Trapped modes in a T-shaped waveguide

We study the discrete spectrum of the Laplace operator with the Dirichlet boundary conditions in a plane waveguide made of a band of unit width and half-band of width h perpendicular to it. The existence of critical width h _* ∈ (1,2] is established: in the case of h ∈ (0, h_*), the discrete spectrum σ _d ^h of the problem contains only one eigenvalur λ₁ ^h , but σ _d ^h = ⊘ at h ≥ h _*. The asymptotics of the eigenvalue λ₁ ^h at h → + 0 is found.     

Quantum information entropies of ultracold atomic gases in a harmonic trap

The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems containing N atoms confined in a D( ≤ 3)-dimensional harmonic trap has a universal form as S_t^(D) = N(a D - b lnN) S_\mathrm{t}^{(D)} = N(a D - b \ln N) , where a ≃ 2.332 and b = 2 for interacting bosonic systems and a ≃ 1.982 and b = 1 for ideal fermionic systems. These results obey the entropic uncertainty relation given by Beckner, Bialynicki-Birula and Myceilski.     

Estimation of the deformation-potential constant for <Emphasis Type="Italic">p</Emphasis>-type isotropic polycrystalline silicon through the deformation potential of a <Emphasis Type="Italic">p</Emphasis>-type silicon single crystal

A method of calculating the effective deformation-potential constant E ₁ for holes and longitudinal acoustic phonons in isotropic polycrystalline silicon is suggested. The deformation-potential constant E ₁ is estimated through the deformation potentials a, b, and d of the silicon single crystal. The procedure of averaging of the squared modulus of the hole and acoustic phonon interaction Hamiltonian written in the plane wave basis over the polycrystal ensemble provides the basis for calculation of the constant E ₁ . It is demonstrated that for T = 200–600 K, hole concentration p = (5.0–10.0)∙10¹⁹ cm^–3, and crystallite size d = 300–3000 ?, the deformationpotential constant E ₁ is independent of the hole concentration p, temperature T, and crystallite size d.     

Waveguides with Combined Dirichlet and Robin Boundary Conditions

We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variable Robin boundary conditions on the other. We prove that, for certain types of Robin boundary conditions, the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Laplacian in a Dirichlet-Robin annulus determined by the geometry of the strip. Moreover, we show that an appropriate combination of the geometric setting and boundary conditions leads to a Hardy-type inequality in infinite strips. As an application, we derive certain stability of the spectrum for the Laplacian in Dirichlet–Neumann strips along a class of curves of sign-changing curvature, improving in this way an initial result of Dittrich and Kříž (J. Phys. A, 35:L269–275, 2002).      

On the Uniqueness of Gravitational Centre

The dual volume of order α of a convex body A in R ⁿ is a function which assigns to every a ∈ A the mean value of α-power of distances of a from the boundary of A with respect to all directions. We prove that this function is strictly convex for α > n or α < 0 and strictly concave for 0 < α < n (for α = 0 and for α = n the function is constant). It implies that the dual volume of a convex body has the unique minimizer for α > n or α < 0 and has the unique maximizer for 0 < α < n. The gravitational centre of a convex body in R³ coincides with the maximizer of dual volume of order 2, thus it is unique.      

A Remark on the Residual Entropy of the Antiferromagnetic Ising Model in the Maximal Critical Field

By means of a transfer matrix method, we show that the residual entropy S of the two-dimensional square lattice antiferromagnetic Ising model in the maximal critical field satisfies (ln λ _n )/(n+1)≤S≤(ln λ _n )/n, where λ _n is the largest eigenvalue of the transfer matrix F _n on a strip of width n. Using these bounds, we numerically calculate the value of S, with precise estimates on the errors, namely, S=0.394198±0.020747.     

On the Residual Entropy of the Blume-Emery-Griffiths Model

By means of a transfer matrix method, we show that the residual entropy S of the two dimensional square lattice Blume-Emery-Griffiths model on the antiquadrupolar-disordered and ferromagnetic-antiquadrupolar-disordered phase boundaries satisfies the inequalities (ln λ _1,n )/(n+1)≤S≤(ln λ _1,n )/n, where λ _1,n is the largest eigenvalue of a transfer matrix F _n on a strip of width n. These bounds imply the existence of a O(1/n) correction in the approximation of S by (ln λ _1,n )/n. Using these bounds, we calculate numerically the value of S, with precise estimates on the errors.     

Towards Treating Correlations in Bose Condensates

 We use the adiabatic hyperspheric expansion and the Faddeev decomposition of the wave function with only s-waves. We derive for a fixed hyperradius an integro-differential equation for the angular eigenvalue and wave function. The correlations lower the interaction energy for N = 20 by about a factor of 5. Received October 22, 2001; accepted for publication November 5, 2001     

Steady State and Time-Resolved Fluorescence Studies of a Hemagglutinin from Moringa oleifera

The saccharide binding and conformational characterization of a hemagglutinin, a low molecular weight protein from the seeds of Moringa oleifera was studied using steady state and time resolved fluorescence. The lectin binds sugars LacNAc (K _a = 1380 M⁻¹) and fructose (K _a = 975 M⁻¹), as determined by the fluorescence spectroscopy. It has a single tryptophan per monomer which is exposed on the surface and is in a strong electropositive environment as revealed by quenching with iodide. Quenching of the fluorescence by acrylamide involved both static (K _s = 0.216 M⁻¹) and collisional (K _sv = 8.19 M⁻¹) components. The native protein showed two different lifetimes, τ ₁ (1.6 ns) and τ ₂ (4.36 ns) which decrease and get converted into a single one, (2.21 ns) after quenching with 0.15 M acrylamide. The bimolecular quenching constant, k _q was 7.55 × 10¹¹ M⁻¹ s⁻¹. ANS binding studies showed that the native protein has exposed hydrophobic patches which get further exposed at extreme acidic or alkaline pH. However, they get buried in the interior of the protein in presence of 1 M GdnHCl or urea.     

Squeezed vacuum as an eigenstate of two-photon annihilation operator

We introduce the inverse annihilation and creation operatorsa ⁻¹ anda ^+-1 by their actions on the number states. We show that the squeezed vacuum exp(1/2;ξa ⁺²]|0> and squeezed first number state exp[1/2;ξa ⁺²]|n=1> are respectively the eigenstates of the operators (a ^†−1 a) and (aa ^+-1) with the eigenvalue ξ.     

The Threshold Effects for the Two-Particle Hamiltonians on Lattices

For a wide class of two-body energy operators h(k) on the d-dimensional lattice ℤ^d, d≥3, k being the two-particle quasi-momentum, we prove that if the following two assumptions (i) and (ii) are satisfied, then for all nontrivial values k, k≠0, the discrete spectrum of h(k) below its threshold is non-empty. The assumptions are: (i) the two-particle Hamiltonian h(0) corresponding to the zero value of the quasi-momentum has either an eigenvalue or a virtual level at the bottom of its essential spectrum and (ii) the one-particle free Hamiltonians in the coordinate representation generate positivity preserving semi-groups.     

Tails in harnesses

We consider space- and time-uniformd-dimensional random processes with linear local interaction, which we call harnesses and which may be used as discrete mathematical models of random interfaces. Their components are rea random variablesa _s ^t , wheres ∈ Z ^d andt=0, 1, 2.,... At every time step two events occur: first, every component turns into a linear combination of itsN neighbors, and second, a symmetric random i.i.d. “noise”v is added to every component. For any σ ∈Z _d ⁺ define Δ_σ a′ _s as follows. If σ=(0,...,0), σ=(0,...,0), Δ_σ a _s ^t =a _s ^t . Then by induction, wheree _i is thed-dimensional vector, whoseith component is one and other components are zeros. Denote |σ| the sum of components of σ. Call a real random variable ϕ symmetric if it is distributed as −ϕ. For any symmetric random variable ϕpower decay or P-decay is defined as the supremum of thoser for which therth absolute moment of ϕ is finite. Convergence a.s., in probability and in law whent→∞ is examined in terms of P-decay(v): Ifd=1, σ=0 ord=2, σ=(0,0), Δ_σ a _s ^t diverges. In all the other cases: If P-decay(v)<(d+2)/(d+|σ|), Δ_σ a _s ^t diverges; if P-decay(v)>(d+2)/(d+|σ|), Δ_σ a _s ^t , converges and P-decay(ν) For any symmetric random variable ϕexponential decay or E-decay is defined as the supremum of thoser for which the expectation of exp(|x|^r) is finite. Let E-decay(v)>0. Whenever Δ_σ a _s ^t converges (that is, ifd>2 or |σ|>0: Ifd>2, E-decay(lima _s ^t )=min(E-decay(v),d+2/2); if |σ|=1, E-decay (lim Δ_σ a _s ^t )=min(E-decay(ν),d+2); if |σ| ⩾, E-decay (lim Δ_σ a _s ^t )=E-decay(ν).     

Surface States and Spectra

Let ℤ₊ ^{d +1}= ℤ⁺×ℤ₊, let H ₀ be the discrete Laplacian on the Hilbert space l ²(ℤ₊ ^{d +1}) with a Dirichlet boundary condition, and let V be a potential supported on the boundary ∂ℤ₊ ^{d +1}. We introduce the notions of surface states and surface spectrum of the operator H=H ₀+V and explore their properties. Our main result is that if the potential V is random and if the disorder is either large or small enough, then in dimension two H has no surface spectrum on σ(H ₀) with probability one. To prove this result we combine Aizenman–Molchanov theory with techniques of scattering theory. Received: 18 September 2000 / Accepted: 21 November 2000     

Halo Structure of 19C via the (p,d) Reaction

 We have investigated the heaviest one-neutron halo candidate, the ¹⁹C nucleus. Few-body model calculations of cross-section angular distributions for the ¹⁹C(p,d)¹⁸C reaction together with test calculations carried out for the ¹⁷C(p,d)¹⁶C reaction at a low incident energy are presented for different possible halo-neutron configurations. We show that there is a clear distinction in particular between l _n  = 0 and l _n  = 2 halo transfers. The sensitivity of the cross sections to the assumed ¹⁹C single-neutron separation energy is discussed. Received October 13, 1999; revised November 25, 1999; accepted for publication April 29, 2000     

Localization of Surface Spectra

We study spectral properties of the discrete Laplacian H on the half-space with random boundary condition ; the V(n) are independent random variables on a probability space and λ is the coupling constant. It is known that if the V(n) have densities, then on the interval [-2(d+1), 2(d+1)] (=σ(H ₀), the spectrum of the Dirichlet Laplacian) the spectrum of H is P-a.s. absolutely continuous for all λ [JL1]. Here we show that if the random potential P satisfies the assumption of Aizenman–Molchanov [AM], then there are constants λ _d and Λ _d such that for |λ|<lambda; _d and |λ|> Λ _d the spectrum of H outside σ(H ₀) is P-a.s. pure point with exponentially decaying eigenfunctions. Received: 3 December 1998 / Accepted: 27 May 1999     

Vacuum ultraviolet gain measurements in optically pumped LiYF4:Nd3+

 We present measurements of the net-induced gain on the 5d–4f transition at 186 nm in LiYF₄ : Nd³⁺ optically pumped by radiation from a molecular fluorine laser. It is found that for LiYF₄ : Nd³⁺, one of a series of potential continuously tunable VUV lasers, relatively strong excited-state absorption results in net-induced loss. The prospects for VUV laser operation being realised in other rare-earth-doped fluorides is discussed. Received: 4 March 1996/Revised version: 10 July 1996     

Scattering of Heavy Charged Particles on Hydrogen Atoms

 Low-energy scattering of heavy positively charged particles on hydrogen atoms (H) is investigated by solving Faddeev equations in configuration space. A resonant value of the pH scattering length, a = 750 ± 5 a.u., in the pp antisymmetric state was found. This large value indicates the existence of a first excited state with a binding energy B = 1.14 × 10⁻⁹ a.u. below the H ground state. Resonances for non-zero angular-momenta states are predicted. Received November 4, 2001; accepted for publication November 12, 2001     

Use of the wake of a small cylinder to Control unsteady loads on a circular cylinder

Simultaneous measurements of lift and drag forces have been performed in order to study passive control of unsteady loads induced on a circular cylinder. For this purpose, an aerodynamic balance has been developed. The balance, developed for a cylinder of 25.4 mm in diameter, was designed to operate in the subcritical regime (Re=32000). This instrument is characterized by its sensitive element that forms a small central part of the cylinder. The static and dynamic calibrations of the balance show the appropriateness of the present design. Moreover, qualification experiments carried out with a single cylinder gave results (mean and rms values of the lift and drag coefficients) that are in good agreement with those found in the literature. The purpose of this paper is to present a passive control experiment performed by means of the wake of a smaller cylinder interacting with a larger one. Firstly, a parametric study was performed by varying the following: i) the diameterdS of the small cylinder for one large cylinder diameterd (7 values in the range 0.047≤d _S /d≤0.125); ii) the center-to-center spacingS/d (11 values in the range 1.375≤S/d≤2.5); and iii) the stagger anglea(0≤a≤90 with a fine angular stepDa fora≤15). A maximum mean drag reduction of about 48% is achieved. Ata=4 to 8, one can observe a peak of mean lift coefficient. Then unsteady fluid forces, vortex shedding frequency and flow pattern were systematically investigated for the small cylinder having a diameterdS=2.4 mm (0.094d). Reductions of 78% and 56% of the rms lift and drag fluctuations respectively were obtained with the small cylinder placed at a slight stagger angle in the range 6<a<9. This leads to an instantaneous force vector that exhibits more steadiness both in angle and amplitude. Moreover, at these stagger angles, the energy of the lift fluctuations at the shedding frequency is significantly reduced compared to the single cylinder case.     

Structure, ferroelectric and piezoelectric properties of?(Bi0.98?xLa0.02Na1?x)0.5BaxTiO3 lead-free ceramics

Lead-free (Bi_0.98−x La_0.02Na_1−x )_0.5Ba _x TiO₃ ceramics have been prepared by an ordinary sintering technique and their structure, ferroelectric and piezoelectric properties have been studied. The results of X-ray diffraction show that La²⁺ and Ba²⁺ diffuse into the Bi_0.5Na_0.5TiO₃ lattices to form a new solid solution with a pure perovskite structure, and a morphotropic phase boundary (MPB) exists at 0.04<x<0.10. Compared with pure Bi_0.5Na_0.5TiO₃ ceramics, the (Bi_0.98−x La_0.02Na_1−x )_0.5Ba _x TiO₃ ceramics possess much smaller coercive field E _c and larger remanent polarization P _r. Because of the low E _c (3.38 kV/mm), large P _r (46.2 μC/cm²) and the formation of the MPB of rhombohedral and tetragonal phases, the piezoelectric properties of the ceramics are significantly enhanced at x=0.06: d ₃₃=181 pC/N and k _p=36.3%. The depolarization temperature T _d reaches a minimum value near the MPB. The ceramics exhibit relaxor characteristic, which is probably a result from the cation disordering in the 12-fold coordination sites. The temperature dependences of the ferroelectric and dielectric properties suggest that the ceramics may contain both polar and non-polar regions at the temperatures above T _d.     

Noncommutative electromagnetism as a large <Emphasis Type="Italic">N</Emphasis> gauge theory

We map noncommutative (NC) U(1) gauge theory on ℝ _C ^d ×ℝ _NC ²ⁿ to U(N→∞) Yang–Mills theory on ℝ _C ^d , where ℝ _C ^d is a d-dimensional commutative spacetime while ℝ _NC ²ⁿ is a 2n-dimensional NC space. The resulting U(N) Yang–Mills theory on ℝ _C ^d is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang–Mills theory onto ℝ _C ^d . We show that the gauge-Higgs system (A _μ ,Φ ^a ) in the U(N→∞) Yang–Mills theory on ℝ _C ^d leads to an emergent geometry in the (d+2n)-dimensional spacetime whose metric was determined by Ward a long time ago. In particular, the 10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry arising from the 4-dimensional N=4{\mathcal{N}}=4 vector multiplet in the AdS/CFT duality. We further elucidate the emergent gravity by showing that the gauge-Higgs system (A _μ ,Φ ^a ) in half-BPS configurations describes self-dual Einstein gravity.