The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing

A connection is made between the exact eigen states of the BCS Hamiltonian and the predictions made by the Tamm-Dancoff Approximation. This connection is made by means of a parametrised algebra, which gives the exact quasi-spin algebra in one limit of the parameter and the Heisenberg-Weyl algebra in the other. Using this algebra to construct the Bethe Ansatz solution of the BCS Hamiltonian, we obtain parametrised Richardson-Gaudin equations, leading to the secular equation of the Tamm-Dancoff Approximation in the bosonic limit. An example is discussed in depth.Comment: Submitted to the proceedings of the Group28 conference (Newcastle-upon-Tyne, UK). Journal of Physics: Conference Serie

Single grain heating due to inelastic cotunneling

We study heating effects of a single metallic quantum dot weakly coupled to two leads. The dominant mechanism for heating at low temperatures is due to inelastic electron cotunneling processes. We calculate the grain temperature profile as a function of grain parameters, bias voltage, and time and show that for nanoscale size grains the heating effects are pronounced and easily measurable in experiments.Comment: 4 pages, 3 figures, revtex4, extended and corrected versio

Collective states of the odd-mass nuclei within the framework of the Interacting Vector Boson Model

A supersymmetric extension of the dynamical symmetry group $Sp^{B}(12,R)$ of the Interacting Vector Boson Model (IVBM), to the orthosymplectic group $OSp(2\Omega/12,R)$ is developed in order to incorporate fermion degrees of freedom into the nuclear dynamics and to encompass the treatment of odd mass nuclei. The bosonic sector of the supergroup is used to describe the complex collective spectra of the neighboring even-even nuclei and is considered as a core structure of the odd nucleus. The fermionic sector is represented by the fermion spin group $SO^{F}(2\Omega)\supset SU^{F}(2)$. The so obtained, new exactly solvable limiting case is applied for the description of the nuclear collective spectra of odd mass nuclei. The theoretical predictions for different collective bands in three odd mass nuclei, namely $^{157}Gd$, $^{173}Yb$ and $^{163}Dy$ from rare earth region are compared with the experiment. The $B(E2)$ transition probabilities for the $^{157}Gd$ and $^{163}Dy$ between the states of the ground band are also studied. The important role of the symplectic structure of the model for the proper reproduction of the $B(E2)$ behavior is revealed. The obtained results reveal the applicability of the models extension.Comment: 18 pages, 8 figure

Mass Spectrometric Calibration Procedure For Real-Time Detection Of Lighter Hydrocarbons

Determining gas compositions from live well fluids on a drilling rig is critical for real time formation evaluation. Development and utilization of a reliable mass spectrometric method to accurately characterize these live well fluids are always challenging due to lack of a robust and effectively selective instrument and procedure. The methods currently utilized need better calibration for the characterization of light hydrocarbons (C-1-C-6) at lower concentrations. The primary goal of this research is to develop and optimize a powerful and reliable analytical method to characterize live well fluid using a quadruple mass spectrometer (MS). The mass spectrometers currently being used in the field have issues with detection, spectra deconvolution, and quantification of analytes at lower concentrations (10-500 ppm), particularly for the lighter (m/z) hydrocarbons. The objectives of the present study are thus to identify the detection issues, develop and optimize a better method, calibrate and QA/QC the MS, and validate the MS method in lab settings. In this study, we used two mass spectrometers to develop a selective and precise method to quantitatively analyze low level lighter analytes (C-1-C-6 hydrocarbons) with masses m/z at concentrations 10-500 ppm. Our results suggest that proper mass selection like using base peaks with m/z 15, 26, 41, 43, 73, and 87, respectively, for methane, ethane, propane, butane, pentane, and hexane can help detect and accurately quantify hydrocarbons from gas streams. This optimized method in quadrupole mass spectrometer (QMS) will be invaluable for early characterization of the fluid components from a live hydrocarbon well in the field in real time

Thermoelectric performance of weakly coupled granular materials

We study thermoelectric properties of inhomogeneous nanogranular materials for weak tunneling conductance between the grains, g_t < 1. We calculate the thermopower and figure of merit taking into account the shift of the chemical potential and the asymmetry of the density of states in the vicinity of the Fermi surface. We show that the weak coupling between the grains leads to a high thermopower and low thermal conductivity resulting in relatively high values of the figure of merit on the order of one. We estimate the temperature at which the figure of merit has its maximum value for two- and three-dimensional samples. Our results are applicable for many emerging materials, including artificially self-assembled nanoparticle arrays.Comment: 4 pages, 3 figure

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

Thermoelectric performance of granular semiconductors

We study thermoelectric properties of granular semiconductors with weak tunneling conductance between the grains, g_t < 1. We calculate the thermopower and figure of merit taking into account the shift of the chemical potential and the asymmetry of the density of states in the vicinity of the Fermi surface due to n- or p-type doping in the Efros-Shklovskii regime for temperatures less than the charging energy. We show that for weakly coupled semiconducting grains the figure of merit is optimized for grain sizes of order 5nm for typical materials and its values can be larger than one. We also study the case of compensated granular semiconductors and show that in this case the thermopower can be still finite, although two to three orders of magnitude smaller than in the uncompensated regime.Comment: 4 pages, 4 figure