Process Of Spontaneous Symmetry Breaking Research Articles

Gribov problem in the eletroweak and gluon confined theories

We show that gauge fields after a spontaneous symmetry breaking (SSB) mechanism do not have a Gribov problem along the broken directions. In order to make this proof, we describe a gauge fixing procedure inspired on Morse’s theory leading to the concept of a gauge fixing generating functional. This approach is specially suited in order to understand the unitary gauges of ’t Hooft. The conclusion is that after a SSB process, the generalized Faddeev-Popov operator acquires a positive definite value along the broken directions. We show how this works in the eletroweak SU(2)XU(1) theory, where such a result is in fact expected as in this case the gauge fields acquire masses after the SSB. Then we apply this development to the SL(3,c) confining model of Amaral [A path to confine gluons and fermions through complex gauge theory, ]. The final result explains why such confining mechanism is actually a solution to the Gribov problem for the confined gauge fields. These cases show that although confinement is not a general effect of the solution of the Gribov problem, as we can infer from the eletroweak example, its solution indeed seems to be necessary in order to achieve confinement. In the end, these conclusions allow us to speculate that the strong interaction confinement may be the result of some hidden SSB mechanism yet to be described. Published by the American Physical Society 2024

Kinetic Investigations on the Chiral Induction by Amino Acids in Porphyrin J-Aggregates.

The self-assembling kinetics of the 5,10,15,20-tetrakis(4-sulfonato-phenyl)porphyrin (TPPS4) into nano-tubular J-aggregates under strong acidic condition and in the presence of amino acids as templating chiral reagents have been investigated through UV/Vis spectroscopy. The ability of the chiral species to transfer its chiral information to the final J-aggregate has been measured through circular dichroism (CD) spectroscopy and compared to the spontaneous symmetry breaking process usually observed in these nano-aggregates. Under the experimental conditions here selected, including mixing protocol, we have observed a large difference in the observed aggregation rates for the various amino acids, those with a positively charged side group being the most effective. On the contrary, these species are less efficient in transferring their chirality, exhibiting a quite low or modest enhancement in the observed dissymmetry g-factors. On the other side, hydrophobic and some hydrophilic amino acids are revealed to be very active in inducing chirality with a discrete increase of intensity of the detected CD bands with respect to the spontaneous symmetry breaking.

Quantum Fluctuations in Vacuum Energy: Cosmic Inflation as a Dynamical Phase Transition

A variety of models of inflation in the early Universe have been proposed and applied to describe successfully the origin of all possible structures in the Universe. On the other hand, inflation theory is still phenomenological and needs systematic physical foundations, including the relation to dark matter and dark energy. The essence of cosmic inflation would be a dynamical phase transition and the spontaneous symmetry breaking process, which are common in ordinary physics in the laboratory. At the beginning of the phase transition, the system is often in an adiabatic ground state and produces a squeezed state. This is widely interpreted as the generation of classical structures; however, it is not. The common notion of decoherence is not sufficient to describe the inflationary phase transition: a particular trajectory must be singled out in the dynamics. When an interaction turns on, dissipation or the energy flow/cascade is possible, and the c-number random field appears. The separation of these classical statistical fluctuations from the deterministic time evolution is indicated by the secular divergence or the infrared divergence of the system. We describe this phase transition based on the closed-time-path method and derive a quantum Langevin equation with classical noise, which sources the development of a coherent state. Introducing the effective action method to describe the evolution of the coherent state, we describe the order parameter that characterizes the phase transition and the associated spontaneous symmetry breaking. Since this phase transition process is common in physics, we discuss further applications of this formalism in other physical systems.

Chirality transfer from a 3D macro shape to the molecular level by controlling asymmetric secondary flows

Homochirality is a fundamental feature of living systems, and its origin is still an unsolved mystery. Previous investigations showed that external physical forces can bias a spontaneous symmetry breaking process towards deterministic enantioselection. But can the macroscopic shape of a reactor play a role in chiral symmetry breaking processes? Here we show an example of chirality transfer from the chiral shape of a 3D helical channel to the chirality of supramolecular aggregates, with the handedness of the helical channel dictating the direction of enantioselection in the assembly of an achiral molecule. By combining numerical simulations of fluid flow and mass transport with experimental data, we demonstrated that the chiral information is transferred top-down thanks to the interplay between the hydrodynamics of asymmetric secondary flows and the precise spatiotemporal control of reagent concentration fronts. This result shows the possibility of controlling enantioselectively molecular processes at the nanometer scale by modulating the geometry and the operating conditions of fluidic reactors.

The solitary solutions of nonlinear Klein-Gordon field with minimal length

The existence of a minimal length is predicted by theories of quantum gravity and it is generally accepted that this minimal length should be of the order of the Planck length and hence can be observed in high energy phenomenon. We study the implications of the presence of the minimal length on the Klein-Gordon filed with ϕ4 self-interaction. Considering the process of spontaneous symmetry breaking, the potential also includes the ϕ3 term. The consequent field equation is a fourth-order differential equation and is considered to have solitary solutions. The sech method is applied and the normalized solutions are obtained in closed forms and the energy spectrum of the solitary fields is determined. The modification parameter of the theory is estimated by the width and the energy of the obtained solitary fields.

Automatic learning of topological phase boundaries.

Topological phase transitions, which do not adhere to Landau's phenomenological model (i.e., a spontaneous symmetry breaking process and vanishing local order parameters), have been actively researched in condensed matter physics. Machine learning of topological phase transitions has generally proved difficult due to the global nature of the topological indices. Only recently has the method of diffusion maps been shown to be effective at identifying changes in topological order. However, previous diffusion map results required adjustments of two hyperparameters: a data length scale and the number of phase boundaries. In this article we introduce a heuristic that requires no such tuning. This heuristic allows computer programs to locate appropriate hyperparameters without user input. We demonstrate this method's efficacy by drawing remarkably accurate phase diagrams in three physical models: the Haldane model of graphene, a generalization of the Su-Schreiffer-Haeger model, and a model for a quantum ring with tunnel junctions. These diagrams are drawn, without human intervention, from a supplied range of model parameters.

Synchronization and temporal nonreciprocity of optical microresonators via spontaneous symmetry breaking

Synchronization is of importance in both fundamental and applied physics, but its demonstration at the micro/nanoscale is mainly limited to low-frequency oscillations such as mechanical resonators. We report the synchronization of two coupled optical microresonators, in which the high-frequency resonances in the optical domain are aligned with reduced noise. It is found that two types of synchronization regimes emerge with either the first- or second-order transition, both presenting a process of spontaneous symmetry breaking. In the second-order regime, the synchronization happens with an invariant topological character number and a larger detuning than that of the first-order case. Furthermore, an unconventional hysteresis behavior is revealed for a time-dependent coupling strength, breaking the static limitation and the temporal reciprocity. The synchronization of optical microresonators offers great potential in reconfigurable simulations of many-body physics and scalable photonic devices on a chip.

Symmetry breaking and functional incompleteness in biological systems

Symmetry-based explanations using symmetry breaking (SB) as the key explanatory tool have complemented and replaced traditional causal explanations in various domains of physics. The process of spontaneous SB is now a mainstay of contemporary explanatory accounts of large chunks of condensed-matter physics, quantum field theory, nonlinear dynamics, cosmology, and other disciplines. A wide range of empirical research into various phenomena related to symmetries and SB across biological scales has accumulated as well. Led by these results, we identify and explain some common features of the emergence, propagation, and cascading of SB-induced layers across the biosphere. These features are predicated on the thermodynamic openness and intrinsic functional incompleteness of the systems at stake and have not been systematically analyzed from a general philosophical and methodological perspective. We also consider possible continuity of SB across the physical and biological world and discuss the connection between Darwinism and SB-based analysis of the biosphere and its history.

Zigzag Solitons and Spontaneous Symmetry Breaking in Discrete Rabi Lattices with Long-Range Hopping

A new type of discrete soliton, which we call zigzag solitons, is founded in two-component discrete Rabi lattices with long-range hopping. The spontaneous symmetry breaking (SSB) of zigzag solitons is also studied. Through numerical simulation, we found that by enhancing the intensity of the long-range linearly-coupled effect or increasing the total input power, the SSB process from the symmetric soliton to the asymmetric soliton will switch from the supercritical to subcritical type. These results can help us better understand both the discrete solitons and the Rabi coupled effect.

The quantum Higgs field and the resolution of the cosmological constant paradox in the Weyl-geometrical Universe

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of the Weyl’s differential geometry: the parallel displacement of vectors in curved spacetime. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the [Formula: see text] as well as on the conformal groups of spacetime Weyl’s transformations is analyzed within the framework of a general-relativistic, conformally-covariant scalar–tensor theory that includes the electromagnetic and the Yang–Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An “effective cosmological potential”: [Formula: see text] is expressed in terms of the dark energy potential: [Formula: see text] via the “mass reduction parameter”: [Formula: see text], a general property of the Universe. The mass of the Higgs boson, which is considered a “free parameter” by the standard electroweak theory, by our theory is found to be proportional to the mass [Formula: see text] which contributes to the measured Cosmological Constant, i.e. the measured content of vacuum-energy in the Universe. The nonintegrable application of the Weyl’s geometry leads to a Proca equation accounting for the dynamics of a [Formula: see text]-particle, a vector-meson proposed as an optimum candidate for Dark Matter. The peculiar mathematical structure of [Formula: see text] offers a clue towards a very general resolution in 4-D of a most intriguing puzzle of modern quantum field theory, the “cosmological constant paradox”(here referred to as: “[Formula: see text]-paradox”). Indeed, our “universal” theory offers a resolution of the “[Formula: see text]-paradox” for all exponential inflationary potentials: [Formula: see text], and for all linear superpositions of these potentials, where [Formula: see text] belongs to the mathematical set of the “real numbers”. An explicit solution of the [Formula: see text]-Paradox is reported for [Formula: see text]. The results of the theory are analyzed in the framework of the recent experimental data of the PLANCK Mission. The average vacuum-energy density in the Universe is found: [Formula: see text], the mass-reduction parameter: [Formula: see text] and the value of the “cosmological constant”: [Formula: see text](eV/c[Formula: see text]. A quite remarkable result of the theory consists of the complete formulation of the Einstein equation including in its structure the “cosmological constant”, [Formula: see text]. This was the term that Einstein added “by hand” to his famous equation. The critical stability of the Universe is also discussed.

The Higgs field and the resolution of the Cosmological Constant Paradox in the Weyl-geometrical Universe.

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of Weyl's differential geometry: the parallel displacement of vectors in curved space-time. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the SU(2) L ⊗U(1) Y as well as on the conformal groups of space-time Weyl's transformations is analysed within the framework of a general-relativistic, conformally covariant scalar-tensor theory that includes the electromagnetic and the Yang-Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An 'effective cosmological potential': Veff is expressed in terms of the dark energy potential: [Formula: see text] via the 'mass reduction parameter': [Formula: see text], a general property of the Universe. The mass of the Higgs boson, which is considered a 'free parameter' by the standard electroweak theory, by our theory is found to be proportional to the mass [Formula: see text] which accounts for the measured cosmological constant, i.e. the measured content of vacuum-energy in the Universe. The non-integrable application of Weyl's geometry leads to a Proca equation accounting for the dynamics of a ϕρ -particle, a vector-meson proposed as an an optimum candidate for dark matter. On the basis of previous cosmic microwave background results our theory leads, in the condition of cosmological 'critical density', to the assessment of the average energy content of the ϕρ -excitation. The peculiar mathematical structure of Veff offers a clue towards a very general resolution of a most intriguing puzzle of modern quantum field theory, the 'Cosmological Constant Paradox' (here referred to as the 'Λ-Paradox'). Indeed, our 'universal' theory offers a resolution of the Λ-Paradox for all exponential inflationary potentials: VΛ (T,ϕ)∝e-nϕ , and for all linear superpositions of these potentials, where n belongs to the mathematical set of the 'real numbers'. An explicit solution of the Λ-Paradox is reported for n=2. The resolution of the Λ-Paradox cannot be achieved in the context of Riemann's differential geometry.This article is part of the themed issue 'Second quantum revolution: foundational questions'.

Inflation, the Higgs field and the resolution of the Cosmological Constant Paradox

The nature of the scalar field responsible for the cosmological inflation, the ”inflaton”, is found to be rooted in the most fundamental concept of the Weyl’s differential geometry: the parallel displacement of vectors in curved space-time. Within this novel dynamical scenario, the standard electroweak theory of leptons based on the SU(2)L ⊗ U(1)Y as well as on the conformal groups of spacetime Weyl’s transformations is analyzed within the framework of a general-relativistic, co-covariant scalar-tensor theory that includes the electromagnetic and the Yang-Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An ”Effective Cosmological Potential”: Veff is expressed in terms of the dark energy potential: via the ”mass reduction parameter”: , a general property of the Universe. The mass of the Higgs boson, which is considered a ”free parameter” by the standard electroweak theory, by our theory is found to be proportional to the geometrical mean: of the Planck mass, MP and of the mass which accounts for the measured Cosmological Constant, i.e. the measured content of vacuum-energy in the Universe. The experimental result obtained by the ATLAS and CMS Collaborations at CERN in the year 2012: MH = 125.09(GeV/c2) leads by our theory to a value: Meff ~ 3.19 · 10−6(eV/c2). The peculiar mathematical structure of Veff offers a clue towards the resolution of a most intriguing puzzle of modern quantum field theory, the ”Cosmological Constant Paradox”.

Hidden phase in a two-dimensional Sn layer stabilized by modulation hole doping

Semiconductor surfaces and ultrathin interfaces exhibit an interesting variety of two-dimensional quantum matter phases, such as charge density waves, spin density waves and superconducting condensates. Yet, the electronic properties of these broken symmetry phases are extremely difficult to control due to the inherent difficulty of doping a strictly two-dimensional material without introducing chemical disorder. Here we successfully exploit a modulation doping scheme to uncover, in conjunction with a scanning tunnelling microscope tip-assist, a hidden equilibrium phase in a hole-doped bilayer of Sn on Si(111). This new phase is intrinsically phase separated into insulating domains with polar and nonpolar symmetries. Its formation involves a spontaneous symmetry breaking process that appears to be electronically driven, notwithstanding the lack of metallicity in this system. This modulation doping approach allows access to novel phases of matter, promising new avenues for exploring competing quantum matter phases on a silicon platform.

Compatibility between the Ginzburg–Landau model and finite-temperature quantum field theory

The formalism of finite-temperature quantum field theory, as developed by Matsubara, is applied to a Hamiltonian of N scalar fields with a quartic self-interaction at large N. A renormalized expression in the lowest quantum approximation is obtained for the squared mass m2 of the field, as a function of the temperature T, from which we study the process of spontaneous symmetry breaking. We find that in a range of values around the critical temperature Tc, the squared mass can be approximated by a linear relation m2 [Formula: see text] (T − Tc). We thus demonstrate the compatibility of the finite-temperature formalism for scalar fields, in the vicinity of criticality, with respect to the Ginzburg–Landau model. We also discuss the effects caused by the presence of a chemical potential and of an external magnetic field applied to the finite-temperature system, which however do not affect the linearity of the relation between the squared mass and the temperature.

Fluctuation-dissipation dynamics of cosmological scalar fields

We show that dissipative effects have a significant impact on the evolution of cosmological scalar fields, leading to friction, entropy production and field fluctuations. We explicitly compute the dissipation coefficient for different scalar fields within the Standard Model and some of its most widely considered extensions, in different parametric regimes. We describe the generic consequences of fluctuation-dissipation dynamics in the post-inflationary universe, focusing in particular on friction and particle production, and analyze in detail two important effects. Firstly, we show that dissipative friction delays the process of spontaneous symmetry breaking and may even damp the the motion of a Higgs field sufficiently to induce a late period of warm inflation. Along with dissipative entropy production, this may parametrically dilute the abundance of dangerous thermal relics. Secondly, we show that dissipation can generate the observed baryon asymmetry without symmetry restoration, and we develop in detail a model of dissipative leptogenesis. We further show that this generically leads to characteristic baryon isocurvature perturbations that can be tested with CMB observations. This work provides a fundamental framework to go beyond the leading thermal equilibrium semi-classical approximation in addressing fundamental problems in modern cosmology.

Spontaneous symmetry breaking discovers the formation of aeroplane-like ZnO nanocrystals

Although symmetry breaking is widely realized as one of the most powerful tools in modern scientific researches, it is unclear how symmetry breaking plays its role in nanocosm. Here, we show a correlation between spontaneous symmetry breaking and the formation of nanocrystals. In our experiments, some ZnO nanocrystals, including ZnO tetrapods, rod-based tetrapods, and aeroplane-like crystals, presented with specific structures and symmetries leading to an unexpected process of spontaneous symmetry breaking. According to the rule of spontaneous symmetry breaking, a hypothesis was proposed that the aeroplane-like nanocrystals might be resulted from the unequal development of the crystal twinnings. Subsequent work supported this hypothesis and proved the dramatic effect of spontaneous symmetry breaking. This work applies the rule of spontaneous symmetry breaking to the formation mechanisms for nanocrystals and highlights the causal contribution of spontaneous symmetry breaking to the intricate behaviors of the particles at nanoscale.

EPR measurement and the origin of cosmic density fluctuations

We explore consistent application of quantum mechanics to the objects in the Universe and in laboratories. The measurement dynamics in quantum mechanics is modeled as a physical process of spontaneous symmetry breaking (SSB) which is de- scribed by the generalized effective action method. A violation of the Bell inequality is observed in this model and the generation of the density fluctuations in the early Universe is described as the SSB process of the spatially translational symmetry.

Non-equilibrium field dynamics of an honest holographic superconductor

Most holographic models of superconducting systems neglect the effects of dynamical boundary gauge fields during the process of spontaneous symmetry-breaking. Usually a global symmetry gets broken. This yields a superfluid, which then is gauged "weakly" afterwards. In this work we build (and probe the dynamics of) a holographic model in which a local boundary symmetry is spontaneously broken instead. We compute two-point functions of dynamical non-Abelian gauge fields in the normal and in the broken phase, and find non-trivial gapless modes. Our AdS3 gravity dual realizes a p-wave superconductor in (1+1) dimensions. The ground state of this model also breaks (1+1)-dimensional parity spontaneously, while the Hamiltonian is parity-invariant. We discuss possible implications of our results for a wider class of holographic liquids.

Threads of Time

The concept of time’s arrow is examined using the principle of least action as given in its original non-Abelian form. When every entity of nature is considered to be composed of quantized actions, such an entity will change, either by absorbing quanta from surrounding actions or by emitting quanta to the surrounding actions. In natural processes, quanta disperse from high-energy density actions to low-energy density actions in quest of consuming free energy in least time. We propose that the flux of quanta embodies the flow of time, and therefore the irreversible consumption of free energy creates time’s arrow in a fundamental physical sense. The cosmological arrow of time results from universal processes that take place, most notably, in stars and other celestial systems, where matter, that is, bound actions, combusts to photons, that is, freely propagating actions. The biological arrow of time manifests itself in maturation processes where quanta absorb to emerging functional structures, leading eventually to aging processes where quanta, on balance, emit from disintegrating organs. Mathematical analysis of an evolutionary equation of motion, given in general terms of a spontaneous symmetry breaking process of actions, reveals the reason why future paths—and the future itself—remain inherently intractable.

Preheating in new inflation

During the last ten years a detailed investigation of preheating was performed for chaotic inflation and for hybrid inflation. However, nonperturbative effects during reheating in the new inflation scenario remained practically unexplored. We do a full analysis of preheating in new inflation, using a combination of analytical and numerical methods. We find that the decay of the homogeneous component of the inflaton field and the resulting process of spontaneous symmetry breaking in the simplest models of new inflation usually occurs almost instantly: for the new inflation on the GUT scale it takes only about 5 oscillations of the field distribution. The decay of the homogeneous inflaton field is so efficient because of a combined effect of tachyonic preheating and parametric resonance. At that stage, the homogeneous oscillating inflaton field decays into a collection of waves of the inflaton field, with a typical wavelength of the order of the inverse inflaton mass. This stage usually is followed by a long stage of decay of the inflaton field into other particles, which can be described by the perturbative approach to reheating after inflation. The resulting reheating temperature typically is rather low.