202 research outputs found
Group Theory Approach to Band Structure: Scarf and Lame Hamiltonians
The group theoretical treatment of bound and scattering state problems is
extended to include band structure. We show that one can realize Hamiltonians
with periodic potentials as dynamical symmetries, where representation theory
provides analytic solutions, or which can be treated with more general spectrum
generating algebraic methods. We find dynamical symmetries for which we derive
the transfer matrices and dispersion relations. Both compact and non-compact
groups are found to play a role.Comment: 4 pages + 2 figs. Revtex/epsf. To appear: Phys Rev Lett, v.83 199
On the chiral anomaly in non-Riemannian spacetimes
The translational Chern-Simons type three-form coframe torsion on a
Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan
four-form. Following Chandia and Zanelli, two spaces with non-trivial
translational Chern-Simons forms are discussed. We then demonstrate, firstly
within the classical Einstein-Cartan-Dirac theory and secondly in the quantum
heat kernel approach to the Dirac operator, how the Nieh-Yan form surfaces in
both contexts, in contrast to what has been assumed previously.Comment: 18 pages, RevTe
Kondo tunneling through real and artificial molecules
When a cerocene molecule is chemisorbed on metallic substrate, or when an
asymmetric double dot is hybridized with itinerant electrons, its singlet
ground state crosses its lowly excited triplet state, leading to a competition
between the Zhang-Rice mechanism of singlet-triplet splitting in a confined
cluster and the Kondo effect (which accompanies the tunneling through quantum
dot under a Coulomb blockade restriction). The rich physics of an underscreened
S=1 Kondo impurity in the presence of low-lying triplet/singlet excitations is
exposed. Estimates of the magnetic susceptibility and the electric conductance
are presented.Comment: 4 two-column revtex pages including 1 eps figur
Kondo effect in systems with dynamical symmetries
This paper is devoted to a systematic exposure of the Kondo physics in
quantum dots for which the low energy spin excitations consist of a few
different spin multiplets . Under certain conditions (to be
explained below) some of the lowest energy levels are nearly
degenerate. The dot in its ground state cannot then be regarded as a simple
quantum top in the sense that beside its spin operator other dot (vector)
operators are needed (in order to fully determine its quantum
states), which have non-zero matrix elements between states of different spin
multiplets . These "Runge-Lenz"
operators do not appear in the isolated dot-Hamiltonian (so in some sense they
are "hidden"). Yet, they are exposed when tunneling between dot and leads is
switched on. The effective spin Hamiltonian which couples the metallic electron
spin with the operators of the dot then contains new exchange terms,
beside the ubiquitous ones . The operators and generate a
dynamical group (usually SO(n)). Remarkably, the value of can be controlled
by gate voltages, indicating that abstract concepts such as dynamical symmetry
groups are experimentally realizable. Moreover, when an external magnetic field
is applied then, under favorable circumstances, the exchange interaction
involves solely the Runge-Lenz operators and the corresponding
dynamical symmetry group is SU(n). For example, the celebrated group SU(3) is
realized in triple quantum dot with four electrons.Comment: 24 two-column page
World Spinors - Construction and Some Applications
The existence of a topological double-covering for the and
diffeomorphism groups is reviewed. These groups do not have finite-dimensional
faithful representations. An explicit construction and the classification of
all , unitary irreducible representations is presented.
Infinite-component spinorial and tensorial fields,
"manifields", are introduced. Particle content of the ladder manifields, as
given by the "little" group is determined. The manifields are
lifted to the corresponding world spinorial and tensorial manifields by making
use of generalized infinite-component frame fields. World manifields transform
w.r.t. corresponding representations, that are constructed
explicitly.Comment: 19 pages, Te
UNDERSTANDING THE SCALAR MESON NONET
It is shown that one can fit the available data on the a0(980), f0(980),
f0(1300) and K*0(1430) mesons as a distorted 0++ qq bar nonet using very few
(5-6) parameters and an improved version of the unitarized quark model. This
includes all light two-pseudoscalar thresholds, constraints from Adler zeroes,
flavour symmetric couplings, unitarity and physically acceptable analyticity.
The parameters include a bare uu bar or dd bar mass, an over-all coupling
constant, a cutoff and a strange quark mass of 100 MeV, which is in accord with
expectations from the quark model.
It is found that in particular for the a0(980) and f0(980) the KK bar
component in the wave function is large, i.e., for a large fraction of the time
the qq bar state is transformed into a virtual KK bar pair. This KK bar
component, together with a similar component of eta' pi for the a0(980) , and
eta eta, eta eta' and eta' eta' components for the f0(980), causes the
substantial shift to a lower mass than what is naively expected from the qq bar
component alone.
Mass, width and mixing parameters, including sheet and pole positions, of the
four resonances are given, with a detailed pedagogical discussion of their
meaning.Comment: 35 pages in plain latex (ZPC in press), 10 figures obtainable from
the author ([email protected]) with regular mail or as a large PS
fil
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