Low-energy Behavior Research Articles

Physical activity patterns across time-segmented youth sport flag football practice

BackgroundYouth sport (YS) reaches a large number of children world-wide and contributes substantially to children’s daily physical activity (PA), yet less than half of YS time has been shown to be spent in moderate-to-vigorous physical activity (MVPA). Physical activity during practice is likely to vary depending on practice structure that changes across YS time, therefore the purpose of this study was 1) to describe the type and frequency of segments of time, defined by contextual characteristics of practice structure, during YS practices and 2) determine the influence of these segments on PA.MethodsResearch assistants video-recorded the full duration of 28 practices from 14 boys’ flag football teams (2 practices/team) while children concurrently (N = 111, aged 5–11 years, mean 7.9 ± 1.2 years) wore ActiGraph GT1M accelerometers to measure PA. Observers divided videos of each practice into continuous context time segments (N = 204; mean-segments-per-practice = 7.3, SD = 2.5) using start/stop points defined by change in context characteristics, and assigned a value for task (e.g., management, gameplay, etc.), member arrangement (e.g., small group, whole group, etc.), and setting demand (i.e., fosters participation, fosters exclusion). Segments were then paired with accelerometer data. Data were analyzed using a multilevel model with segment as unit of analysis.ResultsWhole practices averaged 34 ± 2.4% of time spent in MVPA. Free-play (51.5 ± 5.5%), gameplay (53.6 ± 3.7%), and warm-up (53.9 ± 3.6%) segments had greater percentage of time (%time) in MVPA compared to fitness (36.8 ± 4.4%) segments (p ≤ .01). Greater %time was spent in MVPA during free-play segments compared to scrimmage (30.2 ± 4.6%), strategy (30.6 ± 3.2%), and sport-skill (31.6 ± 3.1%) segments (p ≤ .01), and in segments that fostered participation (36.1 ± 2.7%) than segments that fostered exclusion (29.1 ± 3.0%; p ≤ .01). Significantly greater %time was spent in low-energy stationary behavior in fitness (15.7 ± 3.4%) than gameplay (4.0 ± 2.9%) segments (p ≤ .01), and in sport-skill (17.6 ± 2.2%) than free-play (8.2 ± 4.2%), gameplay, and warm-up (10.6 ± 2.6%) segments (p < .05).ConclusionsThe %time spent in low-energy stationary behavior and in MVPA differed by characteristics of task and setting demand of the segment. Restructuring the routine of YS practice to include segments conducive to MVPA could increase %time spent in MVPA during practice. As YS reaches a large number of children worldwide, increasing PA during YS has the potential to create a public health impact.

Zn clock models and chains of so(n)2 non-Abelian anyons: symmetries, integrable points and low energy properties

We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain quantum clock models, spin chains generalizing the Ising model, and chains of non-Abelian anyons constructed from the so(n)2 fusion category for odd n, both subject to periodic boundary conditions. In spite of the differences between these two types of quantum chains, e.g. their Hilbert spaces being spanned by tensor products of local spin states or fusion paths of anyons, the symmetries of the lattice models are shown to be closely related. Furthermore, under a suitable mapping between the parameters describing the interaction between spins and anyons the respective Hamiltonians share part of their energy spectrum (although their degeneracies may differ). This spin-anyon correspondence can be extended by fine-tuning of the coupling constants leading to exactly solvable models. We show that the algebraic structures underlying the integrability of the clock models and the anyon chain are the same. For n = 3,5,7 we perform an extensive finite size study—both numerical and based on the exact solution—of these models to map out their ground state phase diagram and to identify the effective field theories describing their low energy behaviour. We observe that the continuum limit at the integrable points can be described by rational conformal field theories with extended symmetry algebras which can be related to the discrete ones of the lattice models.

Theory of the magnetic skyrmion glass

Magnetic skyrmions discovered in chiral magnets show unique physical properties due to their nontrivial topology. While their basic properties have been well understood for pure systems, in real materials there is always disorder from, for example, crystal defects or impurities. This glassy nature substantially modifies the low-energy behavior, and hence the investigation of the skyrmion glass is crucial to understanding real materials. Here, the authors theoretically study disordered chiral magnets in terms of replica field theory, and provide a firm basis to explore the glassy state of magnetic skyrmions.

Higher-order Fermi-liquid corrections for an Anderson impurity away from half filling : Equilibrium properties

We study the low-energy behavior of the vertex function of a single Anderson impurity away from half filling for finite magnetic fields, using the Ward identities with careful consideration of the antisymmetry and analytic properties. The asymptotic form of the vertex function ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\sigma}{\ensuremath{\sigma}}^{\ensuremath{'}};{\ensuremath{\sigma}}^{\ensuremath{'}}\ensuremath{\sigma}}^{}(i\ensuremath{\omega},i{\ensuremath{\omega}}^{\ensuremath{'}};i{\ensuremath{\omega}}^{\ensuremath{'}},i\ensuremath{\omega})$ is determined up to terms of linear order with respect to the two frequencies $\ensuremath{\omega}$ and ${\ensuremath{\omega}}^{\ensuremath{'}}$, as well as the ${\ensuremath{\omega}}^{2}$ contribution for antiparallel spins ${\ensuremath{\sigma}}^{\ensuremath{'}}\ensuremath{\ne}\ensuremath{\sigma}$ at ${\ensuremath{\omega}}^{\ensuremath{'}}=0$. From these results, we also obtain a series of the Fermi-liquid relations beyond those of Yamada-Yosida [Prog. Theor. Phys. 54, 316 (1975)]. The ${\ensuremath{\omega}}^{2}$ real part of the self-energy ${\mathrm{\ensuremath{\Sigma}}}_{\ensuremath{\sigma}}^{}(i\ensuremath{\omega})$ is shown to be expressed in terms of the double derivative ${\ensuremath{\partial}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{\ensuremath{\sigma}}^{}(0)/\ensuremath{\partial}{\ensuremath{\epsilon}}_{d\ensuremath{\sigma}}^{2}$ with respect to the impurity energy level ${\ensuremath{\epsilon}}_{d\ensuremath{\sigma}}^{}$, and agrees with the formula obtained recently by Filippone, Moca, von Delft, and Mora (FMvDM) in the Nozi\`eres phenomenological Fermi-liquid theory [Phys. Rev. B 95, 165404 (2017)]. We also calculate the ${T}^{2}$ correction of the self-energy and find that the real part can be expressed in terms of the three-body correlation function $\ensuremath{\partial}{\ensuremath{\chi}}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}/\ensuremath{\partial}{\ensuremath{\epsilon}}_{d,\ensuremath{-}\ensuremath{\sigma}}^{}$, where ${\ensuremath{\chi}}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ is the static susceptibility between antiparallel spins. We also provide an alternative derivation of the asymptotic form of the vertex function. Specifically, we calculate the skeleton diagrams for the vertex function ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\sigma}\ensuremath{\sigma};\ensuremath{\sigma}\ensuremath{\sigma}}^{}(i\ensuremath{\omega},0;0,i\ensuremath{\omega})$ for parallel spins up to order ${U}^{4}$ in the Coulomb repulsion $U$. It directly clarifies the fact that the analytic components of order $\ensuremath{\omega}$ vanish as a result of the cancellation of four related Feynman diagrams, which are related to each other through the antisymmetry operation.

Tunneling conductance in semiconductor-superconductor hybrid structures

We study the differential conductance for charge tunneling into a semiconductor wire--superconductor hybrid structure, which is actively investigated as a possible scheme for realizing topological superconductivity and Majorana zero modes. The calculations are done based on a tight-binding model of the heterostructure using both a Blonder-Tinkham-Klapwijk approach and a Keldysh non-equilibrium Green's function method. The dependence of various tunneling conductance features on the coupling strength between the semiconductor and the superconductor, the tunnel barrier height, and temperature is systematically investigated. We find that treating the parent superconductor as an active component of the system, rather than a passive source of Cooper pairs, has qualitative consequences regarding the low-energy behavior of the differential conductance. In particular, the presence of sub-gap states in the parent superconductor, due to disorder and finite magnetic fields, leads to characteristic particle-hole asymmetric features and to the breakdown of the quantization of the zero-bias peak associated with the presence of Majorana zero modes localized at the ends of the wire. The implications of these findings for the effort toward the realization of Majorana bound states with true non-Abelian properties are discussed.

Electron-capture Isotopes Could Constrain Cosmic-Ray Propagation Models

Abstract Electron capture (EC) isotopes are known to provide constraints on the low-energy behavior of cosmic rays (CRs), such as reacceleration. Here, we study the EC isotopes within the framework of the dynamic spiral-arms CR propagation model in which most of the CR sources reside in the galactic spiral arms. The model was previously used to explain the B/C and sub-Fe/Fe ratios. We show that the known inconsistency between the 49Ti/49V and 51V/51Cr ratios remains also in the spiral-arms model. On the other hand, unlike the general wisdom that says the isotope ratios depend primarily on reacceleration, we find here that the ratio also depends on the halo size (Z h) and, in spiral-arms models, also on the time since the last spiral-arm passage ( ). Namely, EC isotopes can, in principle, provide interesting constraints on the diffusion geometry. However, with the present uncertainties in the lab measurements of both the electron attachment rate and the fragmentation cross sections, no meaningful constraint can be placed.

Parametrizations of three-body hadronic B - and D -decay amplitudes in terms of analytic and unitary meson-meson form factors

We introduce parametrizations of hadronic three-body $B$ and $D$ weak decay amplitudes that can be readily implemented in experimental analyses and are a sound alternative to the simplistic and widely used sum of Breit-Wigner type amplitudes, also known as the isobar model. These parametrizations can be particularly useful in the interpretation of CP asymmetries in the Dalitz plots. They are derived from previous calculations based on a quasi-two-body factorization approach in which two-body hadronic final state interactions are fully taken into account in terms of unitary $S$- and $P$-wave $\pi\pi$, $\pi K$ and $K \bar K$ form factors. These form factors can be determined rigorously, fulfilling fundamental properties of quantum field-theory amplitudes such as analyticity and unitarity, and are in agreement with the low-energy behaviour predicted by effective theories of QCD. They are derived from sets of coupled-channel equations using $T$-matrix elements constrained by experimental meson-meson phase shifts and inelasticities, chiral symmetry and asymptotic QCD. We provide explicit amplitude expressions for the decays $B^\pm \to \pi^+ \pi^- \pi^\pm$, $B \to K \ \pi^+ \pi^-$, $B^\pm \to K^+ K^-K^\pm$, $D^+ \to \pi^- \pi^+ \pi^+ $, $D^+ \to K^- \pi^+ \ \pi^+ $, $D^0 \to K^0_S \ \pi^+\ \pi^- $, for which we have shown in previous studies that this approach is phenomenologically successful, in addition, we provide expressions for the $D^0 \to K^0_S \ K^+ K^-$ decay. Other three-body hadronic channels can be parametrized likewise.

Voltage-Based Concatenatable Full Adder Using Spin Hall Effect Switching

Magnetic tunnel junction (MTJ)-based devices have been studied extensively as a promising candidate to implement hybrid energy-efficient computing circuits due to their nonvolatility, high integration density, and CMOS compatibility. In this paper, MTJs are leveraged to develop a novel full adder (FA) based on 3- and 5-input majority gates. Spin Hall effect (SHE) is utilized for changing the MTJ states resulting in low-energy switching behavior. SHE-MTJ devices are modeled in Verilog-A using precise physical equations. SPICE circuit simulator is used to validate the functionality of 1-bit SHE-based FA. The simulation results show 76% and 32% improvement over previous voltage-mode MTJ-based FA in terms of energy consumption and device count, respectively. The concatanatability of our proposed 1-bit SHE-FA is investigated through developing a 4-bit SHE-FA. Finally, delay and power consumption of an ${ {n}}$ -bit SHE-based adder has been formulated to provide a basis for developing an energy efficient SHE-based ${n}$ -bit arithmetic logic unit.

Two-dimensional nuclear Coulomb scattering of a slow quantum particle

We study two-dimensional scattering of a quantum particle by the superposition of a Coulomb potential and a central short-range potential. We analyze the low-energy asymptotic behavior of all radial wave functions, partial phases, and scattering cross sections of such a particle. We propose two approaches for evaluating the scattering length and the effective radius.

Global inconsistency, ’t Hooft anomaly, and level crossing in quantum mechanics

An 't Hooft anomaly is the obstruction for gauging symmetries, and it constrains possible low-energy behaviors of quantum field theories by excluding trivial infrared theories. Global inconsistency condition is recently proposed as a milder condition but is expected to play an almost same role by comparing high symmetry points in the theory space. In order to clarify the consequence coming from this new condition, we discuss several quantum mechanical models with topological angles and explicitly compute their energy spectra. It turns out that the global inconsistency can be saturated not only by the ground-state degeneracy at either of high symmetry points but also by the level crossing (phase transition) separating those high symmetry points.

Decay estimates and Strichartz estimates of fourth-order Schrödinger operator

We study time decay estimates of the fourth-order Schrödinger operator H=(−Δ)2+V(x) in Rd for d=3 and d≥5. We analyze the low energy and high energy behaviour of resolvent R(H;z), and then derive the Jensen–Kato dispersion decay estimate and local decay estimate for e−itHPac under suitable spectrum assumptions of H. Based on Jensen–Kato type decay estimate and local decay estimate, we obtain the L1→L∞ estimate of e−itHPac in 3-dimension by Ginibre argument, and also establish the endpoint global Strichartz estimates of e−itHPac for d≥5. Furthermore, using the local decay estimate and the Georgescu–Larenas–Soffer conjugate operator method, we prove the Jensen–Kato type decay estimates for some functions of H.

Quantum phase transition and unusual critical behavior in multi-Weyl semimetals

The low-energy behaviors of gapless double- and triple-Weyl fermions caused by the interplay of long-range Coulomb interaction and quenched disorder are studied by performing a renormalization group analysis. It is found that an arbitrarily weak disorder drives the double-Weyl semimetal to undergo a quantum phase transition into a compressible diffusive metal, independent of the disorder type and the Coulomb interaction strength. In contrast, the nature of the ground state of triple-Weyl fermion system relies sensitively on the specific disorder type in the noninteracting limit: The system is turned into a compressible diffusive metal state by an arbitrarily weak random scalar potential or $z$ component of random vector potential but exhibits stable critical behavior when there is only $x$ or $y$ component of random vector potential. In case the triple-Weyl fermions couple to random scalar potential, the system becomes a diffusive metal in the weak interaction regime but remains a semimetal if Coulomb interaction is sufficiently strong. Interplay of Coulomb interaction and $x$, or $y$, component of random vector potential leads to a stable infrared fixed point that is likely to be characterized by critical behavior. When Coulomb interaction coexists with the $z$ component of random vector potential, the system flows to the interaction-dominated strong coupling regime, which might drive a Mott insulating transition. It is thus clear that double- and triple-Weyl fermions exhibit distinct low-energy behavior in response to interaction and disorder. The physical explanation of such distinction is discussed in detail. The role played by long-range Coulomb impurity in triple-Weyl semimetal is also considered.

Perturbative and global anomalies in bosonic analogs of integer quantum Hall and topological insulator phases

We study perturbative and global anomalies at the boundaries of bosonic analogues of integer quantum Hall (BIQH) and topological insulator (BTI) phases using a description of the boundaries of these phases in terms of a nonlinear sigma model (NLSM) with Wess-Zumino term. One of the main results of the paper is that these anomalies are robust against arbitrary smooth deformations of the target space of the NLSM which describes the phase, provided that the deformations also respect the symmetry of the phase. In the first part of the paper we discuss the perturbative $U(1)$ anomaly at the boundary of BIQH states in all odd (spacetime) dimensions. In the second part we study global anomalies at the boundary of BTI states in even dimensions. In a previous work [Phys. Rev. B 95, 035149 (2017)] we argued that the boundary of the BTI phase exhibits a global anomaly which is an analogue of the parity anomaly of Dirac fermions in three dimensions. Here we elevate this argument to a proof for the boundary of the two-dimensional BTI state by explicitly computing the partition function of the gauged NLSM describing the boundary. We then use the powerful equivariant localization technique to show that this global anomaly is robust against all smooth deformations of the target space of the NLSM which preserve the $U(1)\rtimes\mathbb{Z}_2$ symmetry of the BTI state. We also comment on the difficulties of generalizing this latter proof to higher dimensions. Finally, we discuss the expected low energy behavior of the boundary theories studied in this paper when the coupling constants are allowed to flow under the renormalization group.

Competition between disorder and interaction effects in three-dimensional Weyl semimetals

We investigate the low-energy scaling behavior of an interacting 3D Weyl semimetal in the presence of disorder. In order to achieve a renormalization group analysis of the theory, we focus on the effects of a short-ranged-correlated disorder potential, checking nevertheless that this choice is not essential to locate the different phases of the Weyl semimetal. We show that there is a line of fixed-points in the renormalization group flow of the interacting theory, corresponding to the disorder-driven transition to a diffusive metal phase. Along that boundary, the critical disorder strength undergoes a strong increase with respect to the noninteracting theory, as a consequence of the unconventional screening of the Coulomb and disorder-induced interactions. A complementary resolution of the Schwinger-Dyson equations allows us to determine the full phase diagram of the system, showing the prevalence of a renormalized semimetallic phase in the regime of intermediate interaction strength, and adjacent to the non-Fermi liquid phase characteristic of the strong interaction regime of 3D Weyl semimetals.

Latent national subpopulations of early education classroom disengagement of children from underresourced families

This research examined the latent developmental patterns for early classroom disengagement among children from some of the most underresourced families in the nation. Based on standardized teacher observations from the Head Start Impact Study, a nationally representative sample of children (N=1377) was assessed for manifestations of reticent/withdrawn and low energy behavior over four years spanning prekindergarten through first grade. For each form of disengagement, latent growth mixture modeling revealed three distinct subpopulations of change patterns featuring a dominant class associated with generally good classroom adjustment, a medial class that varied close to the population average over time, and a more extreme class (about 10% of the population) whose adjustment was relatively marginal and sometimes reached problematic levels. Whereas reticent/withdrawn behavior ordinarily subsided over time, low energy behavior increased. More extreme low energy behaviors tended to dissipate through schooling and extreme reticence/withdrawal became more accentuated, with both types associated with later academic and social problems. Attendant risk and protective factors are identified and mitigating assessment and prevention measures are discussed.

Effects of random potentials in three-dimensional quantum electrodynamics

Three-dimensional quantum electrodynamics exhibits a number of interesting properties, such as dynamical chiral symmetry breaking, weak confinement, and non-Fermi liquid behavior, and also has wide applications in condensed matter physics. We study the effects of random potentials, which exist in almost all realistic condensed-matter systems, on the low-energy behaviors of massless Dirac fermions by means of renormalization group method, and show that the role of random mass is significantly enhanced by the gauge interaction, whereas random scalar and vector potentials are insusceptible to the gauge interaction at the one-loop order. The static random potential breaks the Lorentz invariance, and as such induces unusual renormalization of fermion velocity. We then consider the case in which three types of random potentials coexist in the system. The random scalar potential is found to play a dominant role in the low-energy region, and drives the system to undergo a quantum phase transition.

Symmetry-protected topological phases of one-dimensional interacting fermions with spin-charge separation

The low energy behavior of a huge variety of one-dimensional interacting spinful fermionic systems exhibits spin-charge separation, described in the continuum limit by two sine-Gordon models decoupled in the charge and spin channels. Interaction is known to induce, besides the gapless Luttinger liquid phase, eight possible gapped phases, among which are the Mott, Haldane, charge-/spin-density, and bond-ordered wave insulators, and the Luther Emery liquid. Here we prove that some of these physically distinct phases have nontrivial topological properties, notably the presence of degenerate protected edge modes with fractionalized charge/spin. Moreover, we show that the eight gapped phases are in one-to-one correspondence with the symmetry-protected topological (SPT) phases classified by group cohomology theory in the presence of particle-hole symmetry P. The latter result is also exploited to characterize SPT phases by measurable nonlocal order parameters which follow the system evolution to the quantum phase transition. The implications on the appearance of exotic orders in the class of microscopic Hubbard Hamiltonians, possibly without P symmetry at higher energies, are discussed.

Resonance expansions for tensor-valued waves on asymptotically Kerr–de Sitter spaces

In recent joint work with András Vasy [25], we analyze the low energy behavior of differential form-valued waves on black hole spacetimes. In order to deduce symptotics and decay from this, one in addition needs high energy estimates for the wave operator acting on sections of the form bundle. The present paper provides these on perturbations of Schwarzschild–de Sitter spaces in all spacetime dimensions n ≥ 4 . In fact, we prove exponential decay, up to a finite-dimensional space of resonances, of waves valued in any finite rank subbundle of the tensor bundle, which in particular includes differential forms and symmetric tensors. As the main technical tool for working on vector bundles that do not have a natural positive definite inner product, we introduce pseudodifferential inner products, which are inner products depending on the position in phase space.

Critical behavior at dynamical phase transition in the generalized Bose-Anderson model

Critical properties of the dynamical phase transition in the quenched generalized Bose-Anderson impurity model are studied in the mean-field limit of an infinite number of channels. The transition separates the evolution toward ground state and toward the branch of stable excited states. We perform numerically exact simulations of a close vicinity of the critical quench amplitude. The relaxation constant describing the asymptotic evolution toward ground state, as well as asymptotic frequency of persistent phase rotation and number of cloud particles at stable excited state are power functions of the detuning from the critical quench amplitude. The critical evolution (separatrix between the two regimes) shows a non-Lyapunov power-law instability arising after a certain critical time. The observed critical behavior is attributed to the irreversibility of the dynamics of particles leaving the cloud and to memory effects related to the low-energy behavior of the lattice density of states.

Disorder-driven destruction of a non-Fermi liquid semimetal studied by renormalization group analysis

We investigate the interplay of Coulomb interactions and short-range-correlated disorder in three dimensional systems where absent disorder the non-interacting band structure hosts a quadratic band crossing. Though the clean Coulomb problem is believed to host a 'non-Fermi liquid' phase, disorder and Coulomb interactions have the same scaling dimension in a renormalization group (RG) sense, and thus should be treated on an equal footing. We therefore implement a controlled $\epsilon$-expansion and apply it at leading order to derive RG flow equations valid when disorder and interactions are both weak. We find that the non-Fermi liquid fixed point is unstable to disorder, and demonstrate that the problem inevitably flows to strong coupling, outside the regime of applicability of the perturbative RG. An examination of the flow to strong coupling suggests that disorder is asymptotically more important than interactions, so that the low energy behavior of the system can be described by a non-interacting sigma model in the appropriate symmetry class (which depends on whether exact particle-hole symmetry is imposed on the problem). We close with a discussion of general principles unveiled by our analysis that dictate the interplay of disorder and Coulomb interactions in gapless semiconductors, and of connections to many-body localized systems with long-range interactions.