65 research outputs found
Geometric Algebra and Star Products on the Phase Space
Superanalysis can be deformed with a fermionic star product into a Clifford
calculus that is equivalent to geometric algebra. With this multivector
formalism it is then possible to formulate Riemannian geometry and an
inhomogeneous generalization of exterior calculus. Moreover it is shown here
how symplectic and Poisson geometry fit in this context. The application of
this formalism together with the bosonic star product formalism of deformation
quantization leads then on space and space-time to a natural appearance of spin
structures and on phase space to BRST structures that were found in the path
integral formulation of classical mechanics. Furthermore it will be shown that
Poincare and Lie-Poisson reduction can be formulated in this formalism.Comment: 35 page
On the pattern of Casimir scaling violation in gluodynamics
Results of lattice analysis indicate that the static potential in SU(3) gauge
theory is proportional to eigenvalue of quadratic Casimir operator for the
corresponding representation with a good accuracy. We discuss the mechanism of
possible deviations from the Casimir scaling in gluodynamics in terms of
correlators of path-ordered gauge-invariant operators defined on the worldsheet
of the confining string.Comment: LaTeX, 12 pages, no figure
Spin-Blockade in Single and Double Quantum Dots in Magnetic Fields: a Correlation Effect
The total spin of correlated electrons in a quantum dot changes with magnetic
field and this effect is generally linked to the change in the total angular
momentum from one magic number to another, which can be understood in terms of
an `electron molecule' picture for strong fields. Here we propose to exploit
this fact to realize a spin blockade, i.e., electrons are prohibited to tunnel
at specific values of the magnetic field. The spin-blockade regions have been
obtained by calculating both the ground and excited states. In double dots the
spin-blockade condition is found to be less stringent than in single dots.Comment: 4pages, to be published in Phys. Rev. B (Rapid Communication
Magic Numbers and Optical Absorption Spectrum in Vertically Coupled Quantum Dots in the Fractional Quantum Hall Regime
Exact diagonalization is used to study the quantum states of vertically
coupled quantum dots in strong magnetic fields. We find a new sequence of
angular momentum magic numbers which are a consequence of the electron
correlation in the double dot. The new sequence occurs at low angular momenta
and changes into the single dot sequence at a critical angular momentum
determined by the strength of the inter-dot electron tunneling. We also propose
that the magic numbers can be investigated experimentally in vertically coupled
dots. Because of the generalized Kohn theorem, the far-infrared optical
absorption spectrum of a single dot is unaffected by correlation but the
theorem does not hold for two vertically coupled dots which have different
confining potentials. We show that the absorption energy of the double dot
should exhibit discontinuities at the magnetic fields where the total angular
momentum changes from one magic number to another.Comment: 4 pages, 3 Postscript figures, RevTeX. (to appear in Phys.Rev.B
Vertically coupled double quantum dots in magnetic fields
Ground-state and excited-state properties of vertically coupled double
quantum dots are studied by exact diagonalization. Magic-number total angular
momenta that minimize the total energy are found to reflect a crossover between
electron configurations dominated by intra-layer correlation and ones dominated
by inter-layer correlation. The position of the crossover is governed by the
strength of the inter-layer electron tunneling and magnetic field. The magic
numbers should have an observable effect on the far infra-red optical
absorption spectrum, since Kohn's theorem does not hold when the confinement
potential is different for two dots. This is indeed confirmed here from a
numerical calculation that includes Landau level mixing. Our results take full
account of the effect of spin degrees of freedom. A key feature is that the
total spin, , of the system and the magic-number angular momentum are
intimately linked because of strong electron correlation. Thus jumps hand
in hand with the total angular momentum as the magnetic field is varied. One
important consequence of this is that the spin blockade (an inhibition of
single-electron tunneling) should occur in some magnetic field regions because
of a spin selection rule. Owing to the flexibility arising from the presence of
both intra-layer and inter-layer correlations, the spin blockade is easier to
realize in double dots than in single dots.Comment: to be published in Phys. Rev. B1
Method to compute the stress-energy tensor for the massless spin 1/2 field in a general static spherically symmetric spacetime
A method for computing the stress-energy tensor for the quantized, massless,
spin 1/2 field in a general static spherically symmetric spacetime is
presented. The field can be in a zero temperature state or a non-zero
temperature thermal state. An expression for the full renormalized
stress-energy tensor is derived. It consists of a sum of two tensors both of
which are conserved. One tensor is written in terms of the modes of the
quantized field and has zero trace. In most cases it must be computed
numerically. The other tensor does not explicitly depend on the modes and has a
trace equal to the trace anomaly. It can be used as an analytic approximation
for the stress-energy tensor and is equivalent to other approximations that
have been made for the stress-energy tensor of the massless spin 1/2 field in
static spherically symmetric spacetimes.Comment: 34 pages, no figure
BPS States in Omega Background and Integrability
We reconsider string and domain wall central charges in N=2 supersymmetric
gauge theories in four dimensions in presence of the Omega background in the
Nekrasov-Shatashvili (NS) limit. Existence of these charges entails presence of
the corresponding topological defects in the theory - vortices and domain
walls. In spirit of the 4d/2d duality we discuss the worldsheet low energy
effective theory living on the BPS vortex in N=2 Supersymmetric Quantum
Chromodynamics (SQCD). We discuss some aspects of the brane realization of the
dualities between various quantum integrable models. A chain of such dualities
enables us to check the AGT correspondence in the NS limit.Comment: 48 pages, 10 figures, minor changes, references added, typos
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