Dynamical Symmetry Research Articles

Environmentally Driven Symmetry Breaking Quenches Dual Fluorescence in Proflavine.

Nonadiabatic couplings between several electronic excited states are ubiquitous in many organic chromophores and can significantly influence optical properties. A recent experimental study demonstrated that the proflavine molecule exhibits surprising dual fluorescence in the gas phase, which is suppressed in polar solvent environments. Here, we uncover the origin of this phenomenon by parametrizing a linear-vibronic coupling Hamiltonian from spectral densities of system-bath coupling constructed along molecular dynamics trajectories, fully accounting for interactions with the condensed-phase environment. The finite-temperature absorption, steady-state emission, and time-resolved emission spectra are then computed using powerful, numerically exact tensor network approaches. We find that the dual fluorescence in vacuum is driven by a single well-defined coupling mode but is quenched in solution due to dynamic solvent-driven symmetry breaking that mixes the two low-lying electronic states. We expect the computational framework developed here to be widely applicable to the study of non-Condon effects in complex condensed-phase environments.

Impact of Cavity on Molecular Ionization Spectra.

Ionization phenomena have been widely studied for decades. With the advent of cavity technology, the question arises how quantum light affects molecular ionization. As the ionization spectrum is recorded from the neutral ground state, it is usually possible to choose cavities which exert negligible effect on the neutral ground state, but have significant impact on the ion and the ionization spectrum. Particularly interesting are cases where the ion exhibits conical intersections between close-lying electronic states, which gives rise to substantial nonadiabatic effects. Assuming single-molecule strong coupling, we demonstrate that vibrational modes irrelevant in the absence of a cavity play a decisive role when the molecule is in the cavity. Here, dynamical symmetry breaking is responsible for the ion-cavity coupling and high symmetry enables control of the coupling via molecular orientation relative to the cavity field polarization. Significant impact on the spectrum by the cavity is found and shown to even substantially increase for less symmetric molecules.

Prolate-oblate shape transitions and O(6) symmetry in even-even nuclei: A theoretical overview

Abstract Prolate to oblate shape transitions have been predicted in an analytic way in the framework of the Interacting Boson Model (IBM), determining O(6) as the symmetry at the critical point. Parameter-independent predictions for prolate to oblate transitions in various regions on the nuclear chart have been made in the framework of the proxy-SU(3) and pseudo-SU(3) symmetries, corroborated by recent non-relativistic and relativistic mean field calculations along series of nuclear isotopes, with parameters fixed throughout, as well as by shell model calculations taking advantage of the quasi-SU(3) symmetry. Experimental evidence for regions of prolate to oblate shape transitions is in agreement with regions in which nuclei bearing the O(6) dynamical symmetry of the IBM have been identified, lying below major shell closures. In addition, gradual oblate to prolate transitions are seen when crossing major nuclear shell closures, in analogy to experimental observations in alkali clusters.

Dynamic Stability, Symmetry, and Smoothness of Gait in People with Neurological Health Conditions.

Neurological disorders such as stroke, Parkinson's disease (PD), and severe traumatic brain injury (sTBI) are leading global causes of disability and mortality. This study aimed to assess the ability to walk of patients with sTBI, stroke, and PD, identifying the differences in dynamic postural stability, symmetry, and smoothness during various dynamic motor tasks. Sixty people with neurological disorders and 20 healthy participants were recruited. Inertial measurement unit (IMU) sensors were employed to measure spatiotemporal parameters and gait quality indices during different motor tasks. The Mini-BESTest, Berg Balance Scale, and Dynamic Gait Index Scoring were also used to evaluate balance and gait. People with stroke exhibited the most compromised biomechanical patterns, with lower walking speed, increased stride duration, and decreased stride frequency. They also showed higher upper body instability and greater variability in gait stability indices, as well as less gait symmetry and smoothness. PD and sTBI patients displayed significantly different temporal parameters and differences in stability parameters only at the pelvis level and in the smoothness index during both linear and curved paths. This study provides a biomechanical characterization of dynamic stability, symmetry, and smoothness in people with stroke, sTBI, and PD using an IMU-based ecological assessment.

On the symmetry algebra of a one-dimensional quantum-mechanical oscillator on a hyperbola

The quantum-mechanical problem of a harmonic oscillator on a hyperbola as a one-dimensional space of constant negative curvature is considered in this article. A generalization to the singular oscillator model in the context of one-dimensional Cayley – Klein geometries is given by the factorization method. The energy spectrum and wave functions of stationary states are found having the curvature of space as a parameter. For the energy levels of the singular oscillator, the effect of non-zero curvature is clearly manifested through a positive or negative term, depending on the sign of the curvature, which is quadratic in the level number. The results obtained are consistent with those previously published. The dynamical symmetry of the problem is shown explicitly as a quadratic Hahn algebra QH(3) or its isomorphic Higgs algebra.

Emergent symmetries of relativistic fluid dynamics from local ergodicity

Emergent symmetries of relativistic fluid dynamics from local ergodicity

The Floquet Baxterisation

Quantum integrability has proven to be a useful tool to study quantum many-body systems out of equilibrium. In this paper we construct a generic framework for integrable quantum circuits through the procedure of Floquet Baxterisation. The integrability is guaranteed by establishing a connection between Floquet evolution operators and inhomogeneous transfer matrices obtained from the Yang-Baxter relations. This allows us to construct integrable Floquet evolution operators with arbitrary depths and various boundary conditions. Furthermore, we focus on the example related to the staggered 6-vertex model. In the scaling limit we establish a connection of this Floquet protocol with a non-rational conformal field theory. Employing the properties of the underlying affine Temperley-Lieb algebraic structure, we demonstrate the dynamical anti-unitary symmetry breaking in the easy-plane regime. We also give an overview of integrability-related quantum circuits, highlighting future research directions.

Dynamic Spatiotemporal Correlation Graph Convolutional Network for Traffic Speed Prediction

Accurate and real-time traffic speed prediction remains challenging due to the irregularity and asymmetry of real-traffic road networks. Existing models based on graph convolutional networks commonly use multi-layer graph convolution to extract an undirected static adjacency matrix to map the correlation of nodes, which ignores the dynamic symmetry change of correlation over time and faces the challenge of oversmoothing during training iterations, making it difficult to learn the spatial structure and temporal trend of the traffic network. To overcome the above challenges, we propose a novel multi-head self-attention gated spatiotemporal graph convolutional network (MSGSGCN) for traffic speed prediction. The MSGSGCN model mainly consists of the Node Correlation Estimator (NCE) module, the Time Residual Learner (TRL) module, and the Gated Graph Convolutional Fusion (GGCF) module. Specifically, the NCE module aims to capture the dynamic spatiotemporal correlations between nodes. The TRL module utilizes a residual structure to learn the long-term temporal features of traffic data. The GGCF module relies on adaptive diffusion graph convolution and gated recurrent units to learn the key spatial features of traffic data. Experimental analysis on a pair of real-world datasets indicates that the proposed MSGSGCN model enhances prediction accuracy by more than 4% when contrasted with state-of-the-art models.

Light-induced switching between singlet and triplet superconducting states

While the search for topological triplet-pairing superconductivity has remained a challenge, recent developments in optically stabilizing metastable superconducting states suggest a new route to realizing this elusive phase. Here, we devise a testable theory of competing superconducting orders that permits ultrafast switching to an opposite-parity superconducting phase in centrosymmetric crystals with strong spin-orbit coupling. Using both microscopic and phenomenological models, we show that dynamical inversion symmetry breaking with a tailored light pulse can induce odd-parity (spin triplet) order parameter oscillations in a conventional even-parity (spin singlet) superconductor, which when driven strongly can send the system to a competing minimum in its free energy landscape. Our results provide new guiding principles for engineering unconventional electronic phases using light, suggesting a fundamentally non-equilibrium route toward realizing topological superconductivity.

The Statistical Mechanics of Ideal Magnetohydrodynamic Turbulence and a Solution of the Dynamo Problem

We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the ‘dynamo problem’, i.e., the problem of determining how a planetary or stellar body produces a global dipole magnetic field. We extend the theory to the case of ideal MHD turbulence with a mean magnetic field that is aligned with a rotation axis. The existing theory is also extended by developing the thermodynamics of ideal MHD turbulence based on entropy. A mathematical model is created by Fourier transforming the MHD equations and dynamical variables, resulting in a dynamical system consisting of the independent Fourier coefficients of the velocity and magnetic fields. This dynamical system has a large but finite-dimensional phase space in which the phase flow is divergenceless in the ideal case. There may be several constants of the motion, in addition to energy, which depend on the presence, or lack thereof, of a mean magnetic field or system rotation or both imposed on the magnetofluid; this leads to five different cases of MHD turbulence that must be considered. The constants of the motion (ideal invariants)—the most important being energy and magnetic helicity—are used to construct canonical probability densities and partition functions that enable ensemble predictions to be made. These predictions are compared with time averages from numerical simulations to test whether or not the system is ergodic. In the cases most pertinent to planets and stars, nonergodicity is observed at the largest length-scales and occurs when the components of the dipole field become quasi-stationary and dipole energy is directly proportional to magnetic helicity. This nonergodicity is evident in the thermodynamics, while dipole alignment with a rotation axis may be seen as the result of dynamical symmetry breaking, i.e., ‘broken ergodicity’. The relevance of ideal theoretical results to real (forced, dissipative) MHD turbulence is shown through numerical simulation. Again, an important result is a statistical solution of the ‘dynamo problem’.

Breaking reflection symmetry: evolving long dynamical cycles in Boolean systems

In interacting dynamical systems, specific local interaction rules for system components give rise to diverse and complex global dynamics. Long dynamical cycles are a key feature of many natural interacting systems, especially in biology. Examples of dynamical cycles range from circadian rhythms regulating sleep to cell cycles regulating reproductive behavior. Despite the crucial role of cycles in nature, the properties of network structure that give rise to cycles still need to be better understood. Here, we use a Boolean interaction network model to study the relationships between network structure and cyclic dynamics. We identify particular structural motifs that support cycles, and other motifs that suppress them. More generally, we show that the presence of dynamical reflection symmetry in the interaction network enhances cyclic behavior. In simulating an artificial evolutionary process, we find that motifs that break reflection symmetry are discarded. We further show that dynamical reflection symmetries are over-represented in Boolean models of natural biological systems. Altogether, our results demonstrate a link between symmetry and functionality for interacting dynamical systems, and they provide evidence for symmetry’s causal role in evolving dynamical functionality.

Schwinger-Keldysh effective field theory for stable and causal relativistic hydrodynamics

We construct stable and causal effective field theories (EFTs) for describing statistical fluctuations in relativistic diffusion and relativistic hydrodynamics. These EFTs are fully non-linear, including couplings to background sources, and enable us to compute n-point time-ordered correlation functions including the effects of statistical fluctuations. The EFTs we construct are inspired by the Maxwell-Cattaneo model of relativistic diffusion and Müller-Israel-Stewart model of relativistic hydrodynamics respectively, and have been derived using both the Martin-Siggia-Rose and Schwinger-Keldysh formalisms. The EFTs non-linearly realise the dynamical Kubo-Martin-Schwinger (KMS) symmetry, which ensures that n-point correlation functions and interactions in the theory satisfy the appropriate fluctuation-dissipation theorems. Since these EFTs typically admit ultraviolet sectors that are not fixed by the low-energy infrared symmetries, we find that they simultaneously admit multiple realisations of the dynamical KMS symmetry. We also comment on certain obstructions to including statistical fluctuations in the recently-proposed stable and causal Bemfica-Disconzi-Noronha-Kovtun model of relativistic hydrodynamics.

Critical branching dynamics in excitable network without refractory periods

Critical state plays an important role in emerged behavior of neural networks. Excitable networks are widely used in simulation studies. However, the simulation of critical state is sophisticated because the state sensitively depends on dynamical and topological features. We study the effect of refractory period of dynamical units and connection symmetry on the excitable network with critical branching ratio. In bidirectional random networks with refractory period, the critical branching ratio is well known. Here, we show that the collective behavior changes from critical state into ceaseless activity, when refractory period vanishes. Instead of mean degree of all nodes, we show that the control parameter is determined by the mean degree of active nodes which is larger than the average degree and induces the transition. When refractory period is present, the number of effective links connected to resting nodes is equal to average degree. The mechanism ensures the critical branching ratio is unity. In directed networks, collective behavior keeps the critical state when refractory period vanished. However, a few reciprocal links make the network without refractory period becoming ceaseless.

Distribution amplitude and decay constant of 1S and 2S state light mesons in the light-front quark model

Studying meson structures is essential for gaining insights into the nonperturbative nature of Quantum Chromodynamics (QCD). This study will focus on calculating the decay constant and distribution amplitudes (DAs) of unflavored light mesons (π and ρ) in the 1S and 2S states using the Light Front Quark Model. This study utilizes the QCD-motivated Hamiltonian, taking into account both contact and smeared spin-spin interactions. The two lowest harmonic oscillator bases are employed in this work to achieve improved results for the 2S states. The study found the optimal mixing parameter in basis expansion coefficients to be θ = 10°. Light meson properties, including the mass spectrum, decay constant, and twist-2 DAs, are then predicted using model parameters fixed through the variational principle. While the contact spin-spin interaction yields poor accuracy, the results from the smeared interaction generally agree well with experimental data and other theoretical models with $ f_{\pi}^{1S}=130 $ MeV and $ f_{\rho}^{1S}=210 $ MeV in the mixed state. Unlike the case for the 1S state, it should be noted that the properties of the 2S state are sensitive to the mixing parameter θ. In addition, we observe that the decay constant for ρ(2S) is $ f_{\rho}^{2S}=116 $ MeV. While for π(2S) the decay constant is extremely small with the value of $ f_{\pi}^{2S}=0.9 $ MeV, which is mainly due to the dynamical chiral symmetry breaking.

Nonsequential double ionization of Ar atoms in counter-rotating two-color elliptically polarized laser fields

Electron correlation behaviors and recollision dynamics in nonsequential double ionization (NSDI) of Ar atoms in counter-rotating two-color elliptically polarized (TCEP) laser fields are investigated with the classical ensemble model. The combined electric field in counter-rotating TCEP laser pulses traces out a trefoil pattern, i.e., the waveform in a period shows three leaves in different directions, and each leaf is called a lobe. Different from counter-rotating two-color circularly polarized laser fields, the combined electric field has no spatial symmetry. The amplitudes of the three field lobes and the angles between them are different. Thus, the returning electron mainly returns to the parent ion from one direction, and the electron momentum distributions show strong asymmetry. Numerical results show that the NSDI yield gradually decreases as the ellipticity increases, and the correlated behavior of the correlated electron momentum along the long axis of the laser polarization plane gradually evolves from correlation behavior mainly located in the first and third quadrants to anti-correlation behavior mainly located in the second and fourth quadrants. In order to further understand the correlation behaviors of electron pairs, different characteristic times in the NSDI processes are discussed, respectively. It is found that single ionization events and recollision events gradually decrease, but single ionization time and recollision time change slightly. This may be the main reason for the decrease in NSDI yield. And as the ellipticity increases, the traveling time and the recollision energy gradually decrease, while the delay time increases. Therefore, we can conclude that ellipticity may be responsible for the NSDI processes. In addition, further analysis finds that the shape of the trajectories becomes more and more triangular as the ellipticity increases due to the counter-rotating TCEP laser fields of the specific dynamical symmetries of the total net electric field. And it is found that whether it is a “short trajectory” or a “long trajectory”, more of the population moves to the second and fourth quadrants as the ellipticity increases. The results show that increasing the ellipticity will gradually change the two electrons from emitting in the same direction to emitting in the opposite direction. This well demonstrates that both ellipticity and travelling time are responsible for the formation of the electron momentum distribution at the recollision time, meaning that both of them affect the emitted directions of both electrons.

A common origin for the QCD axion and sterile neutrinos from SU(5) strong dynamics

We identify the QCD axion and right-handed (sterile) neutrinos as bound states of an SU(5) chiral gauge theory with Peccei-Quinn (PQ) symmetry arising as a global symmetry of the strong dynamics. The strong dynamics is assumed to spontaneously break the PQ symmetry, producing a high-quality axion and naturally generating Majorana masses for the right-handed neutrinos at the PQ scale. The composite sterile neutrinos can directly couple to the left-handed (active) neutrinos, realizing a standard see-saw mechanism. Alternatively, the sterile neutrinos can couple to the active neutrinos via a naturally small mass mixing with additional elementary states, leading to light sterile neutrino eigenstates. The SU(5) strong dynamics therefore provides a common origin for a high-quality QCD axion and sterile neutrinos.

Newton's Off-Center Circular Orbits and the Magnetic Monopole

Introducing a radially dependent magnetic field into Newton's off-center circular orbits potential so as to preserve the $E=0$ dynamical symmetry leads to a unique choice of field that can be identified as the inclusion of a magnetic monopole in the inverse stereographically projected problem. One finds also a phenomenological correspondence with that of the linearly damped Kepler model. The presence of the monopole field deforms the symmetry algebra by a central extension, and the quantum mechanical version of this algebra reveals a number of zero modes equal to that counted using the index theorem of elliptic operators.

Onsager Reciprocal Relation between Anomalous Transverse Coefficients of an Anisotropic Antiferromagnet.

Whenever two irreversible processes occur simultaneously, time-reversal symmetry of microscopic dynamics gives rise, on a macroscopic level, to Onsager's reciprocal relations, which impose constraints on the number of independent components of any transport coefficient tensor. Here, we show that in the antiferromagnetic YbMnBi_{2}, which displays a strong temperature-dependent anisotropy, Onsager's reciprocal relations are strictly satisfied for anomalous electric (σ_{ij}^{A}) and anomalous thermoelectric (α_{ij}^{A}) conductivity tensors. In contradiction with what was recently reported by Pan etal. [Nat. Mater. 21, 203 (2022)NMAACR1476-112210.1038/s41563-021-01149-2], we find that σ_{ij}^{A}(H)=σ_{ji}^{A}(-H) and α_{ij}^{A}(H)=α_{ji}^{A}(-H). This equality holds in the whole temperature window irrespective of the relative weights of the intrinsic or extrinsic mechanisms. The α_{ij}^{A}/σ_{ij}^{A} ratio is close to k_{B}/e at room temperature but peaks to an unprecedented magnitude of 2.9k_{B}/e at ∼150  K, which may involve nondegenerate carriers of small Fermi surface pockets.

Dynamic Oppositional Symmetries for Color, Jungian and Kantian Categories

AbstractThis paper investigates some classical oppositional categories, like synthetic versus analytic, posterior versus prior, imagination versus grammar, metaphor versus hermeneutics, metaphysics versus observation, innovation versus routine, and image versus sound, and the role they play in epistemology and philosophy of science. The epistemological framework of objective cognitive constructivism is of special interest in these investigations. Oppositional relations are formally represented using algebraic lattice structures like the cube and the hexagon of opposition, with applications in the contexts of modern color theory, Kantian philosophy, Jungian psychology, and linguistics.

Description of intruder levels in the 162,164,166Dy nuclei by two different algebraic approaches

In this paper, we tried to describe both normal and intruder levels of the ground and first excited beta and gamma rotational bands of 162,164,166Dy deformed nuclei in the framework of the interacting boson model. A normal Hamiltonian of SU(3) dynamical symmetry limit is extended by adding a 2p-2 h excitation term. Also, the results are compared with the predictions of the partial dynamical symmetry for these levels of considered nuclei. The results show that, this extension removes the degeneracy suggested by the pure SU(3) symmetry and makes satisfactory agreement with the experimental counterparts for the energy levels, too. Also, a comparison between the results of this extended formalism and partial dynamical symmetry shows the advantages of the first one in the description of intruder levels, whereas the latter, makes exact results for the normal energy levels of beta and gamma energy bands. The predictions of pure SU(3), partial dynamical symmetry SU(3) and mixed formalism for different quadrupole transition rates between normal and intruder levels of this nucleus are compared with the predictions of pseudo-SU(3) model and the advantages of each model have explained in detail.