Form Of Spontaneous Symmetry Breaking Research Articles

Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers.

We consider phase transitions, in the form of spontaneous symmetry breaking (SSB) bifurcations of solitons, in dual-core couplers with fractional diffraction and cubic self-focusing acting in each core, characterized by Lévy index α. The system represents linearly coupled optical waveguides with the fractional paraxial diffraction or group-velocity dispersion (the latter system was used in a recent experiment [Nat. Commun. 14, 222 (2023)10.1038/s41467-023-35892-8], which demonstrated the first observation of the wave propagation in an effectively fractional setup). By dint of numerical computations and variational approximation, we identify the SSB in the fractional coupler as the bifurcation of the subcritical type (i.e., the symmetry-breaking phase transition of the first kind), whose subcriticality becomes stronger with the increase of fractionality 2-α, in comparison with very weak subcriticality in the case of the nonfractional diffraction, α=2. In the Cauchy limit of α→1, it carries over into the extreme subcritical bifurcation, manifesting backward-going branches of asymmetric solitons which never turn forward. The analysis of the SSB bifurcation is extended for moving (tilted) solitons, which is a nontrivial problem because the fractional diffraction does not admit Galilean invariance. Collisions between moving solitons are studied too, featuring a two-soliton symmetry-breaking effect and merger of the solitons.

Uncovering the non-equilibrium stationary properties in sparse Boolean networks

Dynamic processes of interacting units on a network are out of equilibrium in general. In the case of a directed tree, the dynamic cavity method provides an efficient tool that characterises the dynamic trajectory of the process for the linear threshold model. However, because of the computational complexity of the method, the analysis has been limited to systems where the largest number of neighbours is small. We devise an efficient implementation of the dynamic cavity method which substantially reduces the computational complexity of the method for systems with discrete couplings. Our approach opens up the possibility to investigate the dynamic properties of networks with fat-tailed degree distribution. We exploit this new implementation to study properties of the non-equilibrium steady-state. We extend the dynamic cavity approach to calculate the pairwise correlations induced by different motifs in the network. Our results suggest that just two basic motifs of the network are able to accurately describe the entire statistics of observed correlations. Finally, we investigate models defined on networks containing bi-directional interactions. We observe that the stationary state associated with networks with symmetric or anti-symmetric interactions is biased towards the active or inactive state respectively, even if independent interaction entries are drawn from a symmetric distribution. This phenomenon, which can be regarded as a form of spontaneous symmetry-breaking, is peculiar to systems formulated in terms of Boolean variables, as opposed to Ising spins.

Scalar and vector supermode solitons owing to competing nonlocal nonlinearities.

We investigate scalar and vector multi-hump spatial solitons resulting from competing Kerr-like nonlinear responses excited in a nonlocal medium by either one or two (mutually incoherent) light beams. Two-color vector supermode solitons are more amenable to control but exhibit an intriguing form of spontaneous symmetry breaking in propagation.

Covert symmetry breaking

Reduction from a higher-dimensional to a lower-dimensional field theory can display special features when the zero-level ground state has nontrivial dependence on the reduction coordinates. In particular, a delayed ‘covert’ form of spontaneous symmetry breaking can occur, revealing itself only at fourth order in the lower-dimensional effective field theory action. This phenomenon is explored in a simple model of (d + 1)-dimensional scalar QED with one dimension restricted to an interval with Dirichlet/Robin boundary conditions on opposing ends. This produces an effective d-dimensional theory with Maxwellian dynamics at the free theory level, but with unusual symmetry breaking appearing in the quartic vector-scalar interaction terms. This simple model is chosen to illuminate the mechanism of effects which are also noted in gravitational braneworld scenarios.

What is a particle-conserving Topological Superfluid? The fate of Majorana modes beyond mean-field theory

We investigate Majorana modes of number-conserving fermionic superfluids from both basic physics principles, and concrete models perspectives. After reviewing a criterion for establishing topological superfluidity in interacting systems, based on many-body fermionic parity switches, we reveal the emergence of zero-energy modes anticommuting with fermionic parity. Those many-body Majorana modes are constructed as coherent superpositions of states with different number of fermions. While realization of Majorana modes beyond mean field is plausible, we show that the challenge to quantum-control them is compounded by particle-conservation, and more realistic protocols will have to balance engineering needs with astringent constraints coming from superselection rules. Majorana modes in number-conserving systems are the result of a peculiar interplay between quantum statistics, fermionic parity, and an unusual form of spontaneous symmetry breaking. We test these ideas on the Richardson–Gaudin–Kitaev chain, a number-conserving model solvable by way of the algebraic Bethe ansatz, and equivalent in mean field to a long-range Kitaev chain.

Correlated spontaneous symmetry breaking induced by zero-point fluctuations in a quantum mixture

We propose a form of spontaneous symmetry breaking driven by zero-point quantum fluctuations. To be specific, we consider the low-energy dynamics of a mixture of two species of spin-1 Bose gases. It is demonstrated that the quantum fluctuations lift a degeneracy regarding the relative orientations of the spin directors of the two species and result in correlation or locking between these macroscopic variables. This locking persists in the presence of the trapping potential and weak magnetic fields, allowing, in principle, an experimental probe of this correlated spontaneous symmetry breaking as a macroscopic manifestation of zero-point quantum fluctuations.

A nanoscale experiment measuring gravity's role in breaking the unitarity of quantum dynamics

Modern, state-of-the-art nanomechanical devices are capable of creating spatial superpositions that are massive enough to begin to experimentally access the quantum to classical crossover, and thus force us to consider the possible ways in which the usual quantum dynamics may be affected. One recent theoretical proposal describes the crossover from unitary quantum mechanics to classical dynamics as a form of spontaneous symmetry breaking. Here, we propose a specific experimental set-up capable of identifying the source of unitarity breaking in such a mechanism. The experiment is aimed specifically at clarifying the role played by gravity, and distinguishes the resulting dynamics from that suggested by alternative scenarios for the quantum to classical crossover. We give both a theoretical description of the expected dynamics, and a discussion of the involved experimental parameter values and the proposed experimental protocol.

Broken Time Translation Symmetry as a Model for Quantum State Reduction

The symmetries that govern the laws of nature can be spontaneously broken, enabling the occurrence of ordered states. Crystals arise from the breaking of translation symmetry, magnets from broken spin rotation symmetry and massive particles break a phase rotation symmetry. Time translation symmetry can be spontaneously broken in exactly the same way. The order associated with this form of spontaneous symmetry breaking is characterised by the emergence of quantum state reduction: systems which spontaneously break time translation symmetry act as ideal measurement machines. In this review the breaking of time translation symmetry is first compared to that of other symmetries such as spatial translations and rotations. It is then discussed how broken time translation symmetry gives rise to the process of quantum state reduction and how it generates a pointer basis, Born’s rule, etc. After a comparison between this model and alternative approaches to the problem of quantum state reduction, the experimental implications and possible tests of broken time translation symmetry in realistic experimental settings are discussed.

Soft random solids and their heterogeneous elasticity

Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the structure of soft random solids is a result of the fluctuations locked-in at their synthesis, which also brings heterogeneity in their elastic properties. Vulcanization theory studies semimicroscopic models of random-solid-forming systems and applies replica field theory to deal with their quenched disorder and thermal fluctuations. The elastic deformations of soft random solids are argued to be described by the Goldstone sector of fluctuations contained in vulcanization theory, associated with a subtle form of spontaneous symmetry breaking that is associated with the liquid-to-random-solid transition. The resulting free energy of this Goldstone sector can be reinterpreted as arising from a phenomenological description of an elastic medium with quenched disorder. Through this comparison, we arrive at the statistics of the quenched disorder of the elasticity of soft random solids in terms of residual stress and Lamé-coefficient fields. In particular, there are large residual stresses in the equilibrium reference state, and the disorder correlators involving the residual stress are found to be long ranged and governed by a universal parameter that also gives the mean shear modulus.

Numerical study of multisoliton configurations in a doped antiferromagnetic Mott insulator

We evaluate from first principles the self-consistent Hartree-Fock energies for multisoliton configurations in a doped, spin-$\frac{1}{2}$, antiferromagnetic Mott insulator on a two-dimensional square lattice. The microscopic Hamiltonian for this system involves a nearest-neighbor electron hopping matrix element t, an on-site Coulomb repulsion U, and a nearest-neighbor Coulomb repulsion V. We find that nearest-neighbor Coulomb repulsion on the energy scale of t stabilizes a regime of charged meron-antimeron vortex soliton pairs over a region of doping from $\ensuremath{\delta}=0.05$ to $0.4$ holes per site for intermediate coupling $3<~U/t<~8$. This stabilization is mediated through the generation of ``spin flux'' in the mean-field antiferromagnetic (AFM) background. Spin flux is a form of spontaneous symmetry breaking in a strongly correlated electron system in which the Hamiltonian acquires a term with the symmetry of spin-orbit coupling at the mean-field level. Spin flux modifies the single quasiparticle dispersion relations from that of a conventional AFM. The modified dispersion is consistent with angle-resolved photoemission studies and has a local minimum at wave vector $\stackrel{\ensuremath{\rightarrow}}{k}=\ensuremath{\pi}/2a(1,1)$, where a is the lattice constant. Holes cloaked by a meron vortex in the spin-flux AFM background are charged bosons. Our static Hartree-Fock calculations provide an upper bound on the energy of a finite density of charged vortices. This upper bound is lower than the energy of the corresponding charged spin-polaron configurations. A finite density of charge carrying vortices is shown to produce a large number of unoccupied electronic levels in the Mott-Hubbard charge transfer gap. These levels lead to significant band tailing and a broad midinfrared band in the optical absorption spectrum as observed experimentally. In the presence of a finite density of charged meron-antimeron pairs, the peak in the magnetic structure at $\stackrel{\ensuremath{\rightarrow}}{Q}=\ensuremath{\pi}/a(1,1)$, corresponding to the undoped AFM, splits into four satellite peaks that evolve with charge carrier concentration as observed experimentally. At very low doping $(\ensuremath{\delta}<0.05)$ the doping charges create extremely tightly bound meron-antimeron pairs or even isolated conventional spin polarons, whereas for very high doping $(\ensuremath{\delta}>0.4)$ the spin background itself becomes unstable to formation of a conventional Fermi liquid and the spin-flux mean field is energetically unfavorable. Our results point to the predominance of a quantum liquid of charged, bosonic, vortex solitons at intermediate coupling and intermediate doping concentrations.

Generalized Group-Theoretical Analysis of Spontaneous Symmetry Breaking

A group-theoretical analysis of spontaneous symmetry breaking is carried out in an extension of Glashow's work. A general theorem is proved which is then used to give several interesting results. Apart from a rederivation of Glashow's result, we are able to show, among other things, the following: If a hadronic triplet exists in nature which is nontrivially coupled to the rest of the hadrons, then octet enhancement immediately follows independently of any dynamical detail; in models containing the vector nonet, φ - ω mixing can, in principle, occur as a particular form of spontaneous symmetry breaking in the octet pattern; and if octet enhancement holds, the very accurate mass formula mφ2+mω2=2mk2* is established without recourse to any dynamical detail. Under the same general assumption, a further relation is found relating the mass of the nonet with the mixing angle, which is 4mk2*−3(cos2θmφ2+sin2θmω2)−mρ2=0.