Low-energy Behavior Research Articles

Theory of low-energy behaviors in topological s-wave pairing superconductors

We construct a low-energy effective theory of topological s-wave pairing superconductors, focusing on the mean-field model of superconductor CuxBi2Se3. Our approach is second-order perturbation with respect to the inverse of the mass (i.e., large-mass expansion) in the Dirac-type electron dispersion from topological insulator Bi2Se3. Since the Dirac-type dispersion with a large mass describes non-relativistic electrons, the large-mass expansion corresponds to a low-energy theory with respect to the original setup. We show that the effective gap function has not only a p-wave-like component as the primary contribution, but also an s-wave-like one as higher-order corrections. The mixture of p- and s-wave explains the numerical results (Nagai et al., 2014) of the non-magnetic impurity effects.

Cosmic expansion and structure formation in running vacuum cosmologies

We investigate the dynamics of the Friedmann–Lemaître–Robertson–Walker (FLRW) flat cosmological models in which the vacuum energy varies with redshift. A particularly well-motivated model of this type is the so-called quantum field vacuum, in which both kind of terms [Formula: see text] and constant appear in the effective dark energy (DE) density affecting the evolution of the main cosmological functions at the background and perturbation levels. Specifically, it turns out that the functional form of the quantum vacuum endows the vacuum energy of a mild dynamical evolution which could be observed nowadays and appears as dynamical DE. Interestingly, the low-energy behavior is very close to the usual Lambda cold dark matter (ΛCDM) model, but it is by no means identical. Finally, within the framework of the quantum field vacuum we generalize the large scale structure properties, namely growth of matter perturbations, cluster number counts and spherical collapse model.

TH-AB-201-11: A Systematic Characterization of the Low Energy Response of Plastic Scintillation Detectors

Purpose: To characterize the low energy behavior of scintillating material used in plastic scintillation detectors. Methods: Four plastic scintillation detectors (PSDs) were developed using three different scintillating material (BCF-10, BCF-12, BCF-60) and one scintillator-free fiber. The scintillators were 1 mm in diameter and 10 mm-long, coupled to a 15 meter long clear PMMA optical fiber. A photomultiplier tube was connected to this fiber to collect the scintillator’s light signal. All fibers were covered by a light-tight polyethylene jacket. The PSDs were exposed to AAPM accredited low energy beam qualities ranging from 20 kVp to 250 kVp. Their response described the dose in polystyrene and was compared to the dose in air measured by a primary calibration chamber located at the beam exit. The mean energy and the spectral method were used to extract the effective mass energy-absorption coefficient using NIST database for each beam quality reference spectrum. Attenuation in air and in the fiber jacket were also considered. The scintillators expected response was compared to the experimental measurements and an energy-dependent correction factor was identified to account for low energy quenching occurring within the scintillators. Results: The clear optical fiber response was below 0.5% of the scintillator’s light, which indicated that a negligible amount of fluorescence contamination was produced. The scintillators response increased by a factor 3.65 ± 0.07 between a 20 kVp and a 250 kVp beam. The correction factor varied with beam energy and remained above 84% for beam qualities of 30 kVp and above, but drops for very low energy (20 kVp) to about 77%. Conclusion: This work describes the PSD energy dependence to low energy beam qualities and identifies a correction factor related to low energy quenching. A detailed comprehension of intrinsic scintillator response is essential when designing accurate PSD dosimeters for radiology purposes. This work was supported in part by a NIH/NCI SBIR grant R44CA153824 and by grant # 435510 from the NSERC. JB is supported by a FQRNT doctoral research scholarchip and acknowledges partial support by the NSERC CREATE Medical Physics Research Training Network grant # 432290.

Unitarity in composite Higgs boson approaches with vector resonances

We examine a simple Composite Higgs Model (CHM) with vector resonances in addition to the Standard Model (SM) fields in perturbation theory by using the $K$-matrix method to implement unitarity constraints. We find that the $W_LW_L$ scattering amplitude has an additional scalar pole (analogous to the $\sigma$ meson of QCD) as in generic strongly interacting extensions of the SM. The mass and width of this dynamically generated scalar resonance are large and the mass behaves contrary to the vector one, so that when the vector resonance is lighter, the scalar one is heavier, and vice versa. We also attempt an interpretation of this new resonance. Altogether, the presence of the vector state with the symmetries of the CHM improve the low-energy unitarity behavior also in the scalar-isoscalar channel.

Local contributions to factorized soft graviton theorems at loop level

We analyze the low-energy behavior of scattering amplitudes involving gravitons at loop level in four dimensions. The single-graviton soft limit is controlled by soft operators which have been argued to separate into a factorized piece and a non-factorizing infrared divergent contribution. In this note we show that the soft operators responsible for the factorized contributions are strongly constrained by gauge and Poincaré invariance under the assumption of a local structure. We show that the leading and subleading orders in the soft-momentum expansion cannot receive radiative corrections. The first radiative correction occurs for the sub-subleading soft graviton operator and is one-loop exact. It depends on only two undetermined coefficients which should reflect the field content of the theory under consideration.

Resonances in coupledπK,ηKscattering from lattice QCD

Coupled-channel $\pi K$ and $\eta K$ scattering amplitudes are determined by studying the finite-volume energy spectra obtained from dynamical lattice QCD calculations. Using a large basis of interpolating operators, including both those resembling a $q\bar{q}$ construction and those resembling a pair of mesons with relative momentum, a reliable excited-state spectrum can be obtained. Working at ${m_\pi=391\,\mathrm{MeV}}$, we find a gradual increase in the $J^P=0^+$ $\pi K$ phase-shift which may be identified with a broad scalar resonance that couples strongly to $\pi K$ and weakly to $\eta K$. The low-energy behavior of this amplitude suggests a virtual bound-state that may be related to the $\kappa$ resonance. A bound state with $J^P=1^-$ is found very close to the $\pi K$ threshold energy, whose coupling to the $\pi K$ channel is compatible with that of the experimental $K^\star(892)$. Evidence is found for a narrow resonance in $J^P=2^+$. Isospin--3/2 $\pi K$ scattering is also studied and non-resonant phase-shifts spanning the whole elastic scattering region are obtained.

Low-energy behavior of strongly interacting bosons on a flat-band lattice above the critical filling factor

Bosons interacting repulsively on a lattice with a flat lowest band energy dispersion may, at sufficiently small filling factors, enter into a Wigner-crystal-like phase. This phase is a consequence of the dispersionless nature of the system, which in turn implies the occurrence of single-particle localized eigenstates. We investigate one of these systems---the sawtooth lattice---filled with strongly repulsive bosons at filling factors infinitesimally above the critical point where the crystal phase is no longer the ground state. We find, in the hard-core limit, that the crystal retains its structure in all but one of its cells, where it is broken. The broken cell corresponds to an exotic kind of repulsively bound state, which becomes delocalized. We investigate the excitation spectrum of the system analytically and find that the bound state behaves as a single particle hopping on an effective lattice with reduced periodicity, and is therefore gapless. Thus, the addition of a single particle to a flat-band system at critical filling is found to be enough to make kinetic behavior manifest.

Resurgence and the Nekrasov-Shatashvili limit: connecting weak and strong coupling in the Mathieu and Lamé systems

The Nekrasov-Shatashvili limit for the low-energy behavior of N=2 and N=2* supersymmetric SU(2) gauge theories is encoded in the spectrum of the Mathieu and Lam'e equations, respectively. This correspondence is usually expressed via an all-orders Bohr-Sommerfeld relation, but this neglects non-perturbative effects, the nature of which is very different in the electric, magnetic and dyonic regions. In the gauge theory dyonic region the spectral expansions are divergent, and indeed are not Borel-summable, so they are more properly described by resurgent trans-series in which perturbative and non-perturbative effects are deeply entwined. In the gauge theory electric region the spectral expansions are convergent, but nevertheless there are non-perturbative effects due to poles in the expansion coefficients, and which we associate with worldline instantons. This provides a concrete analog of a phenomenon found recently by Drukker, Marino and Putrov in the large N expansion of the ABJM matrix model, in which non-perturbative effects are related to complex space-time instantons. In this paper we study how these very different regimes arise from an exact WKB analysis, and join smoothly through the magnetic region. This approach also leads to a simple proof of a resurgence relation found recently by Dunne and Unsal, showing that for these spectral systems all non-perturbative effects are subtly encoded in perturbation theory, and identifies this with the Picard-Fuchs equation for the quantized elliptic curve.

Universal low-energy behavior in three-body systems

We consider a pairwise interacting quantum 3-body system in 3-dimensional space with finite masses and the interaction term V12 + λ(V13 + V23), where all pair potentials are assumed to be nonpositive. The pair interaction of the particles {1, 2} is tuned to make them have a zero energy resonance and no negative energy bound states. The coupling constant λ > 0 is allowed to take the values for which the particle pairs {1, 3} and {2, 3} have no bound states with negative energy. Let λcr denote the critical value of the coupling constant such that E(λ) → −0 for λ → λcr, where E(λ) is the ground state energy of the 3-body system. We prove the theorem, which states that near λcr, one has E(λ) = C(λ − λcr)[ln(λ − λcr)]−1 + h.t., where C is a constant and h.t. stands for “higher terms.” This behavior of the ground state energy is universal (up to the value of the constant C), meaning that it is independent of the form of pair interactions.

Low-energy impact behaviour and damage characterization of carbon fibre reinforced polymer and aluminium hybrid laminates

The purpose of this paper is to investigate the impact behaviour and damage characterization of carbon fibre reinforced aluminium hybrid laminates (Al/CFRP) in comparison to classic carbon fibre reinforced polymer (CFRP) at low-velocity and low-energy impact. Impact damage characteristic with damage initiation and progression, internal failure modes and understanding of the role of the metal layers in the impact behaviour under low-energy were examined and discussed. The damage mechanism of the tested laminates is very complex. There is an internal degradation of the material, with the plastic deformation in case of fibre metal laminates. Characteristic matrix cracks (bending and shearing cracks) running at the fibre–matrix interface in composite layers are the first damage mode. The critical damage mode is delaminations observed between composite layers with different orientation as well as delaminations at the metal–composite interface in fibre metal laminates. For the tested materials, particularly carbon fibre reinforced composites, the absorbed impact energy is mainly connected with elastic response and damage of the laminate. In case of fibre metal laminates the absorbed energy is also connected with plastic deformation of the laminate, occurring especially in the metal layers. High impact resistance of fibre metal laminates indicates that metal (aluminium) layers may prevent delamination propagation and impactor penetration.

Greybody factors for scalar fields emitted by a higher-dimensional Schwarzschild–de Sitter black hole

In this paper, we consider the propagation of scalar particles in a higher-dimensional Schwarzschild--de Sitter black-hole spacetime, both on the brane and in the bulk. Our analysis applies for arbitrary partial modes and for both minimal and nonminimal coupling of the scalar field. A general expression for the greybody factor is analytically derived in each case, and its low-energy behavior is studied in detail. Its profile in terms of scalar properties (angular-momentum number and nonminimal coupling parameter) and spacetime properties (number of extra dimensions and cosmological constant) is thoroughly investigated. In contrast to previous studies, the effect of the cosmological constant is taken into account both close to and far away from the black-hole horizon. The dual role of the cosmological constant, that may act either as a helping agent to the emission of scalar particles or as a deterring effect depending on the value of the nonminimal coupling parameter, is also demonstrated.

Low-energy behavior of gluons and gravitons from gauge invariance

We show that at tree level, on-shell gauge invariance can be used to fully determine the first subleading soft-gluon behavior and the first two subleading soft-graviton behaviors. Our proofs of the behaviors for n-gluon and n-graviton tree amplitudes are valid in D dimensions and are similar to Low's proof of universality of the first subleading behavior of photons. In contrast to photons coupling to massive particles, in four dimensions the soft behaviors of gluons and gravitons are corrected by loop effects. We comment on how such corrections arise from this perspective. We also show that loop corrections in graviton amplitudes arising from scalar loops appear only at the second soft subleading order. This case is particularly transparent because it is not entangled with graviton infrared singularities. Our result suggests that if we set aside the issue of infrared singularities, soft-graviton Ward identities of extended BMS symmetry are not anomalous through the first subleading order.

Mean-field description of odd-frequency superconductivity with staggered ordering vector

A low-energy fixed-point Hamiltonian is constructed for the s-wave odd-frequency pairing state with staggered ordering vector in the two-channel Kondo lattice. The effective model is justified because it reproduces low-energy behaviors of self energy obtained by the dynamical mean-field theory. The retardation effect is essential for the odd-frequency pairing, which comes from the hybridization process between conduction electrons and pseudofermions originating from localized spins at low energies. Using the effective Hamiltonian, the electromagnetic response functions are microscopically calculated. The present system shows the "weak" Meissner effect, where both paramagnetic and diamagnetic parts contribute to the Meissner kernel to give a small total diamagnetic response in the superconducting state. This feature is in contrast to the ordinary s-wave BCS pairing where only the diamagnetic kernel is finite in the ground state. The staggered nature of the odd-frequency order parameter plays an important role for the sign of the Meissner kernel.

Evaluation of neutron nuclear data on tellurium isotopes

Neutron nuclear data on 13 Te isotopes have been evaluated for the next release of Japanese Evaluated Nuclear Data Library (JENDL) general purpose file in the energy region from 10− 5 eV to 20 MeV. Thermal capture cross sections of 120, 121m, 127m, 129m, 131m, 132Te were determined from the latest measurements or from a simplified formula, although the resolved resonance parameters, which describe the low-energy behavior of cross sections, remain unchanged from JENDL-4.0 for 122, 123, 124, 125, 126, 128, 130Te. A statistical model code was applied to evaluate the cross sections above the resolved resonance region. Coupled-channel optical model parameters were employed for the interaction between neutrons and nuclei. Compound, pre-equilibrium, and direct-reaction processes were considered for cross-section calculation in high-energy region. The present results reproduce experimental data very well, and are found to be much better than the JENDL-4.0 data. The evaluated data are compiled into evaluated nuclear data file (ENDF)-formatted data files.

Common non-Fermi liquid phases in quantum impurity physics

We study correlated quantum impurity models that undergo a local quantum phase transition (QPT) from a strong coupling, Fermi liquid phase to a non-Fermi liquid phase with a globally doubly degenerate ground state. Our aim is to establish what can be shown exactly about such ``local moment'' (LM) phases, of which the permanent (zero-field) local magnetization is a hallmark, and an order parameter for the QPT. A description of the zero-field LM phase is shown to require two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the single self-energy of standard field theory. Distinct Friedel sum rules for each phase are obtained, via a Luttinger theorem embodied in the vanishing of appropriate Luttinger integrals. By contrast, the standard Luttinger integral is nonzero in the LM phase but found to have universal magnitude. A range of spin susceptibilites are also considered, including that corresponding to the local order parameter, whose exact form is shown to be RPA-like, and to diverge as the QPT is approached. Particular attention is given to the pseudogap Anderson model, including the basic physical picture of the transition, the low-energy behavior of single-particle dynamics, the quantum critical point itself, and the rather subtle effect of an applied local field. A two-level impurity model that undergoes a QPT (``singlet-triplet'') to an underscreened LM phase is also considered, for which we derive on general grounds some key results for the zero-bias conductance in both phases.

Charmless chiral perturbation theory forNf=2+1+1twisted mass lattice QCD

The chiral Lagrangian describing the low-energy behavior of N_f=2+1+1 twisted mass lattice QCD is constructed through O(a^2). In contrast to existing results the effects of a heavy charm quark are consistently removed, leaving behind a charmless 3-flavor Lagrangian. This Lagrangian is used to compute the pion and kaon masses to one loop in a regime where the pion mass splitting is large and taken as a leading order effect. In comparison with continuum chiral perturbation theory additional chiral logarithms are present in the results. In particular, chiral logarithms involving the neutral pion mass appear. These predict rather large finite volume corrections in the kaon mass which roughly account for the finite volume effects observed in lattice data.

Covalency in transition-metal oxides within all-electron dynamical mean-field theory

A combination of dynamical mean field theory and density functional theory, as implemented in Phys. Rev. B 81, 195107 (2010), is applied to both the early and late transition metal oxides. For fixed value of the local Coulomb repulsion, without fine tuning, we obtain the main features of these series, such as the metallic character of SrVO$_3$ and the the insulating gaps of LaVO$_3$, LaTiO$_3$ and La$_2$CO$_4$ which are in good agreement with experiment. The study highlights the importance of local physics and high energy hybridization in the screening of the Hubbard interaction and how different low energy behaviors can emerge from the a unified treatment of the transition metal series.

Quantum phases of a chain of strongly interacting anyons

Quantum gates for the manipulation of topological qubits rely on interactions between non-Abelian anyonic quasiparticles. We study the collective behavior of systems of anyons arising from such interactions. In particular, we study the effect of favoring different fusion channels of the screened Majorana spins appearing in the recently proposed topological Kondo effect. Based on the numerical solution of a chain of $SO{(5)}_{2}$ anyons we identify two critical phases whose low-energy behavior is characterized by conformal field theories with central charges $c=1$ and $c=8/7$, respectively. Our results are complemented by exact results for special values of the coupling constants which provide additional information about the corresponding phase transitions.

Spectral problems and scattering on noncompact star-shaped graphs containing finite rays

Abstract We consider Schrödinger operators on noncompact star-shaped graphs. The following topics will be treated under suitable decay conditions on the potential: characterization of the set of eigenvalues and expression of each eigen-projection; low-energy behavior of the resolvent, spectral representations of the operator restricted on infinite rays; determination of the Marchenko equations and the inverse scattering problems.

Zero-energy bound state at the interface between ans-wave superconductor and a disordered normal metal with repulsive electron-electron interactions

In recent years, there has been a renewed interest in the proximity effect due to its role in the realization of topological superconductivity. Here, we study a superconductor--normal metal proximity system with repulsive electron-electron interactions in the normal layer. It is known that in the absence of disorder or normal reflection at the superconductor--normal metal interface, a zero-energy bound state forms and is localized to the interface [Fauch\`ere et al., Phys. Rev. Lett. 82, 3336 (1999).]. Using the quasiclassical theory of superconductivity, we investigate the low-energy behavior of the density of states in the presence of finite disorder and an interfacial barrier. We find that as the mean free path is decreased, the zero-energy peak in the density of states is broadened and reduced. In the quasiballistic limit, the bound state eliminates the minigap pertinent to a noninteracting normal layer and a distinct peak is observed. When the mean free path becomes comparable to the normal layer width, the zero-energy peak is strongly suppressed and the minigap begins to develop. In the diffusive limit, the minigap is fully restored and all signatures of the bound state are eliminated. We find that an interfacial potential barrier does not change the functional form of the density of states peak but does shift this peak away from zero energy.