Approximate Degeneracy Research Articles

Assessing observational constraints on dark energy

Observational constraints on time-varying dark energy (e.g., quintessence) are commonly presented on a w0-wa plot that assumes the equation of state of dark energy strictly satisfies w(z)=w0+waz/(1+z) as a function of the redshift z. Recent observations favor a sector of the w0-wa plane in which w0>−1 and w0+wa<−1, suggesting that the equation of state underwent a transition from violating the null energy condition (NEC) at large z to obeying it at small z. In this paper, we demonstrate that this impression is misleading by showing that simple quintessence models satisfying the NEC for all z predict an observational preference for the same sector. We also find that quintessence models that best fit observational data can predict a value for the dark energy equation of state at present that is significantly different from the best-fit value of w0 obtained assuming the parameterization above. In addition, the analysis reveals an approximate degeneracy of the w0-wa parameterization that explains the eccentricity and orientation of the likelihood contours presented in recent observational studies.

Monojet signatures from gluino and squark decays

We study the monojet and dijet channels at the LHC as a tool for searching for squarks and gluinos. We consider two separate R-parity conserving supersymmetric scenarios. In the first scenario we postulate a large mass hierarchy between squarks ( overset{sim }{q} ) and winos ( overset{sim }{W} ), and wino-like neutralino is assumed to be the lightest supersymmetric particle (LSP). The associated squark-wino production, pp → overset{sim }{q}overset{sim }{W} , then leads to a monojet-like signature, where the high pT jet is originated from the squark decay, overset{sim }{q} → q + overset{sim }{W} . We demonstrate that this associated production, as well as the pp → overset{sim }{W}overset{sim }{W} + jets production, have a significant impact on the exclusion limit in the squark-neutralino mass plane. The second scenario postulates that the lighter of the squark and gluino is only a few GeV heavier than the LSP neutralino. The associated squark-gluino production, pp → overset{sim }{q}overset{sim }{g} , then leads to a distinctive monojet signature, where the high pT jet is produced from the decay of the heavier coloured particle into the lighter one ( overset{sim }{q} → q+ overset{sim }{g} for {m}_{tilde{q}} > {m}_{tilde{g}} and overset{sim }{g} → q+ overset{sim }{q} for {m}_{tilde{g}} > {m}_{tilde{q}} ). The lighter coloured particle is effectively regarded as an invisible particle since the decay products are soft due to the approximate mass degeneracy. We recast existing monojet and dijet analyses and find a non-trivial exclusion limit in the squark-gluino mass plane in this scenario.

Spectral fluctuations in the interacting boson model* *Supported by National Natural Science Foundation of China (11875158, 11875171)

The energy dependence of the spectral fluctuations in the interacting boson model (IBM) and its connections to the mean-field structures are analyzed by adopting two statistical measures: the nearest neighbor level spacing distribution measuring the chaoticity (regularity) in energy spectra and the statistics of Dyson and Metha measuring the spectral rigidity. Specifically, the statistical results as functions of the energy cutoff are determined for different dynamical scenarios, including the U(5)-SU(3) and SU(3)-O(6) transitions as well as those near the AW arc of regularity. We observe that most of the changes in spectral fluctuations are triggered near the stationary points of the classical potential, particularly for cases in the deformed region of the IBM phase diagram. Thus, the results justify the stationary point effects from the perspective of statistics. In addition, the approximate degeneracies in the spectrum on the AW arc is also revealed from the statistical calculations.

Comments on the mass sheet degeneracy in cosmography analyses

We make a number of comments regarding modeling degeneracies in strong lensing measurements of the Hubble parameter H 0. The first point concerns the impact of weak lensing associated with different segments of the line of sight. We show that external convergence terms associated with the lens-source and observer-lens segments need to be included in cosmographic modeling, in addition to the usual observer-source term, to avoid systematic bias in the inferred value of H 0. Specifically, we show how an incomplete account of some line of sight terms biases stellar kinematics as well as ray tracing simulation methods to alleviate the mass sheet degeneracy.The second point concerns the use of imaging data for multiple strongly-lensed sources in a given system.We show that the mass sheet degeneracy is not fully resolved by the availability of multiple sources: some degeneracy remains because of differential external convergence between the different sources.Similarly, differential external convergence also complicates the use of multiple sources in addressing the approximate mass sheet degeneracy associated with a local (“internal”) core component in lens galaxies. This internal-external degeneracy is amplified by the non-monotonicity of the angular diameter distance as a function of redshift.For a rough assessment of the weak lensing effects, we provide estimates of external convergence using the nonlinear matter power spectrum, paying attention to non-equal time correlators.

Extended study on the application of the sextic potential in the frame of X(3)-sextic

The main aim of the present paper is to extensively study the γ-rigid Bohr Hamiltonian with anharmonic sextic oscillator potential for the variable β and γ = 0. For the corresponding spectral problem, a finite number of eigenvalues are explicitly found, by algebraic means, the so-called quasi-exact solvability (QES). The evolution of the spectral and electromagnetic properties by considering higher exact solvability orders is investigated, especially the approximate degeneracy of the ground and first two β bands at the critical point of the shape phase transition from a harmonic to an anharmonic prolate β-soft, as well as the shape evolution within an isotopic chain. The numerical results are given for 39 nuclei, namely, 98–108Ru, 100–102Mo, 116–130Xe, 180–196Pt, 172Os, 146–150Nd, 132–134Ce, 152–154Gd, 154–156Dy, 150–152Sm, 190Hg and 222Ra. Across this study, it seems that the higher QES order improves our results by decreasing the root mean square, mostly for deformed nuclei. The nuclei 100,104Ru, 118,120,126,128Xe, 148Nd and 172Os fall exactly at the critical point.

A Detailed Analysis of GW190521 with Phenomenological Waveform Models

Abstract In this paper we present an extensive analysis of the GW190521 gravitational wave event with the current (fourth) generation of phenomenological waveform models for binary black hole coalescences. GW190521 stands out from other events since only a few wave cycles are observable. This leads to a number of challenges, one being that such short signals are prone to not resolving approximate waveform degeneracies, which may result in multimodal posterior distributions. The family of waveform models we use includes a new fast time-domain model (IMRPhenomTPHM), which allows us to extensively test different priors and robustness with respect to variations in the waveform model, including the content of spherical harmonic modes. We clarify some issues raised in a recent paper, Nitz &amp; Capano, associated with possible support for a high-mass-ratio source, but confirm their finding of a multimodal posterior distribution, albeit with important differences in the statistical significance of the peaks. In particular, we find that the support for both masses being outside the pair instability supernova mass gap, and the support for an intermediate-mass-ratio binary are drastically reduced with respect to what Nitz &amp; Capano found. We also provide updated probabilities for associating GW190521 to the potential electromagnetic counterpart from the Zwicky Transient Facility (ZTF) Graham et al.

Pseudospin symmetry in resonant states and its dependence on the shape of potential

The complex momentum representation method is used to explore the single particle resonances in nuclei. The energies, widths, and wavefunctions are obtained by solving the Dirac equation with a Woods-Saxon potential, in which the parameters are determined from the RMF calculations for 132Sn. The pseudospin symmetry is investigated for the resonant states in comparison with bound states. Approximate degeneracy is shown in the energies, widths, and wavefunctions between the pseudospin doublets including the resonant and bound states. The influence of the potential shape on the pseudospin symmetry is checked. The quality of pseudospin symmetry is shown to be dependent of the parameters, which is explained in terms of the change of potential with these parameters. The energy and width splittings between the pseudospin doublets are sensitive to the potential parameters, which is clarified by the change of the derivative of potential with r. Moreover, the pseudospin splitting in the wavefunctions and its dependence on potential shape are analyzed. The wave function splitting between the pseudospin doublets is quantitatively obtained in the momentum space for the resonant states because they are local and square integrable. Considering that a real nuclear field is similar to a Woods-Saxon potential, the change of the parameters in Woods-Saxon potential can reflect the change of nuclear field from stable nuclei to drop-line nuclei. Therefore, the present researches are helpful to understand the level structure of the weakly bound nuclei and their exotic properties.

Gravitational lensing H0 tension from ultralight axion galactic cores

Gravitational lensing time delays offer an avenue to measure the Hubble parameter ${H}_{0}$, with some analyses suggesting a tension with early-type probes of ${H}_{0}$. The lensing measurements must mitigate systematic uncertainties due to the mass modeling of lens galaxies. In particular, a core component in the lens density profile would form an approximate local mass sheet degeneracy and could bias ${H}_{0}$ in the right direction to solve the lensing tension. We consider ultralight dark matter as a possible mechanism to generate such galactic cores. We show that cores of roughly the required properties could arise naturally if an ultralight axion of mass $m\ensuremath{\sim}{10}^{\ensuremath{-}25}\text{ }\text{ }\mathrm{eV}$ makes up a fraction of order 10% of the total cosmological dark matter density. A relic abundance of this order of magnitude could come from vacuum misalignment. Stellar kinematics measurements of well-resolved massive galaxies (including the Milky Way) may offer a way to test the scenario. Kinematics analyses aiming to test the core hypothesis in massive elliptical lens galaxies should not, in general, adopt the perfect mass sheet limit, as ignoring the finite extent of an actual physical core could lead to significant systematic errors.

Dynamical ejecta of neutron star mergers with nucleonic weak processes I: nucleosynthesis

ABSTRACT We present a coherent study of the impact of neutrino interactions on the r-process element nucleosynthesis and the heating rate produced by the radioactive elements synthesized in the dynamical ejecta of neutron star–neutron star (NS–NS) mergers. We have studied the material ejected from four NS–NS merger systems based on hydrodynamical simulations which handle neutrino effects in an elaborate way by including neutrino equilibration with matter in optically thick regions and re-absorption in optically thin regions. We find that the neutron richness of the dynamical ejecta is significantly affected by the neutrinos emitted by the post-merger remnant, in particular when compared to a case neglecting all neutrino interactions. Our nucleosynthesis results show that a solar-like distribution of r-process elements with mass numbers $A \gtrsim 90$ is produced, including a significant enrichment in Sr and a reduced production of actinides compared to simulations without inclusion of the nucleonic weak processes. The composition of the dynamically ejected matter as well as the corresponding rate of radioactive decay heating are found to be rather independent of the system mass asymmetry and the adopted equation of state. This approximate degeneracy in abundance pattern and heating rates can be favourable for extracting the ejecta properties from kilonova observations, at least if the dynamical component dominates the overall ejecta. Part II of this work will study the light curve produced by the dynamical ejecta of our four NS merger models.

Orbital mixing in few-layer graphene and non-Abelian Berry phase

In a magnetic field few-layer graphene supports, at the lowest Landau level, a multiplet of zero-mode levels nearly degenerate in orbitals as well as in spins and valleys. Those pseudo-zero-mode (PZM) levels are generally sensitive to interactions and external perturbations, and have a crossing among themselves or with other higher Landau levels when an external field is swept over a certain range. A close study is made of how such PZM levels evolve when they are gradually brought from empty to filled levels under many-body interactions. It is pointed out that the level spectra generally avoid a crossing via orbital level mixing and that orbital mixing is governed by a non-Abelian Berry phase that derives from an approximate degeneracy and interactions. A look is also taken into evolution/crossing of many-body ground states with increasing external bias in bilayer graphene.

Constraining ultra-light axions with galaxy cluster number counts

In this paper we investigate the potential of current and upcoming cosmological surveys to constrain the mass and abundance of ultra-light axion (ULA) cosmologies with galaxy cluster number counts. ULAs, sometimes also referred to as Fuzzy Dark Matter, are well-motivated in many theories beyond the Standard Model and could potentially solve the ΛCDM small-scale crisis. Galaxy cluster counts provide a robust probe of the formation of structures in the Universe. Their distribution in mass and redshift is strongly sensitive to the underlying linear matter perturbations. In this forecast paper we explore two scenarios, firstly an exclusion limit on axion mass given a no-axion model and secondly constraints on an axion model. With this we obtain lower limits on the ULA mass on the order of m a ≳ 10-24 eV. However, this result depends heavily on the mass of the smallest reliably observable clusters for a given survey. Cluster counts, like many other cosmological probes, display an approximate degeneracy in the ULA mass vs. abundance parameter space, which is dependent on the characteristics of the probe. These degeneracies are different for other cosmological probes. Hence galaxy cluster counts might provide a complementary window on the properties of ultra-light axions.

Partial equilibration of anti-Pfaffian edge modes at ν=5/2

The thermal Hall conductance $K$ of the fractional quantum Hall state at filling fraction $\nu=5/2$ has recently been measured to be $K=2.5 \pi^2k_B^2T/3h$ [M. Banerjee et al., Nature ${\bf 559}$, 205 (2018)]. The half-integer value of this result (in units of $\pi^2k_B^2T/3h$) provides strong evidence for the presence of a Majorana edge mode and a corresponding quantum Hall state hosting quasiparticles with non-Abelian statistics. Whether this measurement points to the realization of the PH-Pfaffian or the anti-Pfaffian state has been the subject of debate. Here we consider the implications of this measurement for anti-Pfaffian edge-state transport. We show that in the limit of a strong Coulomb interaction and an approximate spin degeneracy in the lowest Landau level, the anti-Pfaffian state admits low-temperature edge phases that are consistent with the Hall conductance measurements. These edge phases can exhibit fully-equilibrated electrical transport coexisting with partially-equilibrated heat transport over a range of temperatures. Through a study of the kinetic equations describing low-temperature electrical and heat transport of these edge states, we determine regimes of parameter space, controlling the interactions between the different edge modes, that agree with experiment.

Truncation of lattice fractional quantum Hall Hamiltonians derived from conformal field theory

Conformal field theory has recently been applied to derive few-body Hamiltonians whose ground states are lattice versions of fractional quantum Hall states. The exact lattice models involve interactions over long distances, which is difficult to realize in experiments. It seems, however, that such long-range interactions should not be necessary, as the correlations decay exponentially in the bulk. This poses the question, whether the Hamiltonians can be truncated to contain only local interactions without changing the physics of the ground state. Previous studies have in a couple of cases with particularly much symmetry obtained such local Hamiltonians by keeping only a few local terms and numerically optimizing the coefficients. Here, we investigate a different strategy to construct truncated Hamiltonians, which does not rely on optimization, and which can be applied independent of the choice of lattice. We test the approach on two models with bosonic Laughlin-like ground states with filling factor $1/2$ and $1/4$, respectively. We first investigate how the coupling strengths in the exact Hamiltonians depend on distance, and then we study the truncated models. For the case of $1/2$ filling, we find that the truncated model with truncation radius $\sqrt{2}$ lattice constants on the square lattice and $1$ lattice constant on the triangular lattice has an approximate twofold ground state degeneracy on the torus, and the overlap per site between these states and the states constructed from conformal field theory is higher than $0.99$ for the lattices considered. For the model at $1/4$ filling, our results give some hints that a truncation radius of $\sqrt{5}$ on the square lattice and $\sqrt{7}$ on the triangular lattice might be enough, but the finite size effects are too large to judge whether the topology is, indeed, present in the thermodynamic limit.

Neutrino Phenomenology of a High Scale Supersymmetry Model**Supported by the National Natural Science Foundation of China under Grant Nos. 11375248 and 11875306

CP violation in the lepton sector, and other aspects of neutrino physics, are studied within a high scale supersymmetry model. In addition to the sneutrino vacuum expectation values (VEVs), the heavy vector-like triplet also contributes to neutrino masses. Phases of the VEVs of relevant fields, complex couplings, and Zino mass are considered. The approximate degeneracy of neutrino masses and can be naturally understood. The neutrino masses are then normal ordered, ∼0.020 eV, 0.022 eV, and 0.054 eV. Large CP violation in neutrino oscillations is favored. The effective Majorana mass of the electron neutrino is about 0.02 eV.

Erratum: Approximate degeneracy of J=1 spatial correlators in high temperature QCD [Phys. Rev. D 96 , 094501 (2017)

Erratum: Approximate degeneracy of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>J</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> spatial correlators in high temperature QCD [Phys. Rev. D <b>96</b> , 094501 (2017)

Observation of approximate SU(2)CS and SU(2nf) symmetries in high temperature lattice QCD

We study spatial isovector J = 1 meson correlators in nf = 2 QCD with dynamical domain-wall fermions on 323 × 8 lattices at temperatures T = 220–380 MeV. We observe an approximate degeneracy of all considered correlators with increasing temperature. This approximate degeneracy suggests emergent SU(2)CS and SU(2nf) symmetries at high temperatures, that mix left- and right-handed quarks. Since these symmetries are symmetries of the chromo-electric interaction in QCD we conclude that at 2Tc temperature the elementary objects are quarks with a definite chirality connected by the chromo-electric field.

Pseudo Dirac nodal sphere semimetal

Topological semimetals (TSMs) in which conduction and valence bands cross at zero-dimensional (0D) Dirac nodal points (DNPs) or 1D Dirac nodal lines (DNLs), in 3D momentum space, have recently drawn much attention due to their exotic electronic properties. Here, we generalize the TSM state further to a higher-dimensional Dirac nodal sphere (DNS) or pseudo DNS (PDNS) state, with the band crossings forming a 2D closed or approximate sphere at the Fermi level. This TSM state can exhibit unique electronic properties, making DNS/PDNS a type of fermion beyond the DNP/DNL paradigm. In realistic crystals, we demonstrate two possible types of PDNS states underlain by different crystalline symmetries, which are characterized with a spherical backbone consisting of multiple DNLs and approximate band degeneracy in between the DNLs. We identify all the possible band crossings with pairs of 1D irreducible representations to form the PDNS states in 32 point groups. Importantly, we discover that strained $M{\mathrm{H}}_{3}$ ($M=\text{Y}$, Ho, Tb, Nd) and ${\mathrm{Si}}_{3}{\mathrm{N}}_{2}$ are material candidates to realize these two types of PDNS states, respectively. As a high-symmetry-required state, the PDNS semimetal can be regarded as the ``parent phase'' for other topological gapped and gapless states.

Degeneracy of vector-channel spatial correlators in high temperature QCD

We study spatial isovector meson correlators in Nf = 2 QCD with dynamical domain-wall fermions on 323 × 8 lattices at temperatures up to 380 MeV with various quark masses. We measure the correlators of spin-one isovector operators including vector, axial-vector, tensor and axial-tensor. At temperatures above Tc we observe an approximate degeneracy of the correlators in these channels, which is unexpected because some of them are not related under SU(2)L×SU(2)R nor U(1)A symmetries. The observed approximate degeneracy suggests emergent SU(2)CS (chiral-spin) and SU(4) symmetries at high T.

Approximate degeneracy of J=1 spatial correlators in high temperature QCD

We study spatial isovector meson correlators in $N_f=2$ QCD with dynamical domain-wall fermions on $32^3\times 8$ lattices at temperatures $T=220-380$ MeV. We measure the correlators of spin-one ($J=1$) operators including vector, axial-vector, tensor and axial-tensor. Restoration of chiral $U(1)_A$ and $SU(2)_L \times SU(2)_R$ symmetries of QCD implies degeneracies in vector--axial-vector ($SU(2)_L \times SU(2)_R$) and tensor--axial-tensor ($U(1)_A$) pairs, which are indeed observed at temperatures above $T_c$. Moreover, we observe an approximate degeneracy of all $J=1$ correlators with increasing temperature. This approximate degeneracy suggests emergent $SU(2)_{CS}$ and $SU(4)$ symmeries at high temperatures, that mix left- and right-handed quarks.

Topological quantum error correction in the Kitaev honeycomb model

The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of topological quantum codes that are typically studied, but its exact solubility makes it more amenable to analysis of effects arising in this noncommutative setting than a generic topologically ordered Hamiltonian. Here we study quantum error correction in the honeycomb model using both analytic and numerical techniques. We first prove explicit exponential bounds on the approximate degeneracy, local indistinguishability, and correctability of the code space. These bounds are tighter than can be achieved using known general properties of topological phases. Our proofs are specialized to the honeycomb model, but some of the methods may nonetheless be of broader interest. Following this, we numerically study noise caused by thermalization processes in the perturbative regime close to the toric code renormalization group fixed point. The appearance of non-topological excitations in this setting has no significant effect on the error correction properties of the honeycomb model in the regimes we study. Although the behavior of this model is found to be qualitatively similar to that of the standard toric code in most regimes, we find numerical evidence of an interesting effect in the low-temperature, finite-size regime where a preferred lattice direction emerges and anyon diffusion is geometrically constrained. We expect this effect to yield an improvement in the scaling of the lifetime with system size as compared to the standard toric code.