Richardson-Gaudin integrability in the contraction limit of the quasispin

Background: The reduced, level-independent, Bardeen-Cooper-Schrieffer Hamiltonian is exactly diagonalizable by means of a Bethe Ansatz wavefunction, provided the free variables in the Ansatz are the solutions of the set of Richardson-Gaudin equations. On the one side, the Bethe Ansatz is a simple product state of generalised pair operators. On the other hand, the Richardson-Gaudin equations are strongly coupled in a non-linear way, making them prone to singularities. Unfortunately, it is non-trivial to give a clear physical interpretation to the Richardson-Gaudin variables because no physical operator is directly related to the individual variables. Purpose: The purpose of this paper is to shed more light on the critical behavior of the Richardson-Gaudin equations, and how this is related to the product wave structure of the Bethe Ansatz. Method: A pseudo-deformation of the quasi-spin algebra is introduced, leading towards a Heisenberg-Weyl algebra in the contraction limit of the deformation parameter. This enables an adiabatic connection of the exact Bethe Ansatz eigenstates with pure bosonic multiphonon states. The physical interpretation of this approach is an adiabatic suppression of the Pauli exclusion principle. Results: The method is applied to a so-called "picket-fence" model for the BCS Hamiltonian, displaying a typical critical behavior in the Richardson-Gaudin variables. It was observed that the associated bosonic multiphonon states change collective nature at the critical interaction strengths of the Richardson-Gaudin equations. Conclusions: The Pauli exclusion principle is the main responsible for the critical behavior of the Richardson-Gaudin equations, which can be suppressed by means of a pseudo deformation of the quasispin algebra.Comment: PACS 02.30.Ik, 21.10.Re, 21.60.Ce, 74.20.F

Quantum communication between trapped ions through a dissipative environment

We study two trapped ions coupled to the axial phonon modes of a one-dimensional Coulomb crystal. This system is formally equivalent to the "two spin-boson" model. We propose a scheme to dynamically generate a maximally entangled state of two ions within a decoherence-free subspace. Here the phononic environment of the trapped ions, whatever its temperature and number of modes, serves as the entangling bus. The efficient production of the pure singlet state can be exploited to perform short-ranged quantum communication which is essential in building up a large-scale quantum computer.Comment: 4 pages, 2 figure

An exactly solvable model of a superconducting to rotational phase transition

We consider a many-fermion model which exhibits a transition from a superconducting to a rotational phase with variation of a parameter in its Hamiltonian. The model has analytical solutions in its two limits due to the presence of dynamical symmetries. However, the symmetries are basically incompatible with one another; no simple solution exists in intermediate situations. Exact (numerical) solutions are possible and enable one to study the behavior of competing but incompatible symmetries and the phase transitions that result in a semirealistic situation. The results are remarkably simple and shed light on the nature of phase transitions.Comment: 11 pages including 1 figur

Analytically solvable potentials for γ\gamma-unstable nuclei

An analytical solution of the collective Bohr equation with a Coulomb-like and a Kratzer-like $\gamma-$unstable potential in quadrupole deformation space is presented. Eigenvalues and eigenfunctions are given in closed form and transition rates are calculated for the two cases. The corresponding SO(2,1)$\times$SO(5) algebraic structure is discussed.Comment: 9 pages, 4 figures in one .ps fil

Regulation of the galactose pathway in Saccharomyces cerevisiae: induction of uridyl transferase mRNA and dependency on GAL4 gene function

In Saccharomyces cerevisiae, utilization of galactose requires four inducible enzyme activities. Three of these activities (galactose-1-phosphate uridyl transferase, EC 2.7.7.10; uridine diphosphogalactose 4-epimerase, EC 5.1.3.2; and galactokinase, EC 2.7.1.6) are specified by three tightly linked genes (GAL7, GAL10, and GAL1, respectively) on chromosome II, whereas the fourth, galactose transport, is specified by a gene (GAL2) located on chromosome XII. Although classic genetic analysis has revealed both positive and negative regulatory genes that coordinately affect the appearance of all four enzyme activities, neither the basic events leading to the appearance of enzyme activities nor the roles of the regulatory genes have yet been determined. Regulation of inducible enzyme activity could be mediated by events related to transcription, translation, or enzyme activation. For the purpose of studying galactose pathway induction and its regulation, we have developed an immunoprecipitation assay that enables us to detect the GAL7 specified uridyl transferase polypeptide in yeast extracts and among the polypeptides synthesized in an RNA-dependent in vitro translation system. Use of this immunoprecipitation assay in conjunction with in vivo labeling experiments demonstrates the presence of [(3)H]leucine-labeled transferase in extracts prepared from cells grown in galactose but not from cells grown in glucose. This galactose-specific induction of transferase polypeptide is mediated by the de novo appearance of a functional mRNA species whose synthetic capacity is detectable by the combination of in vitro translation and immunoprecipitation. The appearance of functional transferase mRNA depends on wild-type expression of the positive regulatory gene, GAL4. Cells carrying a nonsense (amber) mutation in the GAL4 gene fail to produce the transferase mRNA, whereas a nonsense suppressor of the GAL4 amber mutant regains the galactose-specific mRNA response. Our results establish that the induction of the GAL7 specified uridyl transferase activity is mediated by de novo appearance of a functional mRNA and that this galactose-specific response is dependent on a wild-type GAL4 gene product

The pairing Hamiltonian for one pair of identical nucleons bound in a potential well

The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing even Grassmann variables. The eigenvectors are analytically expressed solely in terms of these with coefficients fixed by the eigenvalues and the single particle energies. When the latter are those of an harmonic oscillator well an accurate expression is derived for both the collective eigenvalue and for those trapped in between the single particle levels, for any strength of the pairing interaction and for any number of levels. Notably the trapped solutions are labelled through an index upon which they depend parabolically.Comment: 5 pages, 1 postscript figur

Photoassisted tunneling from free-standing GaAs thin films into metallic surfaces

The tunnel photocurrent between a gold surface and a free-standing semiconducting thin film excited from the rear by above bandgap light has been measured as a function of applied bias, tunnel distance and excitation light power. The results are compared with the predictions of a model which includes the bias dependence of the tunnel barrier height and the bias-induced decrease of surface recombination velocity. It is found that i) the tunnel photocurrent from the conduction band dominates that from surface states. ii) At large tunnel distance the exponential bias dependence of the current is explained by that of the tunnel barrier height, while at small distance the change of surface recombination velocity is dominant

Why do drivers become safer over the first three months of driving? A longitudinal qualitative study

Drivers are at high crash risk when they begin independent driving, with liability decreasing steeply over the first three months. Their behavioural development, and other changes underlying improved safety are not well understood. We adopted an innovative longitudinal qualitative design, with thirteen newly qualified drivers completing a total of 36 semi-structured interviews, one, two and three months after acquiring a full UK driving license. The interviews probed high-risk factors for new drivers, as well as allowing space for generating novel road safety issues. Analysis adopted a dual deductive and inductive interpretative thematic approach, identifying three super-ordinate themes: (1) Improvements in car control skills and situation awareness; (2) A reduction in the thrill of taking risks when driving against a background of generally increasing driving speed; (3) Early concerns about their social status in the eyes of other road users during the early stages of driving, which may put pressure on them to drive faster than they felt comfortable with. The study provides important new leads towards understanding how novice driving becomes safer over the first few months of driving, including how well-studied concepts of driving skill and style may change during development of independent driving, and a focus on the less rigorously studied concept of social status