Origin Of Symmetry Breaking Research Articles

Origin of symmetry breaking in the grasshopper model

The planar grasshopper problem, originally introduced by Goulko and Kent [], is a striking example of a model with long-range isotropic interactions whose ground states break rotational symmetry. In this paper we analyze and explain the nature of this symmetry breaking with emphasis on the importance of dimensionality. Interestingly, rotational symmetry is recovered in three dimensions for small jumps, which correspond to the nonisotropic cogwheel regime of the two-dimensional problem. We discuss simplified models that reproduce the symmetry properties of the original system in N dimensions. For the full grasshopper model in two dimensions we obtain quantitative predictions for optimal perturbations of the disk. Our analytical results are confirmed by numerical simulations. Published by the American Physical Society 2024

Thermodynamic Insights into Symmetry Breaking: Exploring Energy Dissipation across Diverse Scales.

Symmetry breaking is a phenomenon that is observed in various contexts, from the early universe to complex organisms, and it is considered a key puzzle in understanding the emergence of life. The importance of this phenomenon is underscored by the prevalence of enantiomeric amino acids and proteins.The presence of enantiomeric amino acids and proteins highlights its critical role. However, the origin of symmetry breaking has yet to be comprehensively explained, particularly from an energetic standpoint. This article explores a novel approach by considering energy dissipation, specifically lost free energy, as a crucial factor in elucidating symmetry breaking. By conducting a comprehensive thermodynamic analysis applicable across scales, ranging from elementary particles to aggregated structures such as crystals, we present experimental evidence establishing a direct link between nonequilibrium free energy and energy dissipation during the formation of the structures. Results emphasize the pivotal role of energy dissipation, not only as an outcome but as the trigger for symmetry breaking. This insight suggests that understanding the origins of complex systems, from cells to living beings and the universe itself, requires a lens focused on nonequilibrium processes.

Characteristic Mueller matrices for direct assessment of the breaking of symmetries.

Mueller polarimetry is a powerful optical technique in the analysis of micro-structural properties of optical samples. However, there is no explicit relationship between individual Mueller matrix elements and the physical properties of the sample. Several matrix decomposition algorithms corresponding to specific optical models have been proposed, which extract the physical information from measured Mueller matrices. Nevertheless, we still need a prior assessment method to decide which model is more suitable for the experimental data. In this Letter, we propose a set of characteristic Mueller matrices that allows us to obtain information about the breaking of rotation, mirror, and reciprocal symmetry properties in the sample by direct inspection of several elements of the Mueller matrix. By further analyzing the possible origin of symmetry breaking, we can learn the type and mixing status of anisotropies in the measured sample. We have verified our theory with Monte Carlo simulations of polarized light scattering in an isotropic or anisotropic medium containing different configurations of spherical and cylindrical scatterers. This study may help experimenters choose more suitable Mueller matrix decomposition methods.

Noncommutative geometry and structure of space–time

I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the Standard Model and the reasons behind the particular form of gauge fields, Higgs fields and fermions as well as the origin of symmetry breaking. It also points that at high energies the Standard Model is a truncation of Pati-Salam unified model of leptons and quarks. The same conclusions are arrived at uniquely without making any assumptions except for an axiom which is a higher form of Heisenberg commutation relations quantizing the volume of space-time. We establish the existence of two kinds of quanta of geometry in the form of unit spheres of Planck length. We provide answers to many of the questions which are not answered by other approaches, however, more research is needed to answer the remaining challenging questions.

Fractal MTW Zeolite Crystals: Hidden Dimensions in Nanoporous Materials

AbstractScrew dislocation structures in crystals are an origin of symmetry breaking in a wide range of dense‐phase crystals. Preparation of such analogous structures in framework‐phase crystals is of great importance in zeolites but is still a challenge. On the basis of crystal‐structure solving and model building, it was found that the two specific intergrowths in MTW zeolite produce this complex fractal and spiral structure. With the structurally determined parameters (spiral pitch h, screw angle θ, and spatial angle ψ) of Burgers circuit, the screw dislocation structure can be constructed by two different dimensional intergrowth sections. Thus the reported complexity of various dimensions in diverse crystals can be unified.

Fractal MTW Zeolite Crystals: Hidden Dimensions in Nanoporous Materials

Screw dislocation structures in crystals are an origin of symmetry breaking in a wide range of dense-phase crystals. Preparation of such analogous structures in framework-phase crystals is of great importance in zeolites but is still a challenge. On the basis of crystal-structure solving and model building, it was found that the two specific intergrowths in MTW zeolite produce this complex fractal and spiral structure. With the structurally determined parameters (spiral pitch h, screw angle θ, and spatial angle ψ) of Burgers circuit, the screw dislocation structure can be constructed by two different dimensional intergrowth sections. Thus the reported complexity of various dimensions in diverse crystals can be unified.

Crystal structure of pollucite

Abstract The crystal structure of pollucite (ANA) (Cs,Na)AlSi2O6 is characterized by single-crystal X-ray diffractometry. The space group C2/c, monoclinic, is found to be the most probable space group for this mineral based on the systematic absences of reflections. Cesium ions or water molecules are disordered at the center of a channel and are slightly apart from the special position. This is the origin of symmetry breaking and the space group becomes lower from Ia-3d (analcime) to C2/c. Sodium ions or vacancies are located at the contact point of the channel. No ordering of aluminum is observed in the pollucite structure.

Symmetry breaking in benzene and larger aromatic molecules within generalized valence bond coupled cluster methods

The origin of symmetry breaking (SB) in benzene in generalized valence bond methods is investigated within a coupled cluster formalism that correlates all valence electrons. Retention of a limited number of pair correlation amplitudes (as in the perfect- and imperfect-pairing models) that incompletely describes interpair correlations leads to symmetry breaking as the orbitals and amplitudes are optimized. Local correlation models that are exact for one, two, and three interacting pairs at the doubles excitation level are compared against the exact pair correlation treatment, which correlates four interacting pairs at once in the connected double substitution operator. For simplicity, this comparison is performed with a second-order model of electron correlation, which is reasonably faithful to the infinite-order result. The significant SB known for the one-pair model (perfect pairing) is not eliminated at the two-pair level, but is virtually eliminated at the three-pair level. Therefore, a tractable hybrid model is proposed, which combines three-pair correlations at the second-order level and infinite-order treatment for the strong imperfect-pairing correlations involving one and two-pair correlations. This model greatly reduces SB in benzene and larger delocalized pi systems such as naphthalene and the phenalenyl cation and anion. The resulting optimized orbitals are localized in the sigma space but exhibit significant delocalization in the pi space. This means that correlation effects associated with different resonance structures are treated in a more balanced way than if the pi orbitals localize, leading to reduced SB.

From Chiral Molecules to Chiral Phases1: Comments on the Chirality of Liquid Crystalline Phases

In liquid crystal science the phenomenon of chirality has often played an important role in the context of phase structures or as an origin of symmetry breaking. Fundamental questions about ‘chirality’ in the context of liquid crystal properties have not been widely discussed or taken into account in the development of suitable concepts. For example, the questions of whether or not the spontaneous polarization or the circular dichroism (CD) with a light beam propagating obliquely to the optical axis of the phase is a chirality observation, have never been asked. With the report in 1996 of chiral liquid crystal phases [1], formed from achiral ‘banana-shaped compounds’, a new era of discussion dawned. Many questions are now raised which seem to be trivial, but are also fundamental, e.g. can a commercial CD instrument measure CD of an anisotropic and inhomogeneous phase without artifacts or whether or not a measured CD is an unequivocal proof for the existence of a chiral structure.