Symmetry Breaking In Systems Research Articles

Hohenberg-Mermin-Wagner-type theorems and dipole symmetry

We study the possibility of spontaneous symmetry breaking in systems with both charge and dipole symmetries. For $d$-dimensional systems at a positive temperature, we show that charge symmetry cannot be spontaneously broken for $d\ensuremath{\le}4$, while dipole symmetry cannot be spontaneously broken for $d\ensuremath{\le}2$. For $T=0$, we show that charge symmetry cannot be spontaneously broken for $d\ensuremath{\le}2$ if the compressibility is finite. We also show that continuum systems with a dipole symmetry have infinite inertial mass density.

Mirror Symmetry Breaking and Network Formation in Achiral Polycatenars with Thioether Tail.

Mirror symmetry breaking in systems composed of achiral molecules is of importance for the design of functional materials for technological applications as well as for the understanding of the mechanisms of spontaneous emergence of chirality. Herein, we report the design and molecular self‐assembly of two series of rod‐like achiral polycatenar molecules derived from a π‐conjugated 5,5’‐diphenyl‐2,2’‐bithiophene core with a fork‐like triple alkoxylated end and a variable single alkylthio chain at the other end. In both series of liquid crystalline materials, differing in the chain length at the trialkoxylated end, helical self‐assembly of the π‐conjugated rods in networks occurs, leading to wide temperature ranges (>200 K) of bicontinuous cubic network phases, in some cases being stable even around ambient temperatures. The achiral bicontinuous cubic Ia 3‾ d phase (gyroid) is replaced upon alkylthio chain elongation by a spontaneous mirror symmetry broken bicontinuous cubic phase (I23) and a chiral isotropic liquid phase (Iso1 [*]). Further chain elongation results in removing the I23 phase and the re‐appearance of the Ia 3‾ d phase with different pitch lengths. In the second series an additional tetragonal phase separates the two cubic phase types.

Phase transition through the splitting of self-dual spectral singularity in optical potentials.

We consider optical media, which feature antilinear symmetries. We show that (i) spectral singularities of such media (if any) are always self-dual, i.e., correspond to coherent perfect absorber lasers; (ii) under the change of a system parameter, the self-dual spectral singularity may split into a pair of isolated complex conjugate eigenvalues, which corresponds to an unconventional and overlooked, in the most of the previous studies, scenario of the phase transition (known as parity-time [PT]-symmetry breaking in systems obeying PT symmetry); (iii) if the antilinear symmetry is local, i.e., does not involve any spatial reflection, then no spectral singularity is possible. Our findings are illustrated with several examples including a PT-symmetric bilayer and other complex potentials discussed in recent literature.

Spontaneous symmetry breaking in vortex systems with two repulsive lengthscales.

Scanning Hall probe microscopy (SHPM) has been used to study vortex structures in thin epitaxial films of the superconductor MgB2. Unusual vortex patterns observed in MgB2 single crystals have previously been attributed to a competition between short-range repulsive and long-range attractive vortex-vortex interactions in this two band superconductor; the type 1.5 superconductivity scenario. Our films have much higher levels of disorder than bulk single crystals and therefore both superconducting condensates are expected to be pushed deep into the type 2 regime with purely repulsive vortex interactions. We observe broken symmetry vortex patterns at low fields in all samples after field-cooling from above Tc. These are consistent with those seen in systems with competing repulsions on disparate length scales, and remarkably similar structures are reproduced in dirty two band Ginzburg-Landau calculations, where the simulation parameters have been defined by experimental observations. This suggests that in our dirty MgB2 films, the symmetry of the vortex structures is broken by the presence of vortex repulsions with two different lengthscales, originating from the two distinct superconducting condensates. This represents an entirely new mechanism for spontaneous symmetry breaking in systems of superconducting vortices, with important implications for pinning phenomena and high current density applications.

Symmetry breaking via hybridization with conduction electrons in frustrated Kondo lattices

In frustrated magnets when magnetic ordering is suppressed down to low temperature, the formation of a quantum spin liquid becomes a possibility. How such a spin liquid manifests in the presence of conduction electrons is a question with potentially rich physical consequences, particularly when both the localized spins and conduction electrons reside on frustrated lattices. We propose a novel mechanism for symmetry breaking in systems where conduction electrons hybridize with a quantum spin liquid through Kondo couplings. We apply this to the pyrochlore iridate Pr2Ir2O7, which exhibits an anomalous Hall effect without clear indications of magnetic order. We show that Kondo hybridization between the localized Pr pseudo-spins and Ir conduction electrons breaks some of the spatial symmetries, in addition to time-reversal regardless of the form ofthe coupling. These broken symmetries result in an anomalous Hall conductivity and induce small magnetic, quadrupolar and charge orderings. Further experimental signatures are proposed.

Independent particle model of spontaneous symmetry breaking in planar π-electron systems

The singlet stability of symmetry adapted (SA), restricted Hartree-Fock (RHF) solutions, and the implied symmetry breaking for several planar, π-electron systems, is investigated using the semiempirical Pariser-Parr-Pople Hamiltonian in the whole range of the coupling constant. We focus here on highly symmetric cyclic polyenes C10H10 and C14H14 and their various distorted analogues of lower symmetry, in particular on the perimeter models of naphthalene and anthracene (p-naphthalene and p-anthracene) modeling the so-called [n]-annulenes. Relying on earlier results for general systems with conjugated double-bonds, we explore the character and properties of both the SA and broken-symmetry (BS) RHF solutions for these systems and relate their behavior to those of highly symmetric cyclic polyenes and corresponding polyacenes. In this way we are able to provide a better understanding of the spontaneous symmetry breaking in these systems at the Hartree-Fock level of approximation.

Experimental studies on kaonic atoms at DAΦNE

With precise X-ray spectroscopy on kaonic hydrogen at the DAΦNE electron-positron collider at Laboratori Natzionali di Frascati the chiral symmetry breaking scenario in the strangeness sector will be investigated by studying the K − p and K − d s-wave interaction at threshold. The strong interaction induced shift and width of the kaonic hydrogen 1 s atomic state was measured with DEAR (DAΦNE Exotic Atom Research) and in future with SIDDHARTA (Silicon Drift Detector for Hadronic Atom Research with Timing Application) the kaonic hydrogen system will be measured with utmost precision. In addition, data for the K − d system will become available for the first time. Kaonic hydrogen together with precision measurements of kaonic helium will allow the study of the sub-threshold Λ(1405) resonance, which might act as a doorway for the formation of antikaon-mediated deeply bound nuclear states in light nuclei. Therefore, these precision measurements are a powerful tool to test chiral symmetry breaking in systems with strangeness.

The localizability of valence space electron–electron correlations in pair-based coupled cluster models

Inspired by the success of very restrictive local active space approaches like Generalized Valence Bond Perfect Pairing (GVB-PP) and Imperfect Pairing (IP), we investigate the localizability of valence correlation in the context of electron pair models. In particular, the role of two-center local excitations in local active space coupled cluster doubles models is examined in the context of a variety of chemical applications. The full two spatial center pairing model is found to recover the majority of the correlation effects missed by GVB-PP and IP, recovering up to 95% of the untruncated valence correlation energy, and could provide an inexpensive reference wave function for the treatment of additional electron–electron correlations. All of these models improve noticeably upon the Hartree–Fock wave function and can be computed for very large systems due to their only cubic computational cost. Their main weakness is a tendency to exhibit symmetry breaking in systems with multiple resonance structures.

The DEAR experiment—first results on kaonic hydrogen

The goal of the DEAR (DAΦNE exotic atom research) experiment is the precise determination of the isospin dependent antikaon–nucleon scattering lengths. The experiment accurately measures the Kα line shift and broadening, due to the strong interaction, in kaonic hydrogen and, for the first time, in kaonic deuterium. A precision measurement of kaonic hydrogen tests chiral symmetry breaking in systems with strangeness. An initial analysis of the DEAR experiment yields a shift ɛ 1 s = − 195 ± 45 eV and a width Γ 1 s = 250 ± 125 eV , which is more precise than the previous kaonic X-ray experiment KpX at KEK, and allows for the first time to disentangle the full pattern of the kaonic hydrogen K-series line Kα, Kβ and Kγ.

Patterns of symmetry breaking in systems of coupled tetrahedra

The phases of a system of weakly coupled tetrahedra(S = 1/2), in the presence of both Heisenberg and antisymmetric Dzyaloshinsky–Moriya interactions,are discussed. While non-magnetic dimer order is dominant for the specific interactionsconsidered, we find that Dzyaloshinsky–Moriya induced magnetic long-range order can alsoemerge. The presence of antisymmetric interactions also leads to non-trivial effects(e.g. ordering) in an external magnetic field.

Hysteretic scaling and dynamical phase transition of three-dimension X-Y Model

We have studied in this paper,by performing the Monte Carlo numerical simulation,both the hysteretic scaling and the dynamical phase transition of a three-dimen sional,(3D) classical X-Y model driven by an sinusoidally oscillating external m agnetic field.A scaling formula has been worked out which relates the hysteresis loop area with the amplitude h0 and frequency ω of the external fie ld as wel l as the reduced temperature T/Tc of the system in the form:Area～hα0ωβ(1-T/Tc)γ.The best-fit expo nents are α=0.57,β=0.34 and γ=0.9.The 3D X- Y model also characterizes a distinctive discrepancy in dynamical transition fea ture after short and long term evolution of magnetization,respectively.Our simul ation disclosed that the short-term evolution of magnetization (period number≤1 0) attains the symmetry-breaking of system with a nonzero dynamical order parame ter (Q≠0) at a either critical amplitude h0c or frequency ωc.The symme try-breaking in short term,however,evolves steadily into a symmetric disorder st ate (Q=0) after a longer term relaxation of system.The specific relaxation times at which the Q value becomes zero from nonzero increase evidently as the temper ature of system drops.

Monte Carlo simulation of liquid-crystal alignment and chiral symmetry-breaking

We carry out Monte Carlo simulations to investigate the effect of molecular shape on liquid-crystal order. In our approach, each model mesogen consists of several soft spheres bonded rigidly together. The arrangement of the spheres may be straight (to represent uniaxial molecules), Z-shaped (for biaxial molecules), or banana-shaped (for bent-core molecules). Using this approach, we investigate the alignment of the nematic phase by substrates decorated with parallel ridges. We compare results for wide and narrow ridge spacing and examine local order near the substrates, and show that our results are consistent with the predictions of Landau theory. We also investigate chiral symmetry-breaking in systems of bent-core molecules. We find a chiral crystalline phase as well as a nonchiral smectic-A phase, but not a chiral smectic-C phase.

Low dimensional models of the wall region in a turbulent boundary layer: New results

Using an optimally convergent representation, a low dimensional model is constructed, which embodies in a streamwise-invariant form the effects of streamwise structure. Results of Stone show that the model is capable of mimicking the stability change due to favorable and unfavorable pressure gradients. Results of Aubry et al. suggest that polymer drag reduction is associated with stabilization of the secondary instabilities, as has been speculated. Results of Bloch and Marsden indicate that drag can be reduced by feedback, and that this is mathematically equivalent to polymer drag reduction. The authors showed that dynamical systems based on the Proper Orthogonal Decomposition have, on the average, the best short term tracking time (the time that a model tracks the true system accurately; essential for control) for a given number of modes. In recent work, the authors have shown that several assumptions made on an intuitive basis in the work of Aubry et al. may be justified formally. Berkooz has made rigorous estimates using the proper orthogonal decomposition showing that a structured turbulent flow, such as the wall layer, has a phase space representation that remains within a thin slab centered on the most energetic modes for most of the time. Campbell and Holmes have shown several results in connection with symmetry breaking in systems with structurally stable heteroclinic cycles. This work is relevant to our models of interacting coherent structures in boundary layers with discrete spanwise symmetry, such as that caused by riblets, which are known to produce drag reduction.

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian\(H = - \sum\nolimits_{xy} {\tilde J_{xy} s_x \cdot s_y } \), with thesx varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if\(\tilde J_{xy} = {{J_{xy} } \mathord{\left/ {\vphantom {{J_{xy} } {\left| {x - y} \right|^\alpha }}} \right. \kern-\nulldelimiterspace} {\left| {x - y} \right|^\alpha }}\) withJxy i.i.d. bounded random variables with zero average, α⩾ 1 in one dimension, and α⩾2 in two dimensions.