Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

Quantum symmetries and the Weyl–Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase space. Each such phase-space representation is a Weyl–Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by 'factorizing' the Weyl–Wigner product. However, not every real, unitary representation on phase space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl–Wigner product and can be factorized. The conditions under which this is possible are examined. Examples are presented.

Gauge fields, geometric phases, and quantum adiabatic pumps

Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. Tunneling from a scanning tunneling microscope tip through a magnetic atom could be used to demonstrate the non-Abelian character of the gauge field.

Self-Similarity of Air-Water Flows in Skimming Flows on Stepped Spillways

Skimming flows on stepped spillways are characterised by a significant rate of turbulent dissipation on the chute. Herein an advanced signal processing of traditional conductivity probe signals is developed to provide further details on the turbulent time and length scales. The technique is applied to a 22° stepped chute operating with flow Reynolds numbers between 3.8 and 7.1 E+5. The new correlation analyses yielded a characterisation of large eddies advecting the bubbles. The turbulent length scales were related to the characteristic depth Y90. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level, and turbulence time and length scales. The self-similarity results were significant because they provided a picture general enough to be used to characterise the air-water flow field in prototype spillways.

Dynamic Similarity and Scale Effects Affecting Air Bubble Entrainment in Hydraulic Jumps

In an open channel, the transition from super- to sub-critical flow is a flow singularity (the hydraulic jump) characterised by a sharp rise in free-surface elevation, strong turbulence and air entrainment in the roller. A key feature of the hydraulic jump flow is the strong free-surface aeration and air-water flow turbulence. In the present study, similar experiments were conducted with identical inflow Froude numbers Fr1 using a geometric scaling ratio of 2:1. The results of the Froude-similar experiments showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers yielding some lesser aeration of the jump roller. The dimensionless bubble count rates were significantly lower in the smaller channel, especially in the mixing layer. The bubble chord time distributions were quantitatively close in both channels, and they were not scaled according to a Froude similitude. Simply the hydraulic jump remains a fascinating two-phase flow motion that is still poorly understood.

Molecular cloning reveals that the p160 myb-binding protein is a novel, predominantly nucleolar protein which may play a role in transactivation by Myb

We have previously detected two related murine nuclear proteins, p160 and p67, that can bind to the leucine zipper motif within the negative regulatory domain of the Myb transcription factor. We now describe the molecular cloning of cDNA corresponding to murine p160. The P160 gene is located on mouse chromosome 11, and related sequences are found on chromosomes 1 and 12. The predicted p160 protein is novel, and in agreement with previous studies, we find that the corresponding 4.5-kb mRNA is ubiquitously expressed. We showed that p67 is an N-terminal fragment of p160 which is generated by proteolytic cleavage in certain cell types. The protein encoded by the cloned p160 cDNA and an engineered protein (p67*) comprising the amino-terminal region of p160 exhibit binding specificities for the Myb and Jun leucine zipper regions identical to those of endogenous p160 and p67, respectively. This implies that the Myb-binding site of p160 lies within the N-terminal 580 residues and that the Jun-binding site is C-terminal to this position. Moreover, we show that p67* but not p160 can inhibit transactivation by Myb. Unexpectedly, immunofluorescence studies show that p160 is localized predominantly in the nucleolus. The implications of these results for possible functions of p160 are discussed.

Anodic-oxide-induced interdiffusion in GaAs/AlGaAs quantum wells

Enhancement of interdiffusion in GaAs/AlGaAs quantum wells due to anodic oxides was studied. Photoluminescence, transmission electron microscopy, and quantum well modeling were used to understand the effects of intermixing on the quantum well shape. Residual water in the oxide was found to increase the intermixing, though it was not the prime cause for intermixing. Injection of defects such as group III vacancies or interstitials was considered to be a driving force for the intermixing. Different current densities used in the experimental range to create anodic oxides had little effect on the intermixing. ©1998 American Institute of Physics.

Integrable multiparametric quantum spin chains

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions, We illustrate how this general formalism applier; to construct multiparametric versions of the supersymmetric t-J and Li models.

Molecular cocrystals of carboxylic acids. XXVII - An investigation into the use of triphenylphosphine oxide cocrystals for non-linear optics: the crystal structure of the adduct of triphenylphosphine oxide with N-methylpyrrole-2-carboxylic acid

Four adducts of triphenylphosphine oxide with aromatic carboxylic acids have been synthesized and tested for second-order non-linear optical properties. These were with N-methylpyrrole-2-carboxylic acid (I), indole-2-carboxylic acid (2), 3-dimethylaminobenzoic acid (3), and thiophen-2-carboxylic acid (4). Compound (1) produced clear, colourless crystals (space group P2(1)2(1)2(1) With a 9.892(1), b 14.033(1), c 15.305(1) Angstrom, Z 4) which allowed the structure to be determined by X-ray diffraction.

Structural analysis and molecular model of a self-incompatibility RNase from wild tomato

Self-incompatibility RNases (S-RNases) are an allelic series of style glycoproteins associated with rejection of self-pollen in solanaceous plants. The nucleotide sequences of S-RNase alleles from several genera have been determined, but the structure of the gene products has only been described for those from Nicotiana alata. We report on the N-glycan structures and the disulfide bonding of the S-3-RNase from wild tomato (Lycopersicon peruvianum) and use this and other information to construct a model of this molecule. The S-3-RNase has a single N-glycosylation site (Asn-28) to which one of three N-glycans is attached. S-3-RNase has seven Cys residues; six are involved in disulfide linkages (Cys-16-Cys-21, Cys-46-Cys-91, and Cys-166-Cys-177), and one has a free thiol group (Cys-150). The disulfide-bonding pattern is consistent with that observed in RNase Rh, a related RNase for which radiographic-crystallographic information is available. A molecular model of the S-3-RNase shows that four of the most variable regions of the S-RNases are clustered on one surface of the molecule. This is discussed in the context of recent experiments that set out to determine the regions of the S-RNase important for recognition during the self-incompatibility response.

Nucleotide sequence of the nifH gene coding for nitrogen reductase in the acetic acid bacterium Acetobacter diazotrophicus

The nifH gene sequence of the nitrogen-fixing bacterium Acetobacter diazotrophicus was determined with the use of the polymerase chain reaction and universal degenerate oligonucleotide primers. The gene shows highest pair-wise similarity to the nifH gene of Azospirillum brasilense. The phylogenetic relationships of the nifH gene sequences were compared with those inferred from 16S rRNA gene sequences. Knowledge of the sequence of the nifH gene contributes to the growing database of nifH gene sequences, and will allow the detection of Acet. diazotrophicus from environmental samples with nifH gene-based primers.