36,531 research outputs found
Explicit Representations for the T-Matrix on Unphysical Energy Sheets and Resonances in Two- and Three-Body Systems
We discuss the structure of the two- and three-body T-matrices, scattering
matrices, and resolvents continued to the unphysical energy sheets. Our
conclusions arise due to the representations that have been found for
analytically continued momentum-space kernels of the T-operators. These
representations are explicitly written only in terms of the physical-sheet
kernels of the T-matrix itself. One of advantages of the representations in the
three-body case is that they show which portions of the physical-sheet
three-body scattering matrix are ``responsible'' for the resonances associated
with a particular unphysical sheet. A resonance appears to be the energy where
the correspondingly truncated scattering matrix (taken on the physical sheet)
has eigenvalue zero. We also mention applications of this approach to some
specific three-body systems, based on the Faddeev differential equations.Comment: Based on a lecture given at the International Workshop ``Critical
Stability of Few-Body Quantum Systems'' (Dresden, October 17--22, 2005
Wine Taxes, Production, Aging and Quality
We consider the impact of taxes on the quantity and quality produced of goods, such as wine, for which market value accrues with age by a competitive producer. Any pair of taxes that includes a volumetric sales tax and any one of three other types of tax – an ad valorem sales tax, an ad valorem storage tax, or a volumetric storage tax – spans the full range of feasible tax revenues with positive tax rates. For any tax system that reduces quality relative to the firm’s no-tax equilibrium, there is another tax system that increases tax revenues, eliminates the quality distortion, and does not increase the quantity distortion. Many wine industry observers believe that most, if not all, existing tax systems tend to result in the suboptimal provision of quality. Our results suggest that the wide variety of wine tax systems is not prima facie evidence that these systems, or most of them, are inefficient. Provided the system includes a volumetric sales tax it may be efficient, regardless of which of the other instruments, or how many of them, are used. Assertions regarding inefficiency must be evaluated on an empirical case-by-case basis. Our analysis provides a theoretical framework for such research.aging, Alchian-Allen effect, tax policy, wine
Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking
We describe a family of phase transitions connecting phases of differing
non-trivial topological order by explicitly constructing Hamiltonians of the
Levin-Wen[PRB 71, 045110] type which can be tuned between two solvable points,
each of which realizes a different topologically ordered phase. We show that
the low-energy degrees of freedom near the phase transition can be mapped onto
those of a Potts model, and we discuss the stability of the resulting phase
diagram to small perturbations about the model. We further explain how the
excitations in the condensed phase are formed from those in the original
topological theory, some of which are split into multiple components by
condensation, and we discuss the implications of our results for understanding
the nature of general achiral topological phases in 2+1 dimensions in terms of
doubled Chern-Simons theories
Spinful Composite Fermions in a Negative Effective Field
In this paper we study fractional quantum Hall composite fermion
wavefunctions at filling fractions \nu = 2/3, 3/5, and 4/7. At each of these
filling fractions, there are several possible wavefunctions with different spin
polarizations, depending on how many spin-up or spin-down composite fermion
Landau levels are occupied. We calculate the energy of the possible composite
fermion wavefunctions and we predict transitions between ground states of
different spin polarizations as the ratio of Zeeman energy to Coulomb energy is
varied. Previously, several experiments have observed such transitions between
states of differing spin polarization and we make direct comparison of our
predictions to these experiments. For more detailed comparison between theory
and experiment, we also include finite-thickness effects in our calculations.
We find reasonable qualitative agreement between the experiments and composite
fermion theory. Finally, we consider composite fermion states at filling
factors \nu = 2+2/3, 2+3/5, and 2+4/7. The latter two cases we predict to be
spin polarized even at zero Zeeman energy.Comment: 17 pages, 5 figures, 4 tables. (revision: incorporated referee
suggestions, note added, updated references
Spin-correlations and magnetic structure in an Fe monolayer on 5d transition metal surfaces
We present a detailed first principles study on the magnetic structure of an
Fe monolayer on different surfaces of 5d transition metals. We use the
spin-cluster expansion technique to obtain parameters of a spin model, and
predict the possible magnetic ground state of the studied systems by employing
the mean field approach and in certain cases by spin dynamics calculations. We
point out that the number of shells considered for the isotropic exchange
interactions plays a crucial role in the determination of the magnetic ground
state. In the case of Ta substrate we demonstrate that the out-of-plane
relaxation of the Fe monolayer causes a transition from ferromagnetic to
antiferromagnetic ground state. We examine the relative magnitude of nearest
neighbour Dzyaloshinskii-Moriya (D) and isotropic (J) exchange interactions in
order to get insight into the nature of magnetic pattern formations. For the
Fe/Os(0001) system we calculate a very large D/J ratio, correspondingly, a spin
spiral ground state. We find that, mainly through the leading isotropic
exchange and Dzyaloshinskii-Moriya interactions, the inward layer relaxation
substantially influences the magnetic ordering of the Fe monolayer. For the
Fe/Re(0001) system characterized by large antiferromagnetic interactions we
also determine the chirality of the N\'eel-type ground state.Comment: 15 pages, 8 figures, 2 table
Hamilton's Turns for the Lorentz Group
Hamilton in the course of his studies on quaternions came up with an elegant
geometric picture for the group SU(2). In this picture the group elements are
represented by ``turns'', which are equivalence classes of directed great
circle arcs on the unit sphere , in such a manner that the rule for
composition of group elements takes the form of the familiar parallelogram law
for the Euclidean translation group. It is only recently that this construction
has been generalized to the simplest noncompact group , the double cover of SO(2,1). The present work develops a theory of
turns for , the double and universal cover of SO(3,1) and ,
rendering a geometric representation in the spirit of Hamilton available for
all low dimensional semisimple Lie groups of interest in physics. The geometric
construction is illustrated through application to polar decomposition, and to
the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late
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