Symmetry Breaking Mechanism Research Articles

Geometric-control formulation and averaging analysis of the unsteady aerodynamics of a wing with oscillatory controls

Differential-geometric-control theory represents a mathematically elegant combination of differential geometry and control theory. Practically, it allows exploitation of nonlinear interactions between various inputs for the generation of forces in non-intuitive directions. Since its early developments in the 1970s, the geometric-control theory has not been duly exploited in the area of fluid mechanics. In this paper, we show the potential of geometric-control theory in the analysis of fluid flows, exemplifying it as a heuristic analysis tool for discovery of symmetry-breaking and unconventional force-generation mechanisms. In particular, we formulate the wing unsteady aerodynamics problem in a geometric-control framework. To achieve this goal, we develop a reduced-order model for the unsteady flow over a pitching–plunging wing that is (i) rich enough to capture the main physical aspects (e.g. nonlinearity of the flow dynamics at large angles of attack and high frequencies) and (ii) efficient and compact enough to be amenable to the analytic tools of geometric nonlinear control theory. We then combine tools from geometric-control theory and averaging to analyse the developed reduced-order dynamical model, which reveals regimes for lift and thrust enhancement mechanisms. The unsteady Reynolds-averaged Navier–Stokes equations are simulated to validate the theoretical findings and scrutinize the underlying physics behind these enhancement mechanisms.

Understanding Symmetry Breaking at the Single-Particle Level via the Growth of Tetrahedron-Shaped Nanocrystals from Higher-Symmetry Precursors.

The vast majority of single crystalline metal nanoparticles adopt shapes in the Oh point group as a consequence of the symmetry of the underlying face-centered cubic (FCC) crystal lattice. Tetrahedra are a notable exception to this rule, and although they have been observed in several syntheses, their growth mechanism, and the symmetry-reduction process that necessarily characterizes it, is poorly understood. Here, a symmetry breaking mechanism is revealed by in situ liquid flow cell transmission electron microscopy (TEM) observation of seeded growth in which tetrahedra nanoparticles are formed from higher symmetry seeds. Real-time observation of the growth demonstrates a kinetically driven pathway during which rhombic dodecahedra nanoparticles transition to tetrahedra through tristetrahedra intermediates, with an accompanying surface facet evolution from {110} to {111} via {hhl} (where h > l), respectively. On the basis of these data, we propose a mechanism that relies on a rapid loss of inversion symmetry in the initial stages of the reaction, followed by differential reactivity of tips vs faces under conditions of relatively high supersaturation and moderate ligand concentration. The application of these insights to ex situ synthesis conditions allowed for an improved yield of tetrahedra nanoparticles. This work sheds an important mechanistic light on the crystallographic underpinnings of nanoparticle shape and symmetry transformations and highlights the importance of single-particle characterization tools for monitoring nanoscale phenomena.

Эффекты общей теории относительности в прецизионных спиновых экспериментах по проверке фундаментальных симметрий

A search for the $P$- and $CP(T)$-violating electric dipole moments (EDM) of atoms, particles and nuclei with sensitivity up to $10^{-15}$ in units of magnetic dipole moments, allowed by all discrete symmetries, is one of the topical problems of modern physics. According to Sakharov, $CP$-violation is one of the three key criteria of baryogenesis in generally accepted paradigm of the Big Bang cosmology. All three criteria are supported by the Standard Model (SM), but it fails to describe the observed baryon asymmetry of the Universe. This is regarded a strong argument in favor of existence of $CP$-symmetry breaking mechanisms beyond minimal SM, which can lead to measurable EDMs of atoms, particles and nuclei. Direct searches for EDM of charged particles and nuclei are possible only in storage rings (COSY, NICA). After successful studies by the JEDI collaboration at the COSY synchrotron, at the forefront is a search for the proton EDM in an electrostatic storage ring with the proton spin frozen at the magic energy with projected sensitivity $d_p\sim 10^{-29}\,e\cdot$cm. Following a brief introduction to the $CP$-violation physics and the baryogenesis, the review presents a detailed discussion of significant contributions to the spin dynamics from the terrestrial gravity along with the new effects of Earth's rotation in ultrasensitive searches for the EDM of charged particles and neutrons. Quite remarkably, for the projected sensitivity to the proton EDM, these false EDM effects can by one to two orders of magnitude exceed the signal of the proton EDM, and become comparable to an EDM contribution in experiments with ultracold neutrons. We also discuss the role of a precessing spin as a detector of the axion-like dark matter, and consider applications of the quantum gravitational anomalies to the dense matter hydrodynamics and the spin phenomena in the non-central nuclear collisions.

Formation of spiral waves in cylindrical containers under orbital excitation

The lowest swirling wave mode arising in upright circular cylinders as a response to circular orbital excitation has been widely studied in the last decade, largely due to its high practical relevance for orbitally shaken bioreactors. Our recent theoretical study (Horstmann et al., J. Fluid Mech., vol. 891, 2020, A22) revealed a damping-induced symmetry breaking mechanism that can cause spiral wave structures manifested in the so far widely disregarded higher rotating wave modes. Building on this work, we develop a linear criterion describing the degree of spiralisation and classify different spiral regimes as a function of the most relevant dimensionless groups. The analysis suggests that high Bond numbers and shallow liquid layers favour the formation of coherent spiral waves. This result paved the way to find the predicted wave structures in our interfacial sloshing experiment. We present two sets of experiments, with different characteristic damping rates, verifying the formation of both coherent and overdamped spiral waves in conformity with the theoretical predictions.

Pseudo-Goldstone excitations in a striped Bose-Einstein condensate

Significant experimental progress has been made recently for observing long-sought supersolidlike states in Bose-Einstein condensates, where spatial translational symmetry is spontaneously broken by anisotropic interactions to form a stripe order. Meanwhile, the superfluid stripe ground state was also observed by applying a weak optical lattice that forces the symmetry breaking. Despite the similarity of the ground states, here we show that these two symmetry breaking mechanisms can be distinguished by their collective excitation spectra. In contrast to gapless Goldstone modes of the spontaneous stripe state, we propose that the excitation spectra of the forced stripe phase can provide direct experimental evidence for the gapped pseudo-Goldstone modes. We characterize the pseudo-Goldstone mode of such lattice-induced stripe phase through its excitation spectrum and static structure factor. Our work may pave the way for exploring spontaneous and forced or approximate symmetry breaking mechanisms in different physical systems.

Asymmetry-induced isolated fully synchronized state in coupled oscillator populations.

A symmetry-breaking mechanism is investigated that creates bistability between fully and partially synchronized states in oscillator networks. Two populations of oscillators with unimodal frequency distribution and different amplitudes, in the presence of weak global coupling, are shown to simplify to a modular network with asymmetrical coupling. With increasing the coupling strength, a synchronization transition is observed with an isolated fully synchronized state. The results are interpreted theoretically in the thermodynamic limit and confirmed in experiments with chemical oscillators.

Field-free spin-orbit torque-induced switching of\xa0perpendicular magnetization in a ferrimagnetic layer with a vertical composition gradient

Current-induced spin-orbit torques (SOTs) are of interest for fast and energy-efficient manipulation of magnetic order in spintronic devices. To be deterministic, however, switching of perpendicularly magnetized materials by SOT requires a mechanism for in-plane symmetry breaking. Existing methods to do so involve the application of an in-plane bias magnetic field, or incorporation of in-plane structural asymmetry in the device, both of which can be difficult to implement in practical applications. Here, we report bias-field-free SOT switching in a single perpendicular CoTb layer with an engineered vertical composition gradient. The vertical structural inversion asymmetry induces strong intrinsic SOTs and a gradient-driven Dzyaloshinskii–Moriya interaction (g-DMI), which breaks the in-plane symmetry during the switching process. Micromagnetic simulations are in agreement with experimental results, and elucidate the role of g-DMI in the deterministic switching processes. This bias-field-free switching scheme for perpendicular ferrimagnets with g-DMI provides a strategy for efficient and compact SOT device design.

Probing the electroweak symmetry breaking with Higgs production at the LHC

The electroweak symmetry breaking (EWSB) mechanism is still an undecided question in particle physics. We propose to utilize the single top quark and Higgs associated production (th), Zh production via gluon fusion at the LHC to probe the couplings between the Higgs and the gauge bosons and further to test the EWSB. We demonstrate that the th and gg→Zh productions are sensitive to the relative sign of couplings (htt¯, hWW) and (htt¯, hZZ), respectively. We find that the relative sign between hWW and hZZ couplings could be fully determined after combining the present measurements from gg→h, tt¯h and the th, Zh channels, as well as tZj and Ztt¯ production at the 13 TeV LHC, and this conclusion is not sensitive to the possible new physics contribution induced by Ztt¯ couplings in the gg→Zh production.

Ultrafast imaging of spontaneous symmetry breaking in a photoionized molecular system

The Jahn-Teller effect is an essential mechanism of spontaneous symmetry breaking in molecular and solid state systems, and has far-reaching consequences in many fields. Up to now, to directly image the onset of Jahn-Teller symmetry breaking remains unreached. Here we employ ultrafast ion-coincidence Coulomb explosion imaging with sub-10 fs resolution and unambiguously image the ultrafast dynamics of Jahn-Teller deformations of {{rm{CH}}}_{4}^{+} cation in symmetry space. It is unraveled that the Jahn-Teller deformation from C3v to C2v geometries takes a characteristic time of 20 ± 7 fs for this system. Classical and quantum molecular dynamics simulations agree well with the measurement, and reveal dynamics for the build-up of the C2v structure involving complex revival process of multiple vibrational pathways of the {{rm{CH}}}_{4}^{+} cation.

Chiral Induction in Buckminsterfullerene Using a Metal–Organic Framework

AbstractChiral induction is an emerging topic of interest in various areas of chemistry because of its relationship to the elusive mechanism of spontaneous symmetry breaking in nature. Buckminsterfullerene (C60) with the shape of a highly symmetric truncated icosahedron has rarely been referred for chiral induction due to the difficult symmetry breaking. In this work, we demonstrate that a chiral metal–organic framework (MOF) can provide a key field for chiral induction. C60 could be incorporated into the chiral nanochannels of the MOF using an in situ self‐assembly strategy. The circular dichroism spectra of the resulting nanocomposites showed an intense chiral signal in the absorption region of C60. Experimental and theoretical studies showed that this unprecedented chiral induction of C60 was attributed to hybridization of the molecular orbitals through a close association with the pore surface of the MOF. Our method can endow highly symmetric achiral compounds with chirality, paving the new way toward fabrication of novel chiral nanomaterials.

NNLO QCD study of polarised W+W\u2212 production at the LHC

Longitudinal polarisation of the weak bosons is a direct consequence of Electroweak symmetry breaking mechanism providing an insight into its nature, and is instrumental in searches for physics beyond the Standard Model. We perform a polarisation study of the diboson production in the pp → {mathrm{e}}^{+}{v}_{mathrm{e}}{mu}^{-}{overline{v}}_{mu } process at NNLO QCD in the fiducial setup inspired by experimental measurements at ATLAS. This is the first polarisation study at NNLO. We employ the double-pole approximation framework for the polarised calculation, and investigate NNLO effects arising in differential distributions.

Quantum tricritical behavior and multistable macroscopic quantum states in generalized Dicke model

In this article, we obtain the multistable macroscopic quantum states and quantum tricritical behavior in generalized Dicke model (DM) analytically by means of spin-coherent-state (SCS) variational method for a finite atom number N. The quantum phase transition (QPT) is characterized by the ground state from the normal phase (NP) to the superradiant phases (SP). The second-order QPT turns to the first-order one at the tricritical point of phase boundary. The tricritical behavior of QPT emerges when the coupling strength of the symmetry breaking mechanism increases to a certain extent, which leads to an additional dimension of phase diagram. Beyond the ground state the symmetry-breaking coupling can manipulate the pseudospin flip of higher-level macroscopic states. The critical property of QPT is also demonstrated from the average photon-number, the atomic population as well as Berry phase.

On symmetry breaking of dual polyhedra of non-crystallographic group H3.

The study of the polyhedra described in this paper is relevant to the icosahedral symmetry in the assembly of various spherical molecules, biomolecules and viruses. A symmetry-breaking mechanism is applied to the family of polytopes {\cal V}_{H_{3}}(\lambda) constructed for each type of dominant point λ. Here a polytope {\cal V}_{H_{3}}(\lambda) is considered as a dual of a {\cal D}_{H_{3}}(\lambda) polytope obtained from the action of the Coxeter group H3 on a single point \lambda\in{\bb R}^{3}. The H3 symmetry is reduced to the symmetry of its two-dimensional subgroups H2, A1 × A1 and A2 that are used to examine the geometric structure of {\cal V}_{H_{3}}(\lambda) polytopes. The latter is presented as a stack of parallel circular/polygonal orbits known as the `pancake' structure of a polytope. Inserting more orbits into an orbit decomposition results in the extension of the {\cal V}_{H_{3}}(\lambda) structure into various nanotubes. Moreover, since a {\cal V}_{H_{3}}(\lambda) polytope may contain the orbits obtained by the action of H3 on the seed points (a, 0, 0), (0, b, 0) and (0, 0, c) within its structure, the stellations of flat-faced {\cal V}_{H_{3}}(\lambda) polytopes are constructed whenever the radii of such orbits are appropriately scaled. Finally, since the fullerene C20 has the dodecahedral structure of {\cal V}_{H_{3}}(a,0,0), the construction of the smallest fullerenes C24, C26, C28, C30 together with the nanotubes C20+6N, C20+10N is presented.

Enhanced ferroelectricity for nanoporous barium titanate: a phase-field prediction

ABSTRACT Porous ferroelectric materials show great potential for achieving competitive dielectric/piezoelectric properties with light weight. In this study, a phase-field model was employed to simulate the ferroelectric domain structure evolution of porous barium titanate. It is suggested that the ferroelectric/dielectric/piezoelectric properties are strongly influenced by the porosity level and the size of pores for porous ceramics. It is demonstrated that the ferroelectric switching behaviour, the remnant polarisation, the dielectric constant and the piezoelectric constant are enhanced in nanoporous ferroelectrics with ellipse-shaped pores by introducing mechanisms of symmetry breaking. By providing a means of achieving enhanced properties, nanoporous ferroelectrics with ellipse-shaped pores may have a broad impact on the applications of ferroelectrics and enhance the utility of the materials for selected applications.

Shape control of size-selected naked platinum nanocrystals

Controlled growth of far-from-equilibrium-shaped nanoparticles with size selection is essential for the exploration of their unique physical and chemical properties. Shape control by wet-chemistry preparation methods produces surfactant-covered surfaces with limited understanding due to the complexity of the processes involved. Here, we report the controlled production and transformation of octahedra to tetrahedra of size-selected platinum nanocrystals with clean surfaces in an inert gas environment. Molecular dynamics simulations of the growth reveal the key symmetry-breaking atomic mechanism for this autocatalytic shape transformation, confirming the experimental conditions required. In-situ heating experiments demonstrate the relative stability of both octahedral and tetrahedral Pt nanocrystals at least up to 700 °C and that the extended surface diffusion at higher temperature transforms the nanocrystals into equilibrium shape.

Pkd2 Affects Cilia Length and Impacts LR Flow Dynamics and Dand5

The left-right (LR) field recognizes the importance of the mechanism involving the calcium permeable channel Polycystin-2. However, whether the early LR symmetry breaking mechanism is exclusively via Polycystin-2 has not been tested. For that purpose, we need to be able to isolate the effects of decreasing the levels of Pkd2 protein from any eventual effects on flow dynamics. Here we demonstrate that curly-up (cup) homozygous mutants have abnormal flow dynamics. In addition, we performed one cell stage Pkd2 knockdowns and LR organizer specific Pkd2 knockdowns and observed that both techniques resulted in shorter cilia length and abnormal flow dynamics. We conclude that Pkd2 reduction leads to LR defects that cannot be assigned exclusively to its putative role in mediating mechanosensation because indirectly, by modifying cell shape or decreasing cilia length, Pkd2 deficit affects LR flow dynamics.

Flavour Hund's coupling, Chern gaps and charge diffusivity in moiré graphene.

Interaction-driven spontaneous symmetry breaking lies at the heart of many quantum phases of matter. In moiré systems, broken spin/valley 'flavour' symmetry in flat bands underlies the parent state from which correlated and topological ground states ultimately emerge1-10. However, the microscopic mechanism of such flavour symmetry breaking and its connection to the low-temperature phases are not yet understood. Here we investigate the broken-symmetry many-body ground state of magic-angle twisted bilayer graphene (MATBG) and its nontrivial topology using simultaneous thermodynamic and transport measurements. We directly observe flavour symmetry breaking as pinning of the chemical potential at all integer fillings of the moiré superlattice, demonstrating the importance of flavour Hund's coupling in the many-body ground state. The topological nature of the underlying flat bands is manifested upon breaking time-reversal symmetry, where we measure energy gaps corresponding to Chern insulator states with Chern numbers 3, 2, 1 at filling factors 1, 2, 3, respectively, consistent with flavour symmetry breaking in the Hofstadter butterfly spectrum of MATBG. Moreover, concurrent measurements of resistivity and chemical potential provide the temperature-dependent charge diffusivity of MATBG in the strange-metal regime11-a quantity previously explored only in ultracold atoms12. Our results bring us one step closer to a unified framework for understanding interactions in the topological bands of MATBG, with and without a magnetic field.

Sir Thomas Walter Bannerman Kibble. 23 December 1932—2 June 2016

Professor Tom Kibble was an internationally-renowned theoretical physicist whose contributions to theoretical physics range from the theory of elementary particles to modern early-Universe cosmology. The unifying theme behind all his work is the theory of non-abelian gauge theories, the Yang–Mills extension of electromagnetism. One of Kibble's most important pieces of work in this area was his study of the symmetry-breaking mechanism whereby the force-carrying vector particles in the theory can acquire a mass accompanied by the appearance of a massive scalar boson. This idea, put forward independently by Brout and Englert, by Higgs, and by Guralnik, Hagen and Kibble in 1964, and generalized by Kibble in 1967, lies at the heart of the Standard Model and all modern unified theories of fundamental particles. It was vindicated in 2012 by the discovery of the Higgs boson at CERN. According to Nobel Laureate Steven Weinberg: ‘Tom Kibble showed us why light is massless’; this is the fundamental basis of electromagnetism.

Casimir Effect for Fermion Condensate in Conical Rings

The fermion condensate (FC) is investigated for a (2+1)-dimensional massive fermionic field confined on a truncated cone with an arbitrary planar angle deficit and threaded by a magnetic flux. Different combinations of the boundary conditions are imposed on the edges of the cone. They include the bag boundary condition as a special case. By using the generalized Abel-Plana-type summation formula for the series over the eigenvalues of the radial quantum number, the edge-induced contributions in the FC are explicitly extracted. The FC is an even periodic function of the magnetic flux with the period equal to the flux quantum. Depending on the boundary conditions, the condensate can be either positive or negative. For a massless field the FC in the boundary-free conical geometry vanishes and the nonzero contributions are purely edge-induced effects. This provides a mechanism for time-reversal symmetry breaking in the absence of magnetic fields. Combining the results for the fields corresponding to two inequivalent irreducible representations of the Clifford algebra, the FC is investigated in the parity and time-reversal symmetric fermionic models and applications are discussed for graphitic cones.

Glueballs and strings in Sp(2N) Yang-Mills theories

Motivated in part by the pseudo-Nambu Goldstone boson mechanism of electroweak symmetry breaking in composite Higgs models, in part by dark matter scenarios with strongly coupled origin, as well as by general theoretical considerations related to the large-$N$ extrapolation, we perform lattice studies of the Yang-Mills theories with $Sp(2N)$ gauge groups. We measure the string tension and the mass spectrum of glueballs, extracted from appropriate two-point correlation functions of operators organized as irreducible representations of the octahedral symmetry group. We perform the continuum extrapolation and study the magnitude of finite-size effects, showing that they are negligible in our calculation. We present new numerical results for $N=1$, 2, 3, 4, combine them with data previously obtained for $N=2$, and extrapolate toward $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We confirm explicitly the expectation that, as already known for $N=1$, 2 also for $N=3$, 4 a confining potential rising linearly with the distance binds a static quark to its antiquark. We compare our results to the existing literature on other gauge groups, with particular attention devoted to the large-$N$ limit. We find agreement with the known values of the mass of the ${0}^{++}$, ${0}^{++*}$, and ${2}^{++}$ glueballs obtained taking the large-$N$ limit in the $SU(N)$ groups. In addition, we determine for the first time the mass of some heavier glueball states at finite $N$ in $Sp(2N)$ and extrapolate the results toward $N\ensuremath{\rightarrow}+\ensuremath{\infty}$ taking the limit in the latter groups. Since the large-$N$ limit of $Sp(2N)$ is the same as in $SU(N)$, our results are relevant also for the study of QCD-like theories.