Dynamical Symmetry Research Articles

Spin-phonon interactions induced anomalous thermal conductivity in nickel (II) oxide

Nickel (II) oxide is a prominent candidate for spintronic and spin-caloritronic applications operating at room temperature. Although there are extensive studies on nickel oxide, the roles of magnon- and spin-phonon interactions on thermal transport are not well understood. In the present work, the relationship between spin-phonon interactions and thermal transport is investigated by performing inelastic neutron scattering, time-domain thermoreflectance thermal conductivity measurements, and atomistic thermal transport calculations. Inelastic neutron scattering measurements of the magnon lifetime imply that magnon thermal conductivity is trivial, and so heat is conducted only by phonons. Time-domain thermoreflectance measurements of the thermal conductivity vs. temperature follow T−1.5 in the antiferromagnetic phase. This temperature dependence cannot be explained by phonon-isotope and phonon-defect scattering or phonon softening. Instead, we attribute this to magnon-phonon scattering and spin-induced dynamic symmetry breaking. The spin-phonon interactions are saturated in the paramagnetic phase and lead to a weaker temperature dependence of T−1.0 at 550–700 K. These results reveal the importance of spin-phonon interactions on lattice thermal transport, shedding light on the engineering of functional antiferromagnetic spintronic and spin-caloritronic materials through these interactions.

Recent Progress in Multiterminal Memristors for Neuromorphic Applications

AbstractThe essential step for developing neuromorphic systems is to construct more biorealistic elementary devices with rich spatiotemporal dynamics to exhibit highly separable responses in dynamic environmental circumstances. Unlike transistor‐based devices and circuits with zeroth‐order complexity, memristors intrinsically express some simple biomimetic functions. However, with only two‐terminal structure, precise control of operation principles to ensure large dynamic space, improved linearity and symmetry, multimodal operation as well as high‐order complexity is hard to achieve in a traditional memristor owing to its limited degree of freedom. Therefore, multiterminal memristors including both concrete terminals and virtual terminals (light, pressure, gas, ferroelectric polarity, etc.) have been proposed to obtain precise modulation of memristive characteristics. This review focuses on the recent progress in multiterminal memristors and their neuromorphic applications. The operation principle, application of multiterminal memristor on neuromorphic computing in different scenarios, existing challenges and future prospects are discussed.

Shape isomers of α -like nuclei in terms of the multiconfigurational dynamical symmetry

Background: The shape isomers of the $N=Z=\mathrm{even}$ nuclei are known from the energy-surface calculations within the Bloch-Brink (BB) $\ensuremath{\alpha}$-cluster model and Nilsson model. As an alternative, a new method (called SCS) has been proposed recently for determining the stable shapes, which is based on the investigation of the stability and consistency of the $\mathrm{SU}(3)$ symmetry (or quadrupole deformation).Purpose: We wish to derive the shape isomers of the $\ensuremath{\alpha}$-like nuclei from the SCS method and compare them with the results of the energy-surface calculation. Furthermore, we intend to study the consequences of the stable symmetries. In particular, we investigate (i) what kind of binary clusterizations are structurally allowed for the shape isomers and (ii) if energy spectra similar to those of the BB model can be obtained with a simple dynamically symmetric Hamiltonian.Methods: We determine the stability and self-consistency of the quadrupole deformation from a systematic calculation with the Nilsson model by applying the concept of the quasidynamical $\mathrm{U}(3)$ symmetry. The allowed cluster configurations are determined from the application of the U(3) and ${\mathrm{U}}^{\mathrm{ST}}(4)$ selection rules. The forbidden ones are characterized quantitatively. The energy spectrum is calculated with a simple dynamically symmetric Hamiltonian of the multiconfigurational dynamical symmetry (MUSY), which proved to be useful for the description of some experimental spectra.Results: The shape isomers found from the SCS method are in good agreement with the results of the energy surface method (BB and Nilsson models). Their allowed binary clusterizations are obtained from structural selection rules, but they give a hint for the available reaction channels, too. Last, a very simple energy functional is able to reproduce the gross features of their energy spectra in a large range of excitation energy and deformation.Conclusions: The similarity of the shape isomers from two very different methods gives a strong support to these predictions. The reasonable reproduction of the energy distribution of the ``ground-band heads'' is especially remarkable, considering the fact that MUSY is able to produce the complete spectra in detail, not only the energy minima.

Multiscale dynamical symmetries and selection rules in nonlinear optics.

Symmetries and their associated selection rules are extremely useful in many fields of science. For systems of electromagnetic (EM) fields interacting with matter, the symmetries of matter and the EM fields' time-dependent polarization determine the properties of the nonlinear responses, and they can be facilitated for controlling light emission and enabling ultrafast symmetry breaking spectroscopy of various properties. Here, we formulate a general theory that describes the macroscopic and microscopic dynamical symmetries (including quasicrystal-like symmetries) of EM vector fields, revealing many previously unidentified symmetries and selection rules in light-matter interactions. We demonstrate an example of multiscale selection rules experimentally in the framework of high harmonic generation. This work paves the way for novel spectroscopic techniques in multiscale systems and for imprinting complex structures in extreme ultraviolet-x-ray beams, attosecond pulses, or the interacting medium itself.

As without, so within: how the brain's temporo-spatial alignment to the environment shapes consciousness.

Consciousness is constituted by a structure that includes contents as foreground and the environment as background. This structural relation between the experiential foreground and background presupposes a relationship between the brain and the environment, often neglected in theories of consciousness. The temporo-spatial theory of consciousness addresses the brain-environment relation by a concept labelled 'temporo-spatial alignment'. Briefly, temporo-spatial alignment refers to the brain's neuronal activity's interaction with and adaption to interoceptive bodily and exteroceptive environmental stimuli, including their symmetry as key for consciousness. Combining theory and empirical data, this article attempts to demonstrate the yet unclear neuro-phenomenal mechanisms of temporo-spatial alignment. First, we suggest three neuronal layers of the brain's temporo-spatial alignment to the environment. These neuronal layers span across a continuum from longer to shorter timescales. (i) The background layer comprises longer and more powerful timescales mediating topographic-dynamic similarities between different subjects' brains. (ii) The intermediate layer includes a mixture of medium-scaled timescales allowing for stochastic matching between environmental inputs and neuronal activity through the brain's intrinsic neuronal timescales and temporal receptive windows. (iii) The foreground layer comprises shorter and less powerful timescales for neuronal entrainment of stimuli temporal onset through neuronal phase shifting and resetting. Second, we elaborate on how the three neuronal layers of temporo-spatial alignment correspond to their respective phenomenal layers of consciousness. (i) The inter-subjectively shared contextual background of consciousness. (ii) An intermediate layer that mediates the relationship between different contents of consciousness. (iii) A foreground layer that includes specific fast-changing contents of consciousness. Overall, temporo-spatial alignment may provide a mechanism whose different neuronal layers modulate corresponding phenomenal layers of consciousness. Temporo-spatial alignment can provide a bridging principle for linking physical-energetic (free energy), dynamic (symmetry), neuronal (three layers of distinct time-space scales) and phenomenal (form featured by background-intermediate-foreground) mechanisms of consciousness.

Four-quark scatterings in QCD I

We investigate dynamical chiral symmetry breaking and the emergence of mesonic bound states from the infrared dynamics of four-quark scatterings. Both phenomena originate from the resonant scalar-pseudoscalar channel of the four-quark scatterings, and we compute the functional renormalisation group (fRG) flows of the Fierz-complete four-quark interaction of up and down quarks with its tt channel momentum dependence. This is done in the isospin symmetric case, also including the flow of the quark two-point function. This system can be understood as the fRG analogues of the complete Bethe-Salpeter equations and quark gap equation. The pole mass of the pion is determined from both direct calculations of the four-quark flows in the Minkowski regime of momenta and the analytic continuation based on results in the Euclidean regime, which are consistent with each other.

The interplay of symmetry with the Rabi oscillation in the non-Hermitian double Jaynes–Cummings model

We study the dynamical evolution and symmetry breaking of the non-Hermitian double Jaynes–Cummings model with symmetry. The results indicate that there exist symmetry maintained and breaking phase in this model, and the non-Hermitian terms lead to different behaviors in two phases. In the symmetry phase, there exists stable Rabi oscillation caused by the interaction between photons and atoms. At the exceptional point, the system shows critical property that the probabilities in each state over time tend to be equal. The system will undergo a transition from the symmetry phase to the symmetry breaking phase, as increasing the coupling constant. In the symmetry breaking phase, complex eigenvalues appear, and the probability in each state increases monotonically in an exponential form. This study can help us to understand the effect of symmetry on the interaction between photons and atoms in non-Hermitian systems.

Unification of the first law of quantum thermodynamics

Underlying the classical thermodynamic principles are analogous microscopic laws, arising from the fundamental axioms of quantum mechanics. These define quantum thermodynamic variables such as quantum work and heat and characterize the possible transformations of open quantum systems. The foremost quantum thermodynamic law is a simple statement concerning the conservation of energy. Nevertheless, there exist ambiguity and disagreement regarding the precise partition of a quantum system’s energy change to work and heat. By treating quantum mechanics as a comprehensive theory, applicable to both the micro and macroscopic domains, and employing dynamical symmetries, we bridge the gaps between five popular thermodynamic approaches to the first law. These include both autonomous and semi-classical formulations, which define work in terms of an ensemble average, as well as the single shot paradigm, where work is defined as a deterministic quantity.

Sufficiently small rotations of Lagrange’s gyro

In this study, the motion of Lagrange’s gyro about its fixed point in the presence of a perturbed torque, a gyroscopic torque, and a varied restoring one is searched. We assume sufficiently small angular velocity components in the direction of the principal axes that differ from the dynamical symmetry one and a restoring torque that is considered to be greater than the perturbing one. In this manner, we replace the familiar small parameter that was used in previous works with a large one. In such cases, the gyro equations for motion (EOM) are formulated in the form of a two-degrees-of-freedom (DOF) autonomous system. We average the obtained system to get periodic solutions and motion’s geometric interpretation of the problem using the large parameter. The regular precession and the pure rotation of the motion are obtained. A numerical study is evaluated for asserted the used techniques and showed the influence of the changing parameters of motion on the gyro behavior. The trajectories of the motions and their stabilities are discussed and analyzed. The novelty of this work lies in how to adapt the method of large parameter (MLP) to solve the rigid body problem, especially since it has been assumed initially that its angular velocity or its initial energy are very small. MSC (2000): 70E20, 70E17, 70E15, 70E05

Regulating droplet impact symmetry by surface engineering

AbstractDroplet impact on solid surfaces is essential both in nature and industry. Precisely regulating the dynamic behavior of droplet impact is of great significance for energy harvesting, anti‐icing, inkjet printing, pesticide spraying, and many other fields. Various rebounding behaviors (deposition, rebounding, rotation, instability control, and so on) and rebounding intrinsic parameters (such as contact time) after droplets impacting on solid surfaces can be regulated by surface engineering. This paper reviews the advances in regulating droplet impact behavior from the perspective of symmetry by modifying solid surfaces from the following aspects: chemical modification and physical structure regulation, in which the symmetry is discussed from mirror symmetry and rotational symmetry. Firstly, the symmetry of the droplet impact dynamics and its influencing factors are introduced. Then the modulation of droplet impact symmetry, using homogeneous and heterogeneous chemically modified solid surfaces, is summarized. The following presents the influence of physical structures, from micro to macro scale compared to the droplet size, on the droplet impact symmetry. Finally, the future challenges and opportunities of the droplet impact behavior regulation are discussed.

Studying the vibrational motion of a rotating symmetrically charged solid body subjected to external forces and moments

This paper studies the rotatory vibrating motion of a dynamically symmetric charged solid body (SB) connected with a spring around a fixed point as a novel model. The body is assumed to be influenced by a Newtonian force field (NFF) besides extrinsic moments like perturbing, restoring, and gyrostatic moment (GM). These moments are guided along the body’s principal axes of inertia. The body is assumed to have a high starting angular velocity in the direction of the dynamic symmetry axis, and the perturbing moments (PM) are thought to be less than the restoring moment. These assumptions provide us with a tiny parameter, to use the averaging technique (AT), and to acquire the averaging system of the regulating one. Several applications are introduced to achieve the solutions of this system separately. These solutions are graphed to reveal the positive influences of the body’s numerical values on the behavior of the body, taking into account the various impacts of the applied moments, the electromagnetic field, and the Newtonian one for all examined applications. The obtained results are considered a generalization of those which were obtained in related previous works. For the projections of the body angular velocity, the proportion of differences as a function of the investigated parameters varies between 17% and 35%, whereas the other parameters are varied between 0.0011% and 0.37%, respectively. Therefore, these outcomes are considered to be significant due to their applications in life specially that based on the theory of vibrating systems in physics and engineering fields.

Quantum sensing of control errors in three-level systems by coherent control techniques

Quantum coherent control of a quantum system with high-fidelity is rather important in quantum computation and quantum information processing. There are many control techniques to reach these targets, such as resonant excitation, adiabatic passages, shortcuts to adiabaticity, and so on. However, for a single pulse to realize population transfer, the external tiny error has a trivial influence on the final population. The repeated application of the same pulse will greatly amplify the error effect, making it easy to be detected. Here, we propose to measure small control errors in three-level quantum systems by coherent amplification of their effects, using several coherent control techniques. For the two types of Hamiltonian with SU(2) dynamic symmetry, we analyze how the fidelity of population transfer are affected by Rabi frequencies fluctuation and static detuning deviation, based on the pulse sequence with alternating and same phases, respectively. It is found that the sensitivity of detecting these errors can be effectively amplified by the control pulse sequences. Furthermore, we discuss the efficiency of sensing the two errors with these control techniques by comparing the full width at half maximum of the population profiles. The results provide an accurate and reliable way for sensing the weak error in three-level quantum systems by applying repeatedly the coherent control pulse.

Algebra of the spinor invariants and the relativistic hydrogen atom

It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac Hamiltonian is invariant with respect to the rotation transformation, which indicates the dynamical (hidden) symmetry SU(2) of the Dirac equation. The total symmetry of the Dirac equation is the symmetry SO(3)⊗SU(2). The generator of the SO(3) symmetry group is given by the total momentum operator, and the generator of SU(2) group is given by the rotation of the vector-states in the spinor space, determined by the Dirac, Johnson–Lippmann, and the new spinor invariants. It is shown that using algebraic approach to the Dirac problem allows one to calculate the eigenstates and eigenenergies of the relativistic hydrogen atom and reveals the fundamental role of the principal quantum number as an independent number, even though it is represented as the combination of other quantum numbers.

Advanced investigations of a restricted gyrostatic motion

In this work, we present advanced investigations and treatments for the problem of a restricted vibrating motion of a connected gyrostat with a spring. It is supposed that the gyrostat spins slowly about the minor or major principal axis of the inertia ellipsoid. The gyrostat is acted upon by a gyrostatic couple vector besides the action of Newtonian and electromagnetic fields. The approach of the large parameter is applied to obtain the periodic solutions for the governing system of equations of motion of the gyrostat. A geometric illustration using the angles of Euler is given for such motion to evaluate and analyze the gyrostatic motion at any instant. The analysis of the obtained solutions is considered in terms of numerical data throughout computer programs. Characterized parametric data are assumed through one of the numerical methods for obtaining numerical solutions that prove the validity of the analytical obtained periodic solutions. The obtained solutions, besides the phase diagrams, have been drawn to describe these solutions’ periodicity and stability procedures. The novelty of this work comes from the imposition of a new initial condition that does not restrict movement around the dynamic symmetry axis. This assumption allows the use of a new technique for the solution called the large parameter. This technique gives solutions in a completely new domain that are different from the ones studied in previous works.

Are Dynamic Shifts Dynamical Symmetries?

AbstractShifts are a well-known feature of the literature on spacetime symmetries. Recently, discussions have focused on so-called dynamic shifts, which by analogy with static and kinematic shifts enact arbitrary linear accelerations of all matter (as well as a change in the gravitational potential). But in mathematical formulations of these shifts, the analogy breaks down: while static and kinematic shift act on the matter field, the dynamic shift acts on spacetime structure instead. I formulate a different, “active,” version of the dynamic shift which does act on matter, and analyse the consequences of this reformulation for Newton–Cartan theory and Maxwell gravitation.

Comparison of static and dynamic symmetry between masseter-innervated and dual-innervated free multivector serratus anterior muscle transfer for complete facial paralysis

In this study, facial symmetry was compared between the masseter-innervated and dual-innervated free multivector serratus anterior muscle transfer (FMSAMT) methods. Eighteen patients with unilateral complete facial paralysis underwent facial reanimation surgery between April 2006 and July 2019. The masseter-innervated FMSAMT group (Group M, n=8) underwent end-to-end coaptation with the ipsilateral masseter nerve in one stage. The dual-innervated FMSAMT group (Group D, n=10) underwent end-to-end coaptation with the masseter nerve and end-to-side coaptation with the contralateral facial nerve via cross-face nerve graft. They were further divided into the one-stage (Group D1, n=5) and two-stage (Group D2, n=5) subgroups. The durations of periods until the first visible muscle contraction with clenching, first spontaneous smile, and the completion of resting tone were evaluated. The possibility of a spontaneous smile and symmetry of the midline and horizontal deviation at rest and during voluntary smiling were compared between each group. Groups M and D differed significantly in the possibility of a spontaneous smile and improvement rate of midline deviation and horizontal deviation at rest (p<0.001, p<0.001, and p=0.001, respectively) but not in the improvement rate of midline and horizontal deviation during voluntary smiling. The duration of the period until the completion of resting tone was significantly shorter in Group D1 than in Group D2 (p=0.048); however, the possibility of a spontaneous smile and the improvement rate of midline and horizontal deviation were not significantly different. Dual-innervated FMSAMT was effective in guaranteeing a symmetrical resting tone, voluntary smiling, and reproducing a spontaneous smile.

Time-translational symmetry in statistical dynamics dictates Einstein relation, Green-Kubo formula, and their generalizations.

A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent, components contributing to the overall fluctuations of the dynamics, representing the uncertainties in the past and in the future. We show that fluctuation-dissipation relations of the two aforementioned components, such as the Einstein relation and the Green-Kubo formula, can be formulated for any stochastic process with a steady state, without additional supposition of the process being Markovian, reversible, or linear. Further, by considering the adjoint process defined by the time reversal at the steady state, we show that reversibility in equilibrium leads to an additional symmetry in the covariance between system's state and drift. Potential directions of further generalizing our results to processes without steady states is briefly discussed.

On the Logical Structure of Composite Symmetries in Atomic Nuclei

This investigation involves composite symmetries, which connect different components of atomic nuclei. In particular, supersymmetry (SUSY) connects boson and fermion sectors, and multiconfigurational symmetry (MUSY) bridges different configurations, such as shell, quartet, or cluster configurations. Both SUSY and MUSY contain a usual dynamical symmetry in each component, and further symmetry connects the components to each other. The varieties of the connecting symmetries and their logical structure are analyzed and compared.

Electron mass anomalous dimension at [formula omitted] in three-dimensional [formula omitted] supersymmetric QED

We consider massless three-dimensional N=1 supersymmetric quantum electrodynamics (QED) with Nf flavours of electrons. Within the dimensional reduction scheme, we compute the critical exponents corresponding to both the electron and selectron field and (parity-even) mass anomalous dimensions at the next-to-leading order in the 1/Nf expansion and in an arbitrary covariant gauge. The equality of the gauge-invariant mass anomalous dimensions of the electron and the selectron is found to result from a subtle role played by the epsilon-scalars. Our general framework also allows us to compute the critical exponents of pure scalar QED and to recover known results in the case of spinor QED. An application of our results to dynamical (s)electron mass generation is considered. We find evidence that, while dynamical flavor symmetry breaking occurs in spinor QED, both pure scalar QED and supersymmetric QED remain in an interacting conformal phase.

Time-Dependent 4D Quantum Harmonic Oscillator and Reacting Hydrogen Atom

With the help of low-dimensional reference equations (ordinary differential equations) and the corresponding coordinate transformations, the non-stationary 4D quantum oscillator in an external field is reduced to an autonomous form. The latter, in particular, reflects the existence of a new type of dynamical symmetry that reduces the equation of motion of a non-stationary oscillator to an autonomous form that does not change with time. By imposing an additional constraint on the wave function of the isotropic oscillator, we have obtained the total wave functions of the reacting hydrogen atom in two different cases: (a) when the non-stationary frequency has two asymptotic values and there is no external field; and (b) when, in addition to the non-stationary frequency, an external force acts on the hydrogen atom. The transition S-matrix elements of various elementary atomic–molecular processes are constructed. The probabilities of quantum transitions of the hydrogen atom to others, including new bound states, are studied in detail, taking into account the influence of external forces.