5,020 research outputs found
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 of
the Interacting Vector Boson Model (IVBM), to the orthosymplectic group
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 .
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 , and from rare earth region are
compared with the experiment. The transition probabilities for the
and 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 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
- …