Anomalous spin-dependent behaviour of one-dimensional subbands

We report a new electron interaction effect in GaAs/AlGaAs quantum wires. Using DC-bias spectroscopy, we show that large and abrupt changes occur to the energies of spin-down (lower energy) states as they populate. The effect is not observed for spin-up energy states. At B=0, interactions have a pronounced effect, in the form of the well-known 0.7 Structure. However, our new results show that interactions strongly affect the energy spectrum at all magnetic fields, from 0 to 16T, not just in the vicinity of the 0.7 Structure.Comment: 4 pages, 2 figure

Energy-level pinning and the 0.7 spin state in one dimension: GaAs quantum wires studied using finite-bias spectroscopy

We study the effects of electron-electron interactions on the energy levels of GaAs quantum wires (QWs) using finite-bias spectroscopy. We probe the energy spectrum at zero magnetic field, and at crossings of opposite-spin-levels in high in-plane magnetic field B. Our results constitute direct evidence that spin-up (higher energy) levels pin to the chemical potential as they populate. We also show that spin-up and spin-down levels abruptly rearrange at the crossing in a manner resembling the magnetic phase transitions predicted to occur at crossings of Landau levels. This rearranging and pinning of subbands provides a phenomenological explanation for the 0.7 structure, a one-dimensional (1D) nanomagnetic state, and its high-B variants.Comment: 6 pages, 4 figure

Small gaps between products of two primes

Let $q_n$ denote the $n^{th}$ number that is a product of exactly two distinct primes. We prove that $$\liminf_{n\to \infty} (q_{n+1}-q_n) \le 6.$$ This sharpens an earlier result of the authors (arXivMath NT/0506067), which had 26 in place of 6. More generally, we prove that if $\nu$ is any positive integer, then $$\liminf_{n\to \infty} (q_{n+\nu}-q_n) \le C(\nu) = \nu e^{\nu-\gamma} (1+o(1)).$$ We also prove several other results on the representation of numbers with exactly two prime factors by linear forms.Comment: 11N25 (primary) 11N36 (secondary

Dynamical preparation of EPR entanglement in two-well Bose-Einstein condensates

We propose to generate Einstein-Podolsky-Rosen (EPR) entanglement between groups of atoms in a two-well Bose-Einstein condensate using a dynamical process similar to that employed in quantum optics. The local nonlinear S-wave scattering interaction has the effect of creating a spin squeezing at each well, while the tunneling, analogous to a beam splitter in optics, introduces an interference between these fields that results in an inter-well entanglement. We consider two internal modes at each well, so that the entanglement can be detected by measuring a reduction in the variances of the sums of local Schwinger spin observables. As is typical of continuous variable (CV) entanglement, the entanglement is predicted to increase with atom number, and becomes sufficiently strong at higher numbers of atoms that the EPR paradox and steering non-locality can be realized. The entanglement is predicted using an analytical approach and, for larger atom numbers, stochastic simulations based on truncated Wigner function. We find generally that strong tunnelling is favourable, and that entanglement persists and is even enhanced in the presence of realistic nonlinear losses.Comment: 15 pages, 19 figure

Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: direct numerical simulations and Lagrangian averaged modeling

We present direct numerical simulations and Lagrangian averaged (also known as alpha-model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha-model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations. The alpha-model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed.Comment: Finite size box effects have been taken into account in the definition of the partition function. This has resulted in a more clear scaling in all figures. Several points are clarified in the tex

Power spectra of velocities and magnetic fields on the solar surface and their dependence on the unsigned magnetic flux density

We have performed power spectral analysis of surface temperatures, velocities, and magnetic fields, using spectro-polarimetric data taken with the Hinode Solar Optical Telescope. When we make power spectra in a field-of-view covering the super-granular scale, kinetic and thermal power spectra have a prominent peak at the granular scale while the magnetic power spectra have a broadly distributed power over various spatial scales with weak peaks at both the granular and supergranular scales. To study the power spectra separately in internetwork and network regions, power spectra are derived in small sub-regions extracted from the field-of-view. We examine slopes of the power spectra using power-law indices, and compare them with the unsigned magnetic flux density averaged in the sub-regions. The thermal and kinetic spectra are steeper than the magnetic ones at the sub-granular scale in the internetwork regions, and the power-law indices differ by about 2. The power-law indices of the magnetic power spectra are close to or smaller than -1 at that scale, which suggests the total magnetic energy mainly comes from either the granular scale magnetic structures or both the granular scale and smaller ones contributing evenly. The slopes of the thermal and kinetic power spectra become less steep with increasing unsigned flux density in the network regions. The power-law indices of all the thermal, kinetic, and magnetic power spectra become similar when the unsigned flux density is larger than 200 Mx cm^-2.Comment: 9 pages, 6 figures, accepted for publication in Ap

Quantum Energies of Interfaces

We present a method for computing the one-loop, renormalized quantum energies of symmetrical interfaces of arbitrary dimension and codimension using elementary scattering data. Internal consistency requires finite-energy sum rules relating phase shifts to bound state energies.Comment: 8 pages, 1 figure, minor changes, Phys. Rev. Lett., in prin

Quantization of the Bianchi type-IX model in supergravity with a cosmological constant

Diagonal Bianchi type-IX models are studied in the quantum theory of $N = 1$ supergravity with a cosmological constant. It is shown, by imposing the supersymmetry and Lorentz quantum constraints, that there are no physical quantum states in this model. The $k = + 1$ Friedmann model in supergravity with cosmological constant does admit quantum states. However, the Bianchi type-IX model provides a better guide to the behaviour of a generic state, since more gravitino modes are available to be excited. These results indicate that there may be no physical quantum states in the full theory of $N = 1$ supergravity with a non-zero cosmological constant. are available to be excited. These results indicate that there may be no physical quantum states in the full theory of $N = 1$ supergravity with a non-zero cosmological constant.Comment: 17 pages report DAMTP R93/3