family of Hamiltonian systems is constrained by the symmetry type of the system. If deformations of a family change the symmetry type, then instabilities can appear at multiple eigenvalues that produce large amplitude changes in the system dynamics. We illustrate this phenomenon in the context of a low-dimensional Hamiltonian normal form, and then analyze the instability of a vortex filament in a strain field

Dynamic scaling and spontaneous symmetry breaking at the gel point.

Abstract: The gel point is a continuous transition between fluid and solid states, and therefore exhibits a variety of scaling laws for the linear viscoelastic behavior. These are derived, together with a scaling law for the nonlinear shear relaxation modulus and a sum rule, valid in both fluid and solid states, which has a counterpart in superconductivity. Our results are generic consequences of both dynamic critical phenomena and spontaneous symmetry breaking, and therefore are not equivalent to some previous predictions, based on an analogy with percolation.

Three-Dimensional Symmetry Identification Part I : Theory

Abstract: A theoretical background necessary for symmetry identification of an arbitrary, finite, threedimensional object at any position and with arbitrary orientation'is presented. It supports construction of an algorithm for identification of a wide range of symmetry types represented by groups of proper and improper rotations and location of corresponding axes and/or planes of symmetry. The prerequisite is that the input object be represented by an octree. The proposed technique is based on examination of the octree obtained by the principal axis transform of the input octree. It is shown that the octree data structure is very convenient for symmetry evaluation, especially for objects whose symmetry types are simpler or equal in complexity with the four-fold rotational symmetry. The cases when the principal axis transform is not uniquely defined are analyzed and possible solutions are offered. Finally, extensions to multidimensional gray-scale images are briefly discussed.

Electroweak breaking in supersymmetric models

Abstract: We discuss the mechanism for electroweak symmetry breaking in supersymmetric versions of the standard model. After briefly reviewing the possible sources of supersymmetry breaking, we show how the required pattern of symmetry breaking can automatically result from the structure of quantum corrections in the theory. We demonstrate that this radiative breaking mechanism works well for a heavy top quark and can be combined in unified versions of the theory with excellent predictions for the running couplings of the model. (To be published in ``Perspectives in Higgs Physics'', G. Kane editor.)

Bounds from Stability and Symmetry Breaking on Parameters in the Two-Higgs-Doublet Potential

Abstract: is caused by the potential ofa single Higgs-SU(2) doublet However, since the exact symmetry breaking mech-anism is not known, it is natural to consider extensions of the Higgs sector Thesimplest such extension is to have another SU(2)-doublet scalar field In fact,there are many reasons to discuss the two-doublet model For associated particlephenomenology, see eg [1, 2] and references therein More recently, the modelhas also received attention in cosmological contexts, mainly in connection withbaryogenesis in the early universe [3]Assume we want to prescribe the minimum of the two-doublet potential as< Φ

Mixed Model of Induced QCD

Abstract: The problems with the $Z_N$ symmetry breaking in the induced QCD are analyzed. We compute the Wilson loops in the strong coupling phase, but we do not find the $Z_N$ symmetry breaking, for arbitrary potential. We suggest to bypass this problem by adding to the model a heavy fermion field in a fundamental representation of $ SU(N) $. Remarkably, the model still can be solved exactly by the Rieman-Hilbert method, for arbitrary number $N_f$ of flavors. At $ N_f \ll N \rightarrow \infty $ there is a new regime, with two vacuum densities. The $Z_N$ symmetry breaking density satisfies the linear integral equation, with the kernel, depending upon the old density. The symmetry breaking requires certain eigenvalue condition, which takes some extra parameter adjustment of the scalar potential.

Computational bifurcation of periodic solutions in systems with symmetry

Abstract: A bifurcation problem given by a Γ-symmetric parameter-dependent system of autonomous ordinary differential equations is considered (Γ a finite group). The main goal is to derive an efficient numerical method for the computation of symmetry breaking, period doubling and symmetry breaking period doubling bifurcations of periodic solutions. For this the bifurcation problem is reformulated in terms of Fourier coefficient vectors. This makes it possible to make use of the spatial and temporal symmetries of periodic solutions in order to reduce the effort for solving the problem effectively