Generation of macroscopic superpositions of quantum states by linear coupling to a bath

We demonstrate through an exactly solvable model that collective coupling to any thermal bath induces effectively nonlinear couplings in a quantum many-body (multispin) system. The resulting evolution can drive an uncorrelated large-spin system with high probability into a macroscopic quantum-superposition state. We discuss possible experimental realizations.     

Dynamics and thermodynamics of the low-temperature strongly interacting Bose gas

We measure the zero-temperature equation of state of a homogeneous Bose gas of (7)Li atoms by analyzing the in situ density distributions of trapped samples. For increasing repulsive interactions our data show a clear departure from mean-field theory and provide a quantitative test of the many-body corrections first predicted in 1957 by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957).]. We further probe the dynamic response of the Bose gas to a varying interaction strength and compare it to simple theoretical models. We deduce a lower bound for the value of the universal constant ξ > 0.44(8) that would characterize the universal Bose gas at the unitary limit.     

Principal modes in fiber amplifiers

The dynamics of the state of polarization in multimode fiber amplifiers is presented. The experimental results reveal that although the state of polarizations at the output can vary over a large range when changing the temperatures of the fiber amplifiers, the variations are significantly reduced when resorting to the principal states of polarization in single-mode fiber amplifiers and principal modes in multimode fiber amplifiers.     

Structural analysis of electrolyte solutions for rechargeable Mg batteries by stereoscopic means and DFT calculations

We present a rigorous analysis of unique, wide electrochemical window solutions for rechargeable magnesium batteries, based on aromatic ligands containing organometallic complexes. These solutions are comprised of the transmetalation reaction products of Ph(x)MgCl(2-x) and Ph(y)AlCl(3-y) in different proportions, in THF. In principle, these reactions involve the exchange of ligands between the magnesium and the aluminum based compounds, forming ionic species and neutral molecules, such as Mg(2)Cl(3)(+)·6THF, MgCl(2)·4THF, and Ph(y)AlCl(4-y)(-) (y = 0-4). The identification of the equilibrium species in the solutions is carried out by a combination of Raman spectroscopy, multinuclear NMR, and single-crystal XRD analyses. The association of the spectroscopic results with explicit identifiable species is supported by spectral analyses of specially synthesized reference compounds and DFT quantum-mechanical calculations. The correlation between the identified solution equilibrium species and the electrochemical anodic stability window is investigated. This study advances both development of new nonaqueous solution chemistry and possible development of high-energy density rechargeable Mg batteries.     

Working group report: Low energy and flavour physics

This is a report of the low energy and flavour physics working group at WHEPP-8, held at the Indian Institute of Technology, Mumbai, India, during 5–16 January 2004.     

Characterization of chick pea <Emphasis Type="Italic">(Cicer arietum L)</Emphasis> pastes using squeezing flow viscometry

Domestic type and commercial chickpea pastes ('humus'), as well as a commercial soy substitute, were squeezed at a constant displacement rate between 150 mm parallel Teflon plates, mounted on an Instron Universal Testing Machine, before and after stirring. At 1 mm height the crosshead was stopped and the stress relaxation followed. The apparent stress at 1 mm height and that after 1 and 2 min relaxation were considered consistency measures of the pastes. They were reproducible parameters, and sensitive enough to monitor differences between the products, batches of the same product and stirred and unstirred samples. A stronger consistency was reflected not only by a high apparent compressive stress before and after relaxation but also in a higher yield stress, as determined in shear with a parallel plates sensor, suggesting that the paste's texture is determined by a solid like matrix. Stirring invariably reduced the pastes consistency presumably by an irreversible disruption of their microstructure. The presence of suspended solid particles had little or no effect on the pastes ability to retain their consistency after stirring.     

Effect of non-homogeneous surface viscosity on the Marangoni migration of a droplet in viscous fluid

Marangoni migration of a single droplet in an unbounded viscous fluid under the additional effect of variable surface viscosity is studied. The surface tension and the surface viscosity depend on concentration of dissolved species. Cases of the motion induced by the presence of a point source and by a given constant concentration gradient are considered. The dependence of the migration velocity on the governing parameters is computed under quasi-stationary approximation. The effect of weak advective transport is studied making use of singular perturbations in the Peclet number, Pe. It is shown that, when the source is time dependent a Basset-type history term appears in the expansion of the concentration and, as a result, the leading order correction to the flow and to the migration velocity is of O(Pe(1/2)). If the source of active substance driving the flow is steady, the effect of convective transport on the migration is weaker.     

Arithmetic Groups,Base Change,and Representation Growth

Consider an arithmetic group \({\mathbf{G}(O_S)}\), where \({\mathbf{G}}\) is an affine group scheme with connected, simply connected absolutely almost simple generic fiber, defined over the ring of S-integers O _S of a number field K with respect to a finite set of places S. For each \({n \in \mathbb{N}}\), let \({R_n(\mathbf{G}(O_S))}\) denote the number of irreducible complex representations of \({\mathbf{G}(O_S)}\) of dimension at most n. The degree of representation growth \({\alpha(\mathbf{G}(O_S)) = \lim_{n \rightarrow\infty}\log R_n(\mathbf{G}(O_S)) / \log n}\) is finite if and only if \({\mathbf{G}(O_S)}\) has the weak Congruence Subgroup Property. We establish that for every \({\mathbf{G}(O_S)}\) with the weak Congruence Subgroup Property the invariant \({\alpha(\mathbf{G}(O_S))}\) is already determined by the absolute root system of \({\mathbf{G}}\). To show this we demonstrate that the abscissae of convergence of the representation zeta functions of such groups are invariant under base extensions \({K{\subset}L}\). We deduce from our result a variant of a conjecture of Larsen and Lubotzky regarding the representation growth of irreducible lattices in higher rank semi-simple groups. In particular, this reduces Larsen and Lubotzky’s conjecture to Serre’s conjecture on the weak Congruence Subgroup Property, which it refines.     

Uniqueness theorems for Fourier transforms

Let Γ be a smooth curve in the plane R², and Λ be any subset of R². When can one recover uniquely a finite measure μ, supported by Γ and absolutely continuous with respect to the arc length measure on Γ, from the restriction to Λ of its Fourier transform? In this note we present two results in the subject, one is concerned with the case when Γ is a circle, and the other with the case when Λ is “close” to a lattice.     

Dense Fast Random Projections and Lean Walsh Transforms

Random projection methods give distributions over k×d matrices such that if a matrix Ψ (chosen according to the distribution) is applied to a finite set of vectors x _i ∈ℝ ^d the resulting vectors Ψx _i ∈ℝ ^k approximately preserve the original metric with constant probability. First, we show that any matrix (composed with a random ±1 diagonal matrix) is a good random projector for a subset of vectors in ℝ ^d . Second, we describe a family of tensor product matrices which we term Lean Walsh. We show that using Lean Walsh matrices as random projections outperforms, in terms of running time, the best known current result (due to Matousek) under comparable assumptions.