261 research outputs found
On Unconventional Electron Pairing In a Periodic Potential
On the assumption that two electrons with the same group velocity effectively
attract each other a simple model Hamiltonian is proposed to question the
existence of unconventional electron pairs formed by electrons in a strong
periodic potential.Comment: 8 page
Analytic Density of States in the Abrikosov-Gorkov Theory
Since the early 1960s, Abrikosov-Gorkov theory has been used to describe
superconductors with paramagnetic impurities. Interestingly, the density of
states resulting from the theoretical framework has to date only been known
approximately, as a numeric solution of a complex polynomial. Here we introduce
an exact analytic solution for the density of states of a superconductor with
paramagnetic impurities. The solution is valid in the whole regime of
Abrikosov-Gorkov theory; both where there is an energy gap and gapless. While
of fundamental interest, we argue that this solution also has computational
benefits in the evaluation of integrals for tunneling conductances and allows
for an analytic description of materials with densities of states that are
modeled from the basic Abrikosov-Gorkov density of states.Comment: 5 pages, 1 figur
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On Demand-side Approaches to Solving the "Tragedy of High Prices" in Fisheries
While overfishing frequently is explained in terms of «the Tragedy of the
Commons» model, it is argued that the economic causes of such long-run resource problems could be more accurately characterised in terms of a «Tragedy of High Prices» due to landings prices exceeding fishing costs at
the socially optimal level of resource use.
In tackling over-exploitation problems, the feasibility and relative efficiency of demand-side measures in attaining management objectives without necessitating introduction of other fishing rights is discussed. Distributional issues associated with using a market mechanism to allocate use rights and potential adoption of demand-side measures within a co-management framework are considered.
Despite apparently desirable properties, solutions based upon demand-side regulation have been much neglected in the literature, and rarely put into practice. Discussion of such systems provides a contribution towards the continuing debate regarding how best to improve fisheries management, to ensure that economic rents are neither purely dissipated, nor simply captured by a first generation of resource users
Excitation spectrum of Bilayer Quantum Hall Systems
Excitation spectra in bilayer quantum Hall systems at total Landau-level
filling are studied by the Hartree-Fock-Bogoliubov approximation. The
systems have the spin degrees of freedom in addition to the layer degrees of
freedom described in terms of pseudospin. On the excitation spectra from
spin-unpolarized and pseudospin-polarized ground state, this approximation
fully preserves the spin rotational symmetry and thus can give not only
spin-triplet but also spin-singlet excitations systematically. It is also found
that the ground-state properties are well described by this approximation.Comment: 5 pages, 3 figures; conference: EP2DS-1
Symmetry-Projected Hartree-Fock-Bogoliubov Equations
Symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations are derived using
the variational ansatz for the generalized one-body density-matrix in the
Valatin form. It is shown that the projected-energy functional can be
completely expressed in terms of the HFB density-matrix and the pairing-tensor.
The variation of this projected-energy is shown to result in HFB equations with
modified expressions for the pairing-potential and the Hartree-Fock field. The
expressions for these quantities are explicitly derived for the case of
particle number-projection. The numerical applicability of this projection
method is studied in an exactly soluble model of a deformed single-j shell.Comment: 24 pages, 1 figur
Lowest Landau-level description of a Bose-Einstein condensate in a rapidly rotating anisotropic trap
A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional
trap can be described with the lowest Landau-level set of states. In this case,
the condensate wave function psi(x,y) is a Gaussian function of r^2 = x^2 +
y^2, multiplied by an analytic function P(z) of the single complex variable z=
x+ i y; the zeros of P(z) denote the positions of the vortices. Here, a similar
description is used for a rapidly rotating anisotropic two-dimensional trap
with arbitrary anisotropy (omega_x/omega_y le 1). The corresponding condensate
wave function psi(x,y) has the form of a complex anisotropic Gaussian with a
phase proportional to xy, multiplied by an analytic function P(zeta), where
zeta is proportional to x + i beta_- y and 0 le beta_- le 1 is a real parameter
that depends on the trap anisotropy and the rotation frequency. The zeros of
P(zeta) again fix the locations of the vortices. Within the set of lowest
Landau-level states at zero temperature, an anisotropic parabolic density
profile provides an absolute minimum for the energy, with the vortex density
decreasing slowly and anisotropically away from the trap center.Comment: 13 pages, 1 figur
The Coherence Field in the Field Perturbation Theory of Superconductivity
We re-examine the Nambu-Gorkov perturbation theory of superconductivity on
the basis of the Bogoliubov-Valatin quasi-particles. We show that two different
fields (and two additional analogous fields) may be constructed, and that the
Nambu field is only one of them. For the other field- the coherence field- the
interaction is given by means of two interaction vertices that are based on the
Pauli matrices tau1 and tau3. Consequently, the Hartree integral for the
off-diagonal pairing self-energy may be finite, and in some cases large. We
interpret the results in terms of conventional superconductivity, and also
discuss briefly possible implications to HTSC
Self-consistency and collective effects in semiclassical pairing theory
A simple model, in which nuclei are represented as homogeneous spheres of
symmetric nuclear matter, is used to study the effects of a self-consistent
pairing interaction on the nuclear response. Effects due to the finite size of
nuclei are suitably taken into account. The semiclassical equations of motion
derived in a previous paper for the time-dependent Hartree-Fock-Bogoliubov
problem are solved in an improved (linear) approximation in which the pairing
field is allowed to oscillate and to become complex. The new solutions are in
good agreement with the old ones and also with the result of well-known quantum
approaches. The role of the Pauli principle in eliminating one possible set of
solutions is also discussed. The pairing-field fluctuations have two main
effects: they restore the particle-number symmetry which is broken in the
constant- approximation and introduce the possibility of collective
eigenfrequencies of the system due to the pairing interaction. A numerical
study with values of parameters appropriate for nuclei, shows an enhancement of
the density-density strength function in the region of the low-energy giant
octupole resonance, while no similar effect is present in the region of the
high-energy octupole resonance and for the giant monopole and quadrupole
resonances.Comment: 31 pages, 6 eps figure
Inequivalent representations of commutator or anticommutator rings of field operators and their applications
Hamiltonian of a system in quantum field theory can give rise to infinitely
many partition functions which correspond to infinitely many inequivalent
representations of the canonical commutator or anticommutator rings of field
operators. This implies that the system can theoretically exist in infinitely
many Gibbs states. The system resides in the Gibbs state which corresponds to
its minimal Helmholtz free energy at a given range of the thermodynamic
variables. Individual inequivalent representations are associated with
different thermodynamic phases of the system. The BCS Hamiltonian of
superconductivity is chosen to be an explicit example for the demonstration of
the important role of inequivalent representations in practical applications.
Its analysis from the inequivalent representations' point of view has led to a
recognition of a novel type of the superconducting phase transition.Comment: 25 pages, 6 figure
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