The coupled SYK model at finite temperature

Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS₂ dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS₂ geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function

Adsorption behavior of arsenic and antimony onto ferrihydrite under competitive conditions

Arsenic (As) and antimony (Sb) are naturally toxic elements widely distributed in a multiple of fields of the environment. They are generally considered to share numerous similarities in chemical properties, adsorption and redox behavior, toxicity and mobility. Elevated concentrations of As and Sb are released into the environment, but very little is known about their simultaneous adsorption behavior in the system containing more than one redox species. First, the competitive interactions between arsenite (As(III)) and arsenate (As(V)) onto ferrihydrite were investigated as a function of initial pH, adsorbent dosage, concentration of coexisting ligands and the order of addition. It was further studied by applying applicable adsorption isotherms and kinetic models. Second, the adsorption and oxidation of Sb(III) at varying Fe/Sb ratios and pH values was evaluated. The simultaneous adsorption of Sb(III) and Sb(V) was also studied. Finally, the simultaneous adsorption behavior of As(III), As(V), Sb(III) and Sb(V) was investigated in multi-component systems. The pH generally had a great impact on As adsorption under both single ion and competitive conditions. However, the presence of As(V) in solution was the controlling factor on As(III) adsorption and As(III) more or less outcompeted As(V) across the pH scale from 4 to 10. As(III) and As(V) was adsorbed almost equally up to a pH of 5 at an adsorbent dosage of 0.5 g/L and up to a pH of 6 at an adsorbent dosage of 1 g/L in binary systems. This was contrary to the theoretical prediction that As(V) should adsorb stronger than As(III) at pH values below the point of zero charge (pzc) of ferrihydrite of about 7 to 8. At low pH As(V) impedes the adsorption of As(III), but to a lesser degree than As(III) impedes As(V) adsorption at a pH above 6. The order of addition of the two As reox species also had significant effects on their competitive adsorption behavior. Both the adsorption of As(III) and As(V) under single and competitive conditions can be successfully described by the Freundlich isotherm model. The adsorption affinity onto ferrihydrite was ordered as follows: As(III)-single > As(III)-binary > As(V)-single > As(V)-binary. The adsorption kinetics for both As(III) and As(V) comply with the pseudo-second order kinetics model. Moreover, the isotherm and kinetic competitive studies showed that As(V) significantly impeded the adsorption of As(III), whereas the presence of As(III) had an insignificant effect on the adsorption of As(V) at pH 5. The FTIR spectra provided the evidence that both As(III) and As(V) could be adsorbed onto ferrihydrite through inner-sphere surface complexes by the formation of Fe-O-As bonds. The simultaneous adsorption and oxidation of Sb(III) was confirmed by the appearance of Sb(V) in the solution at varying Fe/Sb ratios (500, 100 and 8) and varying pH values (3.8, 7 and 9). This newly formed Sb(V) was subsequently removed from solution at a Fe/Sb ratio of 500 or at a pH of 3.8. However, Sb(V) were almost remained alone in the liquid phase at the end of experiments at lower Fe/Sb ratios and higher pH, indicating that competition could take place between the newly formed Sb(V) and Sb(III), and Sb(III) outcompeted Sb(V). This was independently confirmed by simultaneous adsorption experiments of Sb(III) and Sb(V) in binary systems. Under such conditions, the presence of Sb(V) had no influence on the adsorption of Sb(III) while Sb(V) adsorption was significantly inhibited by Sb(III) at a wide pH range (4 to 10). The simultaneous adsorption behavior of As(III), As(V), Sb(III) and Sb(V) were evaluated in multi-component (binary, ternary, quaternary) systems. The presence of Sb(III) had a stronger inhibitory effect on As(III) adsorption than Sb(V), and the presence of As(V) had a stronger inhibitory effect on Sb(V) adsorption than As(III). The adsorption behavior of the four redox species under quaternary conditions was pH dependent. Sb(III) always showed the strongest affinity on ferrihydrite. The Freundlich model provided a good fit for the simultaneous adsorption data under quaternary conditions. The major anions of NO3â , PO43- and SO42- did not compete for the adsorption of As(III) and Sb(III) in ternary systems. The presence of PO43- had a negative influence on the adsorption of As(V) and Sb(V) in ternary systems, while both NO3- and SO42- had no distinct effect on the adsorption of As(V) and Sb(V). This study indicates that Sb(III) and As(V) could be strongly adsorbed on ferrihydrite mainly by inner-sphere complexes, while a combination of outer- and inner-sphere complexes could be involved for the adsorption of Sb(V) and As(III)

The coupled SYK model at finite temperature

Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS₂ dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS₂ geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function

Hydrogenation and Hydro-Carbonation and Etching of Single-Walled Carbon Nanotubes

We present a systematic experimental investigation of the reactions between hydrogen plasma and single-walled carbon nanotubes (SWNTs) at various temperatures. Microscopy, infrared (IR) and Raman spectroscopy and electrical transport measurements are carried out to investigate the properties of SWNTs after hydrogenation. Structural deformations, drastically reduced electrical conductance and increased semiconducting nature of SWNTs upon sidewall hydrogenation are observed. These changes are reversible upon thermal annealing at 500C via dehydrogenation. Harsh plasma or high temperature reactions lead to etching of nanotube likely via hydro-carbonation. Smaller SWNTs are markedly less stable against hydro-carbonation than larger tubes. The results are fundamental and may have implications to basic and practical applications including hydrogen storage, sensing, band-gap engineering for novel electronics and new methods of manipulation, functionalization and etching of nanotubes.Comment: 3 pages, 4 figure