In the seminal work (Weinstein 1999
Physical systems with non-trivial topological order find direct applications in metrology (Klitzing
- NSF-PAR ID:
- 10307589
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- New Journal of Physics
- Volume:
- 21
- Issue:
- 5
- ISSN:
- 1367-2630
- Page Range / eLocation ID:
- Article No. 053021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
Abstract Nonlinearity 12 673), Weinstein considered the question of the ground states for discrete Schrödinger equations with power law nonlinearities, posed on . More specifically, he constructed the so-called normalised waves, by minimising the Hamiltonian functional, for fixed powerP (i.e.l 2mass). This type of variational method allows one to claim, in a straightforward manner, set stability for such waves. In this work, we revisit these questions and build upon Weinstein’s work, as well as the innovative variational methods introduced for this problem in (Laedkeet al 1994Phys. Rev. Lett. 73 1055 and Laedkeet al 1996Phys. Rev. E54 4299) in several directions. First, for the normalised waves, we show that they are in fact spectrally stable as solutions of the corresponding discrete nonlinear Schroedinger equation (NLS) evolution equation. Next, we construct the so-called homogeneous waves, by using a different constrained optimisation problem. Importantly, this construction works for all values of the parameters, e.g.l 2supercritical problems. We establish a rigorous criterion for stability, which decides the stability on the homogeneous waves, based on the classical Grillakis–Shatah–Strauss/Vakhitov–Kolokolov (GSS/VK) quantity . In addition, we provide some symmetry results for the solitons. Finally, we complement our results with numerical computations, which showcase the full agreement between the conclusion from the GSS/VK criterion vis-á-vis with the linearised problem. In particular, one observes that it is possible for the stability of the wave to change as the spectral parameterω varies, in contrast with the corresponding continuous NLS model. -
Abstract We revisit the Haake–Lewenstein–Wilkens approach to Edwards–Anderson (EA) model of Ising spin glass (SG) (Haake
et al 1985Phys. Rev. Lett. 55 2606). This approach consists in evaluation and analysis of the probability distribution of configurations of two replicas of the system, averaged over quenched disorder. This probability distribution generates squares of thermal copies of spin variables from the two copies of the systems, averaged over disorder, that is the terms that enter the standard definition of the original EA order parameter, . We use saddle point/steepest descent (SPSD) method to calculate the average of the Gaussian disorder in higher dimensions. This approximate result suggest that at in 3D and 4D. The case of 2D seems to be a little more subtle, since in the present approach energy increase for a domain wall competes with boundary/edge effects more strongly in 2D; still our approach predicts SG order at sufficiently low temperature. We speculate, how these predictions confirm/contradict widely spread opinions that: (i) There exist only one (up to the spin flip) ground state in EA model in 2D, 3D and 4D; (ii) there is (no) SG transition in 3D and 4D (2D). This paper is dedicated to the memories of Fritz Haake and Marek Cieplak. -
Abstract We present a Keck/MOSFIRE rest-optical composite spectrum of 16 typical gravitationally lensed star-forming dwarf galaxies at 1.7 ≲
z ≲ 2.6 (z mean= 2.30), all chosen independent of emission-line strength. These galaxies have a median stellar mass of and a median star formation rate of . We measure the faint electron-temperature-sensitive [Oiii ]λ 4363 emission line at 2.5σ (4.1σ ) significance when considering a bootstrapped (statistical-only) uncertainty spectrum. This yields a direct-method oxygen abundance of ( ). We investigate the applicability at highz of locally calibrated oxygen-based strong-line metallicity relations, finding that the local reference calibrations of Bian et al. best reproduce (≲0.12 dex) our composite metallicity at fixed strong-line ratio. At fixedM *, our composite is well represented by thez ∼ 2.3 direct-method stellar mass—gas-phase metallicity relation (MZR) of Sanders et al. When comparing to predicted MZRs from the IllustrisTNG and FIRE simulations, having recalculated our stellar masses with more realistic nonparametric star formation histories , we find excellent agreement with the FIRE MZR. Our composite is consistent with no metallicity evolution, at fixedM *and SFR, of the locally defined fundamental metallicity relation. We measure the doublet ratio [Oii ]λ 3729/[Oii ]λ 3726 = 1.56 ± 0.32 (1.51 ± 0.12) and a corresponding electron density of ( ) when considering the bootstrapped (statistical-only) error spectrum. This result suggests that lower-mass galaxies have lower densities than higher-mass galaxies atz ∼ 2. -
Abstract We present the
z ≈ 6 type-1 quasar luminosity function (QLF), based on the Pan-STARRS1 (PS1) quasar survey. The PS1 sample includes 125 quasars atz ≈ 5.7–6.2, with −28 ≲M 1450≲ −25. With the addition of 48 fainter quasars from the SHELLQs survey, we evaluate thez ≈ 6 QLF over −28 ≲M 1450≲ −22. Adopting a double power law with an exponential evolution of the quasar density (Φ(z ) ∝ 10k (z −6);k = −0.7), we use a maximum likelihood method to model our data. We find a break magnitude of , a faint-end slope of , and a steep bright-end slope of . Based on our new QLF model, we determine the quasar comoving spatial density atz ≈ 6 to be . In comparison with the literature, we find the quasar density to evolve with a constant value ofk ≈ −0.7, fromz ≈ 7 toz ≈ 4. Additionally, we derive an ionizing emissivity of , based on the QLF measurement. Given standard assumptions, and the recent measurement of the mean free path by Becker et al. atz ≈ 6, we calculate an Hi photoionizing rate of ΓH I(z = 6) ≈ 6 × 10−16s−1, strongly disfavoring a dominant role of quasars in hydrogen reionization. -
Abstract We present measurements of the rest-frame UV spectral slope,
β , for a sample of 36 faint star-forming galaxies atz ∼ 9–16 discovered in one of the deepest JWST NIRCam surveys to date, the Next Generation Deep Extragalactic Exploratory Public Survey. We use robust photometric measurements for UV-faint galaxies (down toM UV∼ −16), originally published in Leung et al., and measure values of the UV spectral slope via photometric power-law fitting to both the observed photometry and stellar population models obtained through spectral energy distribution (SED) fitting withBagpipes . We obtain a median and 68% confidence interval forβ from photometric power-law fitting of and from SED fitting, for the full sample. We show that when only two to three photometric detections are available, SED fitting has a lower scatter and reduced biases than photometric power-law fitting. We quantify this bias and find that after correction the median . We measure physical properties for our galaxies withBagpipes and find that our faint ( ) sample is low in mass ( ), fairly dust-poor ( mag), and modestly young ( yr) with a median star formation rate of . We find no strong evidence for ultrablue UV spectral slopes (β ∼ −3) within our sample, as would be expected for exotically metal-poor (Z /Z ⊙< 10−3) stellar populations with very high Lyman continuum escape fractions. Our observations are consistent with model predictions that galaxies of these stellar masses atz ∼ 9–16 should have only modestly low metallicities (Z /Z ⊙∼ 0.1–0.2).