Spectral asymptotics for the Schrödinger operator with a non-decaying potential

We study Schrödinger operators H ( h ) = − h 2 Δ + V ( x ) acting in L 2 ( R n ) for non-decaying potentials V. We give a full asymptotic expansion of the spectral shift function for a pair of such operators in the high energy limit. In particular for asymptotically homogeneous potentials W at infinity of degree zero, we also study the semiclassical asymptotics to give a Weyl formula of the spectral shift function above the threshold max W and Mourre estimates in the range of W except at its critical values.

A Stellar Constraint on Eddington-inspired Born–Infeld Gravity from Cataclysmic Variable Binaries

Eddington-inspired Born–Infeld gravity is an important modification of Einstein’s general relativity, which can give rise to nonsingular cosmologies at the classical level, and avoid the end-stage singularity in a gravitational collapse process. In the Newtonian limit, this theory gives rise to a modified Poisson’s equation, as a consequence of which stellar observables acquire model dependent corrections, compared to the ones computed in the low energy limit of general relativity. This can in turn be used to establish astrophysical constraints on the theory. Here, we obtain such a constraint using observational data from cataclysmic variable binaries. In particular, we consider the tidal disruption limit of the secondary star by a white dwarf primary. The Roche lobe filling condition of this secondary star is used to compute stellar observables in the modified gravity theory in a numerical scheme. These are then contrasted with the values obtained by using available data on these objects, via a Monte Carlo error progression method. This way, we are able to constrain the theory within the 5σ confidence level.

Dual Superconductor Model of Confinement: Quantum-String Representation of the 4D Yang–Mills Theory on a Torus and the Correlation Length away from the London Limit

This paper is devoted to the dual superconductor model of confinement in the 4D Yang–Mills theory. In the first part, we consider the latter theory compactified on a torus, and use the dual superconductor model in order to obtain the Polchinski–Strominger term in the string representation of a Wilson loop. For a certain realistic critical value of the product of circumferences of the compactification circles, which is expressed in terms of the gluon condensate and the vacuum correlation length, the coupling of the Polchinski–Strominger term turns out to be such that the string conformal anomaly cancels out, making the string representation fully quantum. In the second part, we use the analogy between the London limit of the dual superconductor and the low-energy limit of the 4D compact QED, to obtain the partition function of the dual superconductor model away from the London limit. There, we find a decrease of the vacuum correlation length, and derive the corresponding potential of monopole currents.

Asymmetric Lineshapes of Efimov Resonances in Mass-Imbalanced Ultracold Gases

The resonant profile of the rate coefficient for three-body recombination into a shallow dimer is investigated for mass-imbalanced systems. In the low-energy limit, three atoms collide with zero-range interactions, in a regime where the scattering lengths of the heavy–heavy and the heavy–light subsystems are positive and negative, respectively. For this physical system, the adiabatic hyperspherical representation is combined with a fully semi-classical method and we show that the shallow dimer recombination spectra display an asymmetric lineshape that originates from the coexistence of Efimov resonances with Stückelberg interference minima. These asymmetric lineshapes are quantified utilizing the Fano profile formula. In particular, a closed-form expression is derived that describes the width of the corresponding Efimov resonances and the Fano lineshape asymmetry parameter q. The profile of Efimov resonances exhibits a q-reversal effect as the inter- and intra-species scattering lengths vary. In the case of a diverging asymmetry parameter, i.e., |q|→∞, we show that the Efimov resonances possess zero width and are fully decoupled from the three-body and atom–dimer continua, and the corresponding Efimov metastable states behave as bound levels.

Unitarity violation and the geometry of Higgs EFTs

We derive the scale of unitarity violation from the geometry of Effective Field Theory (EFT) extensions of the Standard Model Higgs sector. The high-energy behavior of amplitudes with more than four scalar legs depends on derivatives of geometric invariants with respect to the physical Higgs field h, such that higher-point amplitudes begin to reconstruct the scalar manifold away from our vacuum. In theories whose low-energy limit can be described by the Higgs EFT (HEFT) but not the Standard Model EFT (SMEFT), non-analyticities in the vicinity of our vacuum limit the radius of convergence of geometric invariants, leading to unitarity violation at energies below 4πv. Our results unify approaches to the HEFT/SMEFT dichotomy based on unitarity, analyticity, and geometry, and more broadly illustrate the sense in which observables probe the geometry of an EFT. Along the way, we provide novel basis-independent results for Goldstone/Higgs boson scattering amplitudes expressed in terms of geometric covariant quantities.

Plasma-catalytic NOx production in a three-level coupled rotating electrodes air plasma combined with nano-sized TiO2

A novel three-level coupled rotating electrodes air plasma with nano-sized TiO2 photocatalysts is developed for plasma-catalytic NOx production. The effects of plasma catalysis on NOx production with different air flow rates, different N2 fractions and different humidity levels are evaluated. Final results show that the exceptionally synergistic effect between TiO2 and three-level coupled rotating electrodes air plasma significantly increases the NOx concentration by 68.32% (from 4952 to 8335 ppm) and reduces the energy cost by 40.55% (from 2.91 to 1.73 MJ mol-1) at an air flow rate of 12 l min-1 and relative humidity level of 12%, which beats the ideal thermodynamic energy limit ~2.5MJ/mol for the thermal gas-phase process. A possible mechanism for enhanced NOx production with TiO2 is discussed: Highly energetic electrons in plasma contribute to the formations of the electron–hole pairs and oxygen vacancy (Vo) on the TiO2 catalyst surface, it may facilitate the dissociative adsorption of O2 molecules to form superoxide radical groups (like O2.-), and H2O molecules to form surface hydroxyl groups (like OH.), and thus, improving energy efficiency.