Off-equilibrium fluctuation-dissipation relations in the 3d Ising spin glass in a magnetic field

We study the fluctuation-dissipation relations for a three dimensional Ising spin glass in a magnetic field both in the high temperature phase as well as in the low temperature one. In the region of times simulated we have found that our results support a picture of the low temperature phase with broken replica symmetry, but a droplet behavior cannot be completely excluded.

Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator

We study the helical edge states of a two-dimensional topological insulator without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of axial spin symmetry can lead to so-called generic helical edge states, which have energy-dependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spin-orbit coupling within the Bernevig-Hughes-Zhang model, for both a single isolated edge and for a finite width ribbon. In the single-edge case, we analytically quantify the energy dependence of the spin orientation, which turns out to be weak for a realistic HgTe quantum well. Nevertheless, finite size effects combined with Rashba spin-orbit coupling result in two avoided crossings in the energy dispersions, where the spin orientation variation of the edge states is very significantly increased for realistic parameters. Finally, our analytical results are found to compare well to a numerical tight-binding regularization of the model.

Dynamical generation of a gauge symmetry in the double-exchange model

It is shown that a bosonic formulation of the double-exchange model, one of the classical models for magnetism, generates dynamically a gauge-invariant phase in a finite region of the phase diagram. We use analytical methods, Monte Carlo simulations and finite-size scaling analysis. We study the transition line between that region and the paramagnetic phase. The numerical results show that this transition line belongs to the universality class of the antiferromagnetic RP^(2) model. The fact that one can define a universality class for the antiferromagnetic RP^(2) model, different from the one of the O(N) models, is puzzling and somehow contradicts naive expectations about universality.

Multistabilities and symmetry-broken one-color and two-color states in closely coupled single-mode lasers

We theoretically investigate the dynamics of two mutually coupled, identical single-mode semi-conductor lasers. For small separation and large coupling between the lasers, symmetry-broken one-color states are shown to be stable. In this case the light outputs of the lasers have significantly different intensities while at the same time the lasers are locked to a single common frequency. For intermediate coupling we observe stable symmetry-broken two-color states, where both lasers lase simultaneously at two optical frequencies which are separated by up to 150 GHz. Using a five-dimensional model, we identify the bifurcation structure which is responsible for the appearance of symmetric and symmetry-broken one-color and two-color states. Several of these states give rise to multistabilities and therefore allow for the design of all-optical memory elements on the basis of two coupled single-mode lasers. The switching performance of selected designs of optical memory elements is studied numerically.

Fermion Mass Generation without Spontaneous Symmetry Breaking

The conventional mechanism of fermion mass generation in the Standard Model involves Spontaneous Symmetry Breaking (SSB). In this thesis, we study an alternate mechanism for the generation of fermion masses that does not require SSB, in the context of lattice field theories. Being inherently strongly coupled, this mechanism requires a non-perturbative approach like the lattice approach.

In order to explore this mechanism, we study a simple lattice model with a four-fermion interaction that has massless fermions at weak couplings and massive fermions at strong couplings, but without any spontaneous symmetry breaking. Prior work on this type of mass generation mechanism in 4D, was done long ago using either mean-field theory or Monte-Carlo calculations on small lattices. In this thesis, we have developed a new computational approach that enables us to perform large scale quantum Monte-Carlo calculations to study the phase structure of this theory. In 4D, our results confirm prior results, but differ in some quantitative details of the phase diagram. In contrast, in 3D, we discover a new second order critical point using calculations on lattices up to size $ 60^3$. Such large scale calculations are unprecedented. The presence of the critical point implies the existence of an alternate mechanism of fermion mass generation without any SSB, that could be of interest in continuum quantum field theory.

Broadband Dual-Polarized Antenna with High Port Isolation and Polarization Purity

This paper presents a novel high symmetry balun which significantly improves the performance of dipole-based dual-polarized antennas. The new balun structure provides enhanced differential capability leading to high performance in terms of port-to-port isolation and far-field cross polarization. An example antenna using this balun is proposed. The simulated results show 53.5% of fractional bandwidth within the band 1.71−2.96 GHz (VSWR<1.5) and port-to-port isolation >59 dB. The radiation characteristic shows around 9 dBi of gain and far-field cross polarization <−48 dBi over the entire bandwidth. The detailed balun functioning and full antenna measurements will be presented during the conference. Performance comparison with similar structures will be also provided.

Driving Flows in Laboratory Astrophysical Plasma Jets: The Mochi.LabJet Experiment

Thesis (Master's)--University of Washington, 2016-08

Aspects of Chiral Symmetry Breaking in Lattice QCD

Thesis (Ph.D.)--University of Washington, 2016-08

Symmetry properties of one- and two- electron molecular integrals

The maximum numbers of distinct one- and two-electron integrals that arise in calculating the electronic energy of a molecule are discussed. It is shown that these may be calculated easily using the character table of the symmetry group of the set of basis functions used to express the wave function. Complications arising from complex group representations and from a conflict of symmetry between the basis set and the nuclear configuration are considered and illustrated by examples.

Fast assembly of fock matrices utilising symmetry properties of the basis set

A method of assembling the elements of the Fock matrix is described which is a modification of that due to Dacre. Lists of symmetry equivalent one-electron integrals are used as pointers to abbreviate the process of collecting two-electron integrals into the Fock matrix.

Symmetry reduction due to gallium substitution in the garnet Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12

Single-crystal structure refinements on lithium lanthanum zirconate (LLZO; Li7La3Zr2O12) substituted with gallium were successfully carried out in the cubic symmetry space group I [Formula: see text]3d. Gallium was found on two lithium sites as well as on the lanthanum position. Due to the structural distortion of the resulting Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12 (Ga-LLZO) single crystals, a reduction of the LLZO cubic garnet symmetry from Ia[Formula: see text] d to I [Formula: see text]3d was necessary, which could hardly be analysed from X-ray powder diffraction data.

Calculable lepton masses, seesaw relations, and four neutrino mixings in a 3-3-1 model with an extra U(1) symmetry

We propose a scheme in which the masses of the heavier leptons obey seesaw type relations. The light lepton masses, except the electron and the electron neutrino ones, are generated by one loop level radiative corrections. We work in a version of the 3-3-1 electroweak model that predicts singlets (charged and neutral) of heavy leptons beyond the known ones. An extra U(1)(Omega) symmetry is introduced in order to avoid the light leptons getting masses at the tree level. The electron mass induces an explicit symmetry breaking at U(1)(Omega). We discuss also the mixing matrix among four neutrinos. The new energy scale required is not higher than a few TeV.

Symmetry-breaking in chiral polymerisation

We propose a model for chiral polymerisation and investigate its symmetric and asymmetric solutions. The model has a source species which decays into left- and right-handed types of monomer, each of which can polymerise to form homochiral chains; these chains are susceptible to `poisoning' by the opposite handed monomer. Homochiral polymers are assumed to influence the proportion of each type of monomer formed from the precursor. We show that for certain parameter values a positive feedback mechanism makes the symmetric steady-state solution unstable. The kinetics of polymer formation are then analysed in the case where the system starts from zero concentrations of monomers and chains. We show that following a long induction time, extremely large concentrations of polymers are formed for a short time, during this time an asymmetry introduced into the system by a random external perturbation may be massively amplified. The system then approaches one of the steady-state solutions described above.

Impact of the cation symmetry on the mutual solubilities between water and imidazolium-based ionic liquids

Aiming at the evaluation of the impact of the ionic liquids (ILs) cation symmetry on their phase behaviour, in this work, novel mutual solubilities with water of the symmetric series of [C(n)C(n)im][NTf2] (with n=1-5) were determined and compared with their isomeric forms of the asymmetric [C(n)C(1)im][NTf2] group. While the solubility of isomeric ILs in water was found to be similar, the solubility of water in ILs follows the same trend up to a maximum cation alkyl side chain length. For n >= 4 in [C(n)C(n)im][NTf2] the solubility of water in the asymmetric ILs is slightly higher than that observed in the symmetric counterparts. The thermodynamic properties of solution and solvation derived from the experimental solubility data of ILs in water at infinite dilution, namely the Gibbs energy, enthalpy and entropy were used to evaluate the cation symmetry effect on the ILs solvation. It is shown that the solubility of ILs in water is entropically driven and highly influenced by the cation size. Accordingly, it was found that the ILs solubility in water of both symmetric and asymmetric series depends on their molecular volume. Based on these findings, a linear correlation between the logarithm of the solubility of ILs in water and their molar volume is here proposed for the [NTf2]-based ILs at a fixed temperature.