Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials

We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. Such transitions have been extensively studied for magnetic fields corresponding to Abelian gauges; they occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields, which can be realized with atoms with two pairs of degenerate internal states. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum and the minimum energy viewed as a function of momentum exhibits a step structure. Other key characteristics of the non-Abelian case include the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta.Comment: 4 pages, 4 figures, see http://physics.gmu.edu/~isatija/recentpub.htm for high resolution figure

Pion Photoproduction Amplitude Relations in the 1/N_c Expansion

We derive expressions for pion photoproduction amplitudes in the 1/N_c expansion of QCD, and obtain linear relations directly from this expansion that relate electromagnetic multipole amplitudes at all energies. The leading-order relations in 1/N_c compare favorably with available data, while the next-to-leading order relations seem to provide only a small improvement. However, when resonance parameters are compared directly, the agreement at O(1/N_c) or O(1/N_c^2) is impressive.Comment: 19 pages, ReVTeX, 50 eps files combine into 5 compound figure

HADRONIC INTERACTIONS IN LARGE N_c QCD: STUDIES OF EXCITED BARYON DECAYS AND SCATTERING RELATIONS

Decays and scattering events are two of the principal ways to learn about particle physics. Decays, in which a particle spontaneously disintegrates and we examine the debris, are quantified by a decay width. The decay of a resonance state provides information about the structure of the state and the interaction between its components. In particular, we can learn about the dynamics of quarks and gluons by studying the decay of hadrons. Scattering, in which particles are directed towards each other and interact, are quantified by partial-wave amplitudes. These amplitudes give us information about the interaction between the scattered particles. In principle, all of hadronic physics follows from quantum chromodynamics (QCD), which describes the interactions of quarks and gluons. However, the techniques of perturbation theory are not applicable to QCD at low energy because the strong coupling constant (the natural choice for the expansion parameter) is large at the energy scale of hadronic physics. A powerful model-independent method is the 1/N_c expansion in which the number of quark color degrees of freedom (N_c) is treated as a large number. This thesis presents the application of the 1/N_c expansion to the calculation of physical observables for excited baryons, pion-nucleon scattering, and pion photoproduction. The framework of the contracted SU(4) group that emerges in large N_c QCD is applied to the study of excited baryon decays. The N_c power scaling of the excited baryon's decay width depends on the symmetry of its spin-flavor wavefunction. The scaling with N_c for different symmetries is discussed in the context of a quark-shell model that permits mixing of different symmetry types. The subtle issues concerning the legitimacy of applying the contracted SU(4) group theory to excited baryons are discussed. The contracted SU(4) spin-flavor symmetry severely restricts the angular momentum and isospin dependence of partial-wave amplitudes. The consequences of this restriction on pion-nucleon scattering and pion photoproduction are discussed. In particular, model-independent linear relations among different hadronic scattering amplitudes holding to leading order in 1/N_c are obtained and compared with experimental data. The group-theoretic structure of large N_c QCD allows for a systematic expansion of scattering amplitudes in powers of 1/N_c which leads to model-independent relations holding to next-to-leading order in 1/N_c. These relations are derived and shown to compare more favorably with experiments to the extent expected for the 1/N_c expansion

Pion-Nucleon Scattering Relations at Next-to-Leading Order in 1/N_c

We obtain relations between partial-wave amplitudes for pi-N-->pi-N and pi-N-->pi-Delta directly from large N_c QCD. While linear relations among certain amplitudes holding at leading order (LO) in 1/N_c were derived in the context of chiral soliton models two decades ago, the present work employs a fully model-independent framework based on consistency with the large N_c expansion. At LO we reproduce the soliton model results; however, this method allows for systematic corrections. At next-to-leading order (NLO), most relations require additional unknown functions beyond those appearing at leading order (LO) and thus have little additional predictive power. However, three NLO relations for the pi-N-->pi-Delta reaction are independent of unknown functions and make predictions accurate at this order. The amplitudes relevant to two of these relations were previously extracted from experiment. These relations describe experiment dramatically better than their LO counterparts.Comment: 8 pages, 2 figures; references adde

Two-Dimensional Electron Gas with Cold Atoms in Non-Abelian Gauge Potentials

Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we explore the richness and complexity of non-interacting two-dimensional electron gases (2DEGs) in a lattice, subjected to such fields. In the continuum limit, a non-Abelian system characterized by a two-component "magnetic flux" describes a harmonic oscillator existing in two different charge states (mimicking a particle-hole pair) where the coupling between the states is determined by the non-Abelian parameter, namely the difference between the two components of the "magnetic flux." A key feature of the non-Abelian system is a splitting of the Landau energy levels, which broaden into bands, as the spectrum depends explicitly on the transverse momentum. These Landau bands result in a coarse-grained "moth," a continuum version of the generalized Hofstadter butterfly. Furthermore, the bands overlap, leading to effective relativistic effects. Importantly, similar features also characterize the corresponding two-dimensional lattice problem when at least one of the components of the magnetic flux is an irrational number. The lattice system with two competing "magnetic fluxes" penetrating the unit cell provides a rich environment in which to study localization phenomena. Some unique aspects of the transport properties of the non-Abelian system are the possibility of inducing localization by varying the quasimomentum, and the absence of localization of certain zero-energy states exhibiting a linear energy-momentum relation. Furthermore, non-Abelian systems provide an interesting localization scenario where the localization transition is accompanied by a transition from relativistic to non-relativistic theory.Comment: A version with higher resolution figures is available at http://physics.gmu.edu/~isatija/NALFinal.pd

Nucleon-Nucleon Scattering under Spin-Isospin Reversal in Large-N_c QCD

The spin-flavor structure of certain nucleon-nucleon scattering observables derived from the large N_c limit of QCD in the kinematical regime where time-dependent mean-field theory is valid is discussed. In previous work, this regime was taken to be where the external momentum was of order N_c which precluded the study of differential cross sections in elastic scattering. Here it is shown that the regime extends down to order N_c^{1/2} which includes the higher end of the elastic regime. The prediction is that in the large N_c limit, observables describable via mean-field theory are unchanged when the spin and isospin of either nucleon are both flipped. This prediction is tested for proton-proton and neutron-proton elastic scattering data and found to fail badly. We argue that this failure can be traced to a lack of a clear separation of scales between momentum of order N_c^{1/2} and N_c^1 when N_c is as small as three. The situation is compounded by an anomalously low particle production threshold due to approximate chiral symmetry.Comment: 5 pages, 1 figur

Excited Baryon Decay Widths in Large N_c QCD

We study excited baryon decay widths in large N_c QCD. It was suggested previously that some spin-flavor mixed-symmetric baryon states have strong couplings of O(N_c^{-1/2}) to nucleons [implying narrow widths of O(1/N_c)], as opposed to the generic expectation based on Witten's counting rules of an O(N_c^0) coupling. The calculation obtaining these narrow widths was performed in the context of a simple quark-shell model. This paper addresses the question of whether the existence of such narrow states is a general property of large N_c QCD. We show that a general large N_c QCD analysis does not predict such narrow states; rather they are a consequence of the extreme simplicity of the quark model.Comment: 9 page

Phase 2a randomised controlled feasibility trial of a new ‘balanced binocular viewing’ treatment for unilateral amblyopia in children age 3–8 years : trial protocol

Introduction Treatments for amblyopia, the most common vision deficit in children, often have suboptimal results. Occlusion/atropine blurring are fraught with poor adherence, regression and recurrence. These interventions target only the amblyopic eye, failing to address imbalances of cortical input from the two eyes (‘suppression’). Dichoptic treatments manipulate binocular visual experience to rebalance input. Poor adherence in early trials of dichoptic therapies inspired our development of balanced binocular viewing (BBV), using movies as child-friendly viewable content. Small observational studies indicate good adherence and efficacy. A feasibility trial is needed to further test safety and gather information to design a full trial. Methods/analysis We will carry out an observer-masked parallel-group phase 2a feasibility randomised controlled trial at two sites, randomising 44 children aged 3–8 years with unilateral amblyopia to either BBV or standard occlusion/atropine blurring, with 1:1 allocation ratio. We will assess visual function at baseline, 8 and 16 weeks. The primary outcome is intervention safety at 16 weeks, measured as change in interocular suppression, considered to precede the onset of potential diplopia. Secondary outcomes include safety at other time points, eligibility, recruitment/retention rates, adherence, clinical outcomes. We will summarise baseline characteristics for each group and assess the treatment effect using analysis of covariance. We will compare continuous clinical secondary endpoints between arms using linear mixed effect models, and report feasibility endpoints using descriptive statistics. Ethics/dissemination This trial has been approved by the London-Brighton & Sussex Research Ethics Committee (18/LO/1204), National Health Service Health Research Authority and Medicines and Healthcare products Regulatory Agency. A lay advisory group will be involved with advising on and disseminating the results to non-professional audiences, including on websites of funder/participating institutions and inputting on healthcare professional audience children would like us to reach. Reporting to clinicians and scientists will be via internal and external meetings/conferences and peer-reviewed journals

Feasibility of a new ‘balanced binocular viewing’ treatment for unilateral amblyopia in children aged 3–8 years (BALANCE):results of a phase 2a randomised controlled feasibility trial

Objectives This study aimed to evaluate the safety of dichoptic balanced binocular viewing (BBV) for amblyopia in children, plus feasibility, adherence, acceptability, trial methodology and clinical measures of visual function. Design We carried out an observer-masked parallel-group phase 2a feasibility randomised controlled trial. Setting Two study sites, a secondary/tertiary and a community site. Participants We enrolled 32 children aged 3–8 years with unilateral amblyopia who had completed optical adaptation where indicated. 20 children attended the 16-week exit visit (retention 63%). Interventions Children were randomised to BBV (movies customised to interocular acuity difference at baseline) for 1 hour a day (active intervention) or standard management as per parental choice (part-time occlusion or atropine blurring, control). All interventions were used at home, daily for 16 weeks. Primary outcome measure ‘VacMan suppression test’ of interocular balance at 16 weeks from randomisation. Secondary outcome measures: feasibility outcomes (recruitment and retention ratios, adherence with the allocated intervention); safety outcomes at other time points (changes in prevalence of diplopia, manifest strabismus, suppression/interocular balance on a range of tests); efficacy outcomes (clinical measures of visual function, such as best-corrected visual acuity, BCVA). Outcome measures were identical to those planned in the protocol. Results Primary outcome: At baseline, values for the interocular balance point were higher (indicating greater suppression of the amblyopic eye) in the occlusion group than in the BBV group. These values shifted downwards on average for the occlusion group, significantly decreasing from baseline to week 16 (t8=4.49, p=0.002). Balance values did not change between baseline and week 16 for the BBV group (t9=−0.82, p=0.435). At 16 weeks, there was no statistical difference in interocular balance/suppression change over time between the two arms. The difference at follow-up between the arms, adjusted for baseline, was −0.02 (95% CI −0.28 to 0.23, p=0.87). Feasibility: We prescreened 144 records of potentially eligible children. Between 28 October 2019 and 31 July 2021, including an interruption due to the COVID-19 pandemic, 32 children were screened and randomised (recruitment rate 22%), 16 to BBV and 16 to standard treatment. 20 children attended the 16-week exit visit (retention 63%). Mean adherence with BBV as proportion of viewing time prescribed was 56.1% (SD36) at 8 and 57.9% (SD 30.2) at 16 weeks. Mean adherence with prescribed occlusion time was 90.1% (SD 19.7) at 8 and 59.2% (SD 24.8) at 16 weeks. Secondary safety/efficacy outcomes One child in the BBV arm reported transient double vision, which resolved; two reported headaches, which led to withdrawal. BCVA improved from mean 0.47 (SD0.18) logMAR at randomisation to 0.26 (0.14) with standard treatment, and from 0.55 (0.28) to 0.32 (0.26) with BBV. Outcomes at 16 weeks did not differ between treatments. Participant experience Families were generally positive about BBV, but families found both patching and BBV difficult to integrate into family routines. Conclusions Recruitment rates indicate that a future phase 3 trial will require multiple sites or a longer enrolment period. Retention and adherence rates were lower than anticipated, which will influence future study designs. Dichoptic treatment may be equal to occlusion treatment in safety and efficacy; headaches may lead to discontinuation. Integration into family routines may constitute a barrier to implementation

Adaptive Sampling of Information in Perceptual Decision-Making

In many perceptual and cognitive decision-making problems, humans sample multiple noisy information sources serially, and integrate the sampled information to make an overall decision. We derive the optimal decision procedure for two-alternative choice tasks in which the different options are sampled one at a time, sources vary in the quality of the information they provide, and the available time is fixed. To maximize accuracy, the optimal observer allocates time to sampling different information sources in proportion to their noise levels. We tested human observers in a corresponding perceptual decision-making task. Observers compared the direction of two random dot motion patterns that were triggered only when fixated. Observers allocated more time to the noisier pattern, in a manner that correlated with their sensory uncertainty about the direction of the patterns. There were several differences between the optimal observer predictions and human behaviour. These differences point to a number of other factors, beyond the quality of the currently available sources of information, that influences the sampling strategy