Absence of Cooper-type bound states in three- and few-electron systems

It is shown that the appearance of a fixed-point singularity in the kernel of the two-electron Cooper problem is responsible for the formation of the Cooper pair for an arbitrarily weak attractive interaction between two electrons. This singularity is absent in the problem of three and few superconducting electrons at zero temperature on the full Fermi sea. Consequently, such three- and few-electron systems on the full Fermi sea do not form Cooper-type bound states for an arbitrarily weak attractive pair interaction.

Weakly bound atomic trimers in ultracold traps

The scaling dependence of the recombination parameter as a function of the ratio between the energies of the atomic dimer and the most excited trimer states was derived. The scaling function tends to a unversal function in the limit of zero-range interaction or infinite scattering length. This paper reports on how one can obtain the trimer binding energy of a trapped atomic system, from the three-body recombination rate and the corresponding two-body scattering length.

Three-body recombination in ultracold systems: Prediction of weakly-bound atomic trimer energies

The three-body recombination coefficient of an ultracold atomic system, together with the corresponding two-body scattering length a, allow us to predict the energy E 3 of the shallow trimer bound state, using a universal scaling function. The production of dimers in trapped Bose-Einstein condensates, from three-body recombination processes, in the regime of short magnetic pulses near a Feshbach resonance, is also studied in line with the experimental observation.

Scattering and bound states of fermions in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mass-Imbalanced Three-Body Systems in 2D: Bound States and the Analytical Approach to the Adiabatic Potential

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Scattering and bound states of fermions in the modified Hulthen potential

In the present work the scattering of a fermion in the modified Hulthen potential is considered with a general vector and scalar and we solved the Dirac equation in the one-dimensional space. The transmission and reflection coefficients are reported. The bound-state solution is also given. The study shows the asymptotic behavior of the wave function in bound-state and scattering states solutions.

Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'.

One dimensional extended Hubbard model: two-particle bound states and resonances.

In questo lavoro di tesi è stato svolto uno studio analitico sul modello di Hubbard esteso unidimensionale al fine di osservare la presenza di eventuali risonanze che possano dare origine alla formazione di stati legati di due particelle. L'esistenza di uno stato legato stabile ha suscitato grande interesse negli ultimi anni, sia in ambito teorico che sperimentale, poichè è alla base di molti fenomeni che vengono osservati nei sistemi a molti corpi a basse temperature, come il BCS-BEC crossover. Pertanto si è ritenuto utile studiare il problema a due corpi nel modello di Hubbard esteso, che in generale non è integrabile. Il modello considerato contiene interazioni a primi e secondi vicini, in aggiunta all'interazione di contatto presente nel modello di Hubbard. Il problema è stato indagato analiticamente attraverso il Bethe ansatz, che consente di trovare tutti gli autovalori e le autofunzioni dell'Hamiltoniana. L'ansatz di Bethe sulla funzione d'onda è stato generalizzato per poter tener conto dei termini di interazione a più lungo raggio rispetto all'interazione di contatto. Si trova che, in questo modello, nel limite termodinamico, possono avvenire delle risonanze (o quasi-risonanze) in cui la lunghezza di scattering diverge, contrariamente a quanto avviene nel modello di Hubbard. Tale fenomeno si verifica quando il livello energetico discreto degli stati legati “tocca” la banda di scattering. Inoltre, con l'aggiunta di nuovi termini di interazione emergono nuovi stati legati. Nel caso in esame, si osservano due famiglie di stati legati, se lo spin totale delle due particelle è 1, e tre famiglie di stati legati, se lo spin totale è 0.

Michel decay spectrum for a muon bound to a nucleus

The spectrum of electrons from muons decaying in an atomic bound state is significantly modified by their interaction with the nucleus. Somewhat unexpectedly, its first measurement, at the Canadian laboratory TRIUMF, differed from basic theory. We show, using a combination of techniques developed in atomic, nuclear, and high-energy physics, that radiative corrections eliminate the discrepancy. In addition to solving that outstanding problem, our more precise predictions are potentially useful for interpreting future high-statistics muon experiments that aim to search for exotic interactions at 10−16 sensitivity.

Structural invariance of constitutively active and inactive mutants of Acanthamoeba myosin IC bound to F-actin in the rigor and ADP-bound states

The three single-headed monomeric myosin I isozymes of Acanthamoeba castellanii (AMIs)—AMIA, AMIB, and AMIC—are among the best-studied of all myosins. We have used AMIC to study structural correlates of myosin’s actin-activated ATPase. This activity is normally controlled by phosphorylation of Ser-329, but AMIC may be switched into constitutively active or inactive states by substituting this residue with Glu or Ala, respectively. To determine whether activation status is reflected in structural differences in the mode of attachment of myosin to actin, these mutant myosins were bound to actin filaments in the absence of nucleotide (rigor state) and visualized at 24-Å resolution by using cryoelectron microscopy and image reconstruction. No such difference was observed. Consequently, we suggest that regulation may be affected not by altering the static (time-averaged) structure of AMIC but by modulating its dynamic properties, i.e., molecular breathing. The tail domain of vertebrate intestinal brush-border myosin I has been observed to swing through 31° on binding of ADP. However, it was predicted on grounds of differing kinetics that any such effects with AMIC should be small [Jontes, J. D., Ostap, E. M., Pollard, T. D. & Milligan, R. A. (1998) J. Cell Biol. 141, 155–162]. We have confirmed this hypothesis by observing actin-associated AMIC in its ADP-bound state. Finally, we compared AMIC to brush-border myosin I and AMIB, which were previously studied under similar conditions. In each case, the shape and angle of attachment to F-actin of the catalytic domain is largely conserved, but the domain structure and disposition of the tail is distinctively different for each myosin.

ATP bound to the origin recognition complex is important for preRC formation

The origin recognition complex (ORC) binds origins of replication and directs the assembly of a higher order protein complex at these sites. ORC binds and hydrolyzes ATP in vitro. ATP binding to the largest subunit of ORC, Orc1p, stimulates specific binding to origin DNA; however, the function of ATP hydrolysis by ORC is unknown. To address the role of ATP hydrolysis, we have generated mutants within Orc1p that are dominant lethal. At physiological ATP concentrations, these mutants are defective for ATP hydrolysis but not ATP binding in the absence of DNA. These mutants inhibit formation of the prereplicative complex when overexpressed. The dominant lethal phenotype of these mutant ORC complexes is suppressed by simultaneous overexpression of wild-type, but not mutant, Cdc6p. Our findings suggest that these hydrolysis-defective mutants inhibit growth by titrating Cdc6p away from the origin. Based on these observations, we propose that Cdc6p specifically recognizes the ATP-bound state of Orc1p and that ATP hydrolysis is coupled to preRC disassembly.

Problems of the railroads. Hearings before the Subcommittee on Surface Transportation of the Committee on Interstate and Foreign Commerce, United States Senate, Eighty-fifth Congress, second session.

Hearings held January 13-April 3, 1958

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation

We address the breakup (splitting) of multisoliton solutions of the nonlinear Schrödinger equation (NLSE), occurring due to linear loss. Two different approaches are used for the study of the splitting process. The first one is based on the direct numerical solution of the linearly damped NLSE and the subsequent analysis of the eigenvalue drift for the associated Zakharov-Shabat spectral problem. The second one involves the multisoliton adiabatic perturbation theory applied for studying the evolution of the solution parameters, with the linear loss taken as a small perturbation. We demonstrate that in the case of strong nonadiabatic loss the evolution of the Zakharov-Shabat eigenvalues can be quite nontrivial. We also demonstrate that the multisoliton breakup can be correctly described within the framework of the adiabatic perturbation theory and can take place even due to small linear loss. Eventually we elucidate the occurrence of the splitting and its dependence on the phase mismatch between the solitons forming a two-soliton bound state. © 2007 The American Physical Society.

Bound dissipative-pulse evolution in the all-normal dispersion fiber laser using a 45° tilted fiber grating

The formation and evolution of bound dissipative pulses in the all-normal dispersion Yb-fiber laser based on a novel 45° tilted fiber grating (TFG) are first investigated both numerically and experimentally. Based on the nonlinear polarization rotation technique, the TFG and two polarization controllers (PCs) are exploited for stable self-started passive mode locking. Numerical results show that the formation of bound-state pulses in the all-normal dispersion region is the progress of soliton shaping through the dispersive waves and follows the soliton energy quantization effect. Theoretical and experimental results demonstrate that the formation mechanism of bound-state pulses can be attributed to the high pump strength and effective filter bandwidth. The obtained bound-state dissipative pulses with quasi-rectangular spectral profile have fixed pulse separation as a function of pump power. © 2013 Astro Ltd.