Phenomenon Of Spontaneous Symmetry Breaking Research Articles

Indications for an alternative breaking of symmetry in fracture-induced electromagnetic emissions recorded prior to the 2023 Mw7.8 and Mw7.5 Turkey Earthquakes

Several evidence has been reported corroborating the view that the MHz band fracture-induced electromagnetic emissions (FEME), also known as fracture-induced electromagnetic radiation (FEMR), which are detected prior to shallow main earthquakes (EQs) of moment magnitude Mw>5.5 with epicenters on land or near coastline, can be studied in analogy to a Z(2) spin system undergoing a second-order phase transition. Specifically, by analyzing MHz FEME/FEMR time series recorded prior to several earthquakes in the past >20 years, information has been extracted about the organization to critical state, the critical state itself, as well as for the step-by-step development of the spontaneous symmetry breaking (SSB) phenomenon. Using the “method of critical fluctuations” (MCF) and a recently proposed method for the wavelet-based detection of scaling behavior in noisy experimental data, we identified for the first time a different way of breaking the symmetry embedded in the MHz FEME/FEMR time series recorded by the hELlenic Seismo-ElectroMagnetics Network (ELSEM-Net) prior to the devastating (Mw=7.8 and Mw=7.5) EQs that occurred in south-east Turkey on 06/02/2023. Particularly, after the achievement of the critical state, indications were found that, although the underlying system started to break the symmetry according to the second-order phase transition mechanism (through SSB), SSB was not completed. Instead, the system seems to have changed symmetry and presented indications that the break of symmetry was finally achieved according to the first-order phase transition mechanism. Specifically, after the incomplete SSB, it was found to present tricritical behavior, followed by indications of triple degeneration of the order parameter fixed-point. This change of behavior observed in the MHz FEME/FEMR is a puzzling phenomenon for several reasons, which are discussed in detail, whereas suggestions are expressed as a first attempt for the possible explanation of the new findings.

Exclusion processes on a roundabout traffic model with constrained resources.

Motivated by the vehicular traffic phenomenon at roundabouts, we examine how the limited availability of resources affects the movement of two distinct types of particles on bidirectional lanes connected by two bridges, with each bridge specifically designated for the transportation of one species. To provide a theoretical ground for our findings, we employ a mean-field framework and successfully validate them through dynamic Monte Carlo simulations. Based on the theoretical analysis, we analytically derive various stationary properties, such as the particle densities, phase boundaries, and particle currents, for all the possible symmetric as well as asymmetric phases. The qualitative as well as quantitative behavior of the system is significantly affected by the constraint on the number of resources. The complexity of the phase diagram shows a nonmonotonic behavior with an increasing number of particles in the system. Analytical arguments enable the identification of several critical values for the total number of particles, leading to a qualitative change in the phase diagrams. The interplay of the finite resources and the bidirectional transport yields unanticipated and unusual features such as back-and-forth transition, the presence of two congested phases where particle movement is halted, as well as shock phases induced by boundaries and the bulk of the system. Also, it is found that spontaneous symmetry-breaking phenomena are induced even for very few particles in the system. Moreover, we thoroughly examine the location of shocks by varying the parameters controlling the system's boundaries, providing insights into possible phase transitions.

Selective Encapsulation and Chiral Induction of C60 and C70 Fullerenes by Axially Chiral Porous Aromatic Cages

AbstractChiral induction has been an important topic in chemistry, not only for its relevance in understanding the mysterious phenomenon of spontaneous symmetry breaking in nature but also due to its critical implications in medicine and the chiral industry. The induced chirality of fullerenes by host–guest interactions has been rarely reported, mainly attributed to their chiral resistance from high symmetry and challenges in their accessibility. Herein, we report two new pairs of chiral porous aromatic cages (PAC), R‐PAC‐2, S‐PAC‐2 (with Br substituents) and R‐PAC‐3, S‐PAC‐3 (with CH3 substituents) enantiomers. PAC‐2, rather than PAC‐3, achieves fullerene encapsulation and selective binding of C70 over C60 in fullerene carbon soot. More significantly, the occurrence of chiral induction between R‐PAC‐2, S‐PAC‐2 and fullerenes is confirmed by single‐crystal X‐ray diffraction and the intense CD signal within the absorption region of fullerenes. DFT calculations reveal the contribution of electrostatic effects originating from face‐to‐face arene‐fullerene interactions dominate C70 selectivity and elucidate the substituent effect on fullerene encapsulation. The disturbance from the differential interactions between fullerene and surrounding chiral cages on the intrinsic highly symmetric electronic structure of fullerene could be the primary reason accounting for the induced chirality of fullerene.

Selective Encapsulation and Chiral Induction of C60 and C70 Fullerenes by Axially Chiral Porous Aromatic Cages.

Chiral induction has been an important topic in chemistry, not only for its relevance in understanding the mysterious phenomenon of spontaneous symmetry breaking in nature but also due to its critical implications in medicine and the chiral industry. The induced chirality of fullerenes by host-guest interactions has been rarely reported, mainly attributed to their chiral resistance from high symmetry and challenges in their accessibility. Herein, we report two new pairs of chiral porous aromatic cages (PAC), R-PAC-2, S-PAC-2 (with Br substituents) and R-PAC-3, S-PAC-3 (with CH3 substituents) enantiomers. PAC-2, rather than PAC-3, achieves fullerene encapsulation and selective binding of C70 over C60 in fullerene carbon soot. More significantly, the occurrence of chiral induction between R-PAC-2, S-PAC-2 and fullerenes is confirmed by single-crystal X-ray diffraction and the intense CD signal within the absorption region of fullerenes. DFT calculations reveal the contribution of electrostatic effects originating from face-to-face arene-fullerene interactions dominate C70 selectivity and elucidate the substituent effect on fullerene encapsulation. The disturbance from the differential interactions between fullerene and surrounding chiral cages on the intrinsic highly symmetric electronic structure of fullerene could be the primary reason accounting for the induced chirality of fullerene.

The connection between nonzero density and spontaneous symmetry breaking for interacting scalars

We consider U(1)-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that, in d > 2 spacetime dimensions, this expectation is always realized at one loop for arbitrary non-derivative interactions, confirming that the physically distinct phenomena of nonzero charge density and spontaneous symmetry breaking occur simultaneously in these systems. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of μ above which a nonzero density develops coincides with the pole mass in the unbroken, Poincaré invariant vacuum of the theory. The same conclusions hold non-perturbatively for an O(N) theory with quartic interactions in d = 3 and 4, at leading order in the 1/N expansion. We derive these results by computing analytically the zero-temperature, finite-μ one-loop effective potential, paying special attention to subtle points related to the iε terms. We check our results against the one-loop low-energy effective action for the superfluid phonons in λϕ4 theory in d = 4 previously derived by Joyce and ourselves, which we further generalize to arbitrary potential interactions and arbitrary dimensions. As a byproduct, we find analytically the one-loop scaling dimension of the lightest charge-n operator for the λϕ6 conformal superfluid in d = 3, at leading order in 1/n, reproducing a numerical result of Badel et al. For a λϕ4 superfluid in d = 4, we also reproduce the Lee-Huang-Yang relation and compute relativistic corrections to it. Finally, we discuss possible extensions of our results beyond perturbation theory.

Pair of optical solitons in parallel planar waveguides coupled by linear photonic crystal

We propose a simple optical model, which consists of two Kerr nonlinear parallel planar waveguides sandwiching a one-dimensional photonic crystal for demonstrating the phenomenon of spontaneous symmetry breaking in optics. We study the shape and stability of soliton pairs propagating in two planar waveguides and the spontaneous symmetry breaking of the power distribution of solitons in the two waveguides. The results of numerical simulation show that there is supercritical type of spontaneous symmetry breaking in this system. More optical power P and smaller refractive index of photonic crystals [Formula: see text] make soliton solutions more prone to spontaneous symmetry breaking bifurcation. Asymmetric soliton solutions and symmetric soliton solutions correspond to different dispersion relations. Under the given total power P, for the symmetric soliton solutions, the propagation constant k increases linearly with [Formula: see text], and for asymmetric soliton solutions, the propagation constant k decreases nonlinearly with [Formula: see text]. The minimum point of [Formula: see text] is just the demarkation between the symmetric soliton solutions and the asymmetric soliton solutions. If [Formula: see text] is fixed, the minimum point of the Hamiltonian of the system, [Formula: see text], is also the critical point of the two different kinds of soliton solutions. We also study stable and unstable distributions of two kinds of soliton solutions.

Temporal manipulation of period-2 polarization domain wall solitons in a nonlinear fiber Kerr resonator

We report on the experimental demonstration of temporal manipulations of dissipative polarization domain wall solitons in a Kerr nonlinear resonator operated in a period-doubled configuration. Our experiments are performed in a coherently driven normally dispersive fiber ring cavity, in which polarization domains emerge in virtue of a spontaneous symmetry breaking phenomenon. The addition of a lumped birefringent defect into the cavity forces their polarization components to swap on a two-round-trip cycle, thus protecting them from the deleterious impact of the system’s asymmetries. We exploit these symbiotic dynamics in proof-of-concept buffering experiments, in which these dissipative structures are addressed individually and temporally manipulated through phase-encoded perturbations imprinted onto the driving beam. Our results provide new insights into the practical exploitation of spontaneous symmetry breaking mechanisms and the use of two-component dissipative structures for all-optical data storage applications.

Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed p-spin Glass Models

Spontaneous symmetry breaking phenomena in the transverse field mixed $p$-spin glass model in finite dimensions are studied with Nishimori's gauge theory. Useful identities in the gauge theory enable us to study $\mathbb Z_2$-symmetry breaking. It is proven that ferromagnetic long-range order and spontaneous magnetization at an arbitrary temperature are bounded by those on the Nishimori line in the corresponding classical model. These bounds imply that neither ferromagnetic long-range order nor spontaneous magnetization exists in spin glass phase. It is proven also that the ferromagnetic susceptibility has an upper bound in paramagnetic and spin glass phases.

Spontaneous symmetry breaking and ghost states in two-dimensional fractional nonlinear media with non-Hermitian potential

The interaction of fractional diffraction and parity-time ({{{{{mathcal{PT}}}}}}) symmetric would bring some unique properties to certain physical system. Here we report a spontaneous symmetry breaking (SSB) phenomenon and ghost states of solitons supported by the two-dimensional (2D) fractional nonlinear Schrödinger (FNLS) equation with focusing and defocusing Kerr media under 2D non-Hermitian {{{{{mathcal{PT}}}}}}-symmetric potential. The continuous asymmetric soliton bifurcates out in a SSB way. For the focusing regime, as the power exceeds a critical value, the asymmetric soliton bifurcates from fundamental symmetric solitons, and when it turns to the defocusing regime, the symmetry breaking phenomenon is found in the branch of the first excited state. The symmetric solitons (including fundamental one and first excited state) are destabilized at this point. Intriguingly, the branches of asymmetry solitons are existing with complex conjugate propagation constants (alias ghost states), which is solely in fractional media. Moreover, we investigate the dependence of fractional Lévy index (α) on the symmetry breaking of solitons in detail. And the stabilities of fundamental symmetric soliton, asymmetric solitons, as well as the first excited states are explored. Moreover, The management of optical field propagation is achieved by modulation of the external potential. Meanwhile, we find the stable excitations of solitons via adiabatic excitations of system parameters. These results will provide some theoretical basis for the study of SSB phenomena and related physical experiments in the 2D fractional media with {{{{{mathcal{PT}}}}}}-symmetric potentials.

Group contraction in physics: History and potential

This article serves as a review of the mathematical tool of group contraction with an emphasis on physical applications. It was implicitly understood that some theories contain others as a special case (e.g., the relation between special relativity and Newtonian mechanics), but until the 1950s there was no firm mathematical grounding for such relations. We discuss the historical development of these concepts, their application to symmetry groups of space and time, and their relevance to the phenomenon of spontaneous symmetry breaking. Finally, we close by proposing a speculative chronology of space-time symmetries in the early universe.

Two-dimensional fractional [formula omitted]-symmetric cubic–quintic NLS equation: Double-loop symmetry breaking bifurcations, ghost states and dynamics

In this paper, we address the double-loop symmetry breaking bifurcations of optical vortex solitons in the two-dimensional (2D) fractional cubic–quintic nonlinear Schrödinger (FCQNLS) equation with an imprinted partially parity-time (PPT) symmetric complex potential. The continuous branches of asymmetric solitons bifurcate from the fundamental one as the power exceeds some critical value. It is found that the symmetry breaking point is exactly the point at which the fundamental symmetric soliton is destabilized. Intriguingly, the branches of asymmetry solitons (alias ghost states) are existing with complex conjugate propagation constants, which is solely in fractional media. Moreover, the branch of asymmetric solitons crosses the branch of fundamental symmetric ones when it reaches the second critical value, and eventually merges back into it at the third critical power point. The imaginary part of the propagation constant also exhibits a circular shape. And the stability of the fundamental symmetric soliton is restored. In addition, the stability of two branches of asymmetric solitons differs from each other. The reason generating this phenomenon is analyzed in detail. Besides, the branch of dipole solitons for the first excited state is also discussed numerically, which is always stable in the process of symmetry breaking. The stability and dynamics of symmetric (fundamental and the first excited ones) and asymmetric solitons are explored via the linear stability analysis, direct simulation, modulation as well as adiabatic excitation. These results will provide some theoretical basis for the study of spontaneous symmetry breaking phenomena and related experiments in fractional media with PPT-symmetric potentials.

Symmetry phases of asymmetric simple exclusion processes on two lanes with an intersection

This paper studies two-lane asymmetric simple exclusion processes (ASEPs) with an intersection. In the upstream segments of the intersection, one particle can move to the next site with rate 1 if the site is empty, and the other particle can move forward with rate p in the sites of downstream segments. The parameter p can represent the rate of slowing of motion, and the parameter is introduced to investigate spontaneous symmetry breaking (SSB) phenomenon. Extensive Monte Carlo simulations are carried out. It is shown that three symmetric phases exist and the SSB does not exist in the system. Simple mean field approach in which correlation of sites is ignored is firstly adopted to analyze the system, and the system is divided into four independent segments. It is found that the analytical results deviate from the simulation ones, especially when p is small. In addition, the inexsitence of SSB can only be explained qualitatively. Motivated by this, we carry out the cluster mean field analysis in which correlation of five sites is considered. It is shown that densities of the two upstream segments are equal, which demonstrates that the SSB does not exist. It is also shown that, as expected, the cluster mean field analysis performs much better than the simple mean field analysis.

Spontaneous symmetry breaking and ghost states supported by the fractional PT-symmetric saturable nonlinear Schrödinger equation.

We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. Intriguingly, the symmetry of fundamental solitons is broken into two branches of asymmetry solitons (alias ghost states) with complex conjugate propagation constants, which is solely in fractional media. Besides, the dipole and tripole solitons (i.e., first and second excited states) are also studied numerically. Moreover, we analyze the influences of fractional Lévy index ( α) and saturable nonlinear parameters (S) on the symmetry breaking of solitons in detail. The stability of fundamental symmetric soliton, asymmetric, dipole, and tripole solitons is explored via the linear stability analysis and direct propagations. Moreover, we explore the elastic/semi-elastic collision phenomena between symmetric and asymmetric solitons. Meanwhile, we find the stable excitations from the fractional diffraction with saturation nonlinearity to integer-order diffraction with Kerr nonlinearity via the adiabatic excitations of parameters. These results will provide some theoretical basis for the study of spontaneous symmetry breaking phenomena and related physical experiments in the fractional media with PT-symmetric potentials.

The suppressed high density phase in three-lane asymmetric exclusion processes with narrow entrances

This paper studies totally asymmetric simple exclusion processes (TASEPs) on three lanes with narrow entrances. Three types of particles move on three parallel lanes, and changing lanes is forbidden. One particle cannot enter one lane if exit site of the neighboring lane is occupied. Simple mean field approach in which correlation of sites is ignored is firstly carried out in the analysis of the system. It is shown that high density is suppressed in the middle lane, and the other two lanes are always symmetric. In addition, the analysis indicates that there are only four phases in the system, and spontaneous symmetry breaking phenomenon does not exist. Extensive Monte Carlo simulations are carried out to confirm the analysis. However, the simple mean field analytical results of phases boundaries deviate that of simulations in the phase diagram. Motivated by this, cluster mean field approach is carried out, and correlations of vertical cluster sites are considered. It is found that the cluster mean field analysis performs much better than the simple mean field analysis.

Experimental Demonstration of Self-Oscillation Microcomb in a Mode-Splitting Microresonator

Self-oscillation and bifurcation as many-body dynamics solutions in a high-Q microresonator have induced substantial interest in nonlinear optics and ultrafast science. Strong mode coupling between clockwise (CW) wave and counterclockwise (CCW) wave induces mode-splitting and optical self-oscillation in the optical cavity. This study experimentally demonstrates the self-oscillation microcomb formation in a microresonator with strong backward Rayleigh scattering. When a pump laser sweeps across a resonance, both spontaneous symmetry breaking (SSB) and self-oscillation phenomenon are observed. The breathing soliton and stable soliton state can switch to each other through careful tuning of the pump detuning. Our experiments provide a reliable scheme for breather soliton microcomb generation. Meanwhile, the rich physics process enhances the comprehension of nonlinear optics in a cavity.

Simulating quantum mechanics with a θ -term and an ’t Hooft anomaly on a synthetic dimension

A topological $\theta$-term in gauge theories, including quantum chromodynamics in 3+1 dimensions, gives rise to a sign problem that makes classical Monte Carlo simulations impractical. Quantum simulations are not subject to such sign problems and are a promising approach to studying these theories in the future. In the near term, it is interesting to study simpler models that retain some of the physical phenomena of interest and their implementation on quantum hardware. For example, dimensionally-reducing gauge theories on small spatial tori produces quantum mechanical models which, despite being relatively simple to solve, retain interesting vacuum and symmetry structures from the parent gauge theories. Here we consider quantum mechanical particle-on-a-circle models, related by dimensional reduction to the 1+1d Schwinger model, that possess a $\theta$-term and realize an 't Hooft anomaly or global inconsistency at $\theta = \pi$. These models also exhibit the related phenomena of spontaneous symmetry breaking and instanton-anti-instanton interference in real time. We propose an experimental scheme for the real-time simulation of a particle on a circle with a $\theta$-term and a $\mathbb{Z}_n$ potential using a synthetic dimension encoded in a Rydberg atom. Simulating the Rydberg atom with realistic experimental parameters, we demonstrate that the essential physics can be well-captured by the experiment, with expected behavior in the tunneling rate as a function of $\theta$. Similar phenomena and observables can also arise in more complex quantum mechanical models connected to higher-dimensional nonabelian gauge theories by dimensional reduction.

Characterizing the E⊗e Jahn–Teller Potential Energy Surfaces by Differential Geometry Tools

The term ‘mathematical chemistry’ is mostly associated with applications of graph theory in topological issues of 3D chemical structures, thought of as a collection of atoms as dots and bonds as lines. We propose here new directions in this field, coming from the side of theoretical chemistry approached with modern computational tools. Possible challenges are proposed in using ancillary tools of differential geometry for examining the potential energy surfaces of certain specific structural prototypes. Concretely, we describe here the geodesics on the surfaces related to the potential energy functions of the so-called E⊗e Jahn–Teller effect, a spontaneous symmetry-breaking phenomenon also known as a case of conical intersection. To illustrate the case, first-principles (ab initio) quantum chemical calculations are performed on the cyclo-propenyl molecular radical C3H3.

Post-spontaneous-symmetry-breaking power-laws after a very strong earthquake: Indication for the preparation of a new strong earthquake or not?

It has recently been found that the evolution of the preparation of a strong earthquake (EQ), as it is monitored through fracture-induced electromagnetic emissions (EME) in the MHz band, presents striking similarity with the evolution of a thermal system as temperature drops, since distinct steps of the evolution of the phenomenon of spontaneous symmetry breaking (SSB) can be identified. Here, the study of fracture-induced EME in the MHz band in analogy to thermal systems is extended to the phase of local fracture structures that follow after the SSB (and the occurrence of the main EQ). By comparing fracture-induced MHz EME associated with the strongest EQs (MW=6.9) that occurred in Greece during the last twenty years with the 3D Ising model, a way to distinguish whether a possible identification of post-SSB power-laws immediately after a very strong EQ is a sign for the preparation of a new strong EQ or not is provided. In the suggested approach, the time series analysis method known as the method of critical fluctuations is used, enhanced by the autocorrelation function.

The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets.

Persistence of spontaneous symmetry breaking in bidirectional transport system with reservoir crowding

Motivated by the impact of limited resources on the entry and exit of entities on a pathway in many transport systems, we investigate a system comprising of a bidirectional totally asymmetric simple exclusion process coupled to a reservoir featuring crowding effect. The entry and exit of particles from both ends are regulated depending upon the occupancy of the reservoir. The steady state properties of the system have been theoretically analyzed, and the phase boundaries have been obtained. Our findings display a rich behavior, emphasizing on the non-trivial effects of reservoir crowding giving rise to symmetric as well as asymmetric phases. Further, the system exhibits a novel feature in the form of a back-and-forth transition. Also, it is found that spontaneous symmetry breaking phenomena is induced even for very few particles in the system. All the findings are validated by extensive Monte Carlo simulations. The effect of system size on Monte Carlo simulation results have been examined.