11,692 research outputs found
Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows
Rotating shear flows, when angular momentum increases and angular velocity
decreases as functions of radiation coordinate, are hydrodynamically stable
under linear perturbation. The Keplerian flow is an example of such systems
which appears in astrophysical context. Although decaying eigenmodes exhibit
large transient energy growth of perturbation which could govern nonlinearity
into the system, the feedback of inherent instability to generate turbulence
seems questionable. We show that such systems exhibiting growing
pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the
logarithmic norm of the involved nonnormal operators, thus exhibiting feedback
of inherent instability. This supports the existence of turbulence of
hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence,
this enlightens the mismatch between the linear theory and
experimental/observed data and helps in resolving the outstanding question of
origin of turbulence therein.Comment: 12 pages including 4 figures; to appear in New Journal of Physic
Dynamical supersymmetry analysis of conformal invariance for superstrings in type IIB R-R plane-wave
In a previous work (arXiv:0902.3750 [hep-th]) we studied the world-sheet
conformal invariance for superstrings in type IIB R-R plane-wave in
semi-light-cone gauge. Here we give further justification to the results found
in that work through alternative arguments using dynamical supersymmetries. We
show that by using the susy algebra the same quantum definition of the
energy-momentum (EM) tensor can be derived. Furthermore, using certain Jacobi
identities we indirectly compute the Virasoro anomaly terms by calculating
second order susy variation of the EM tensor. Certain integrated form of all
such terms are shown to vanish. In order to deal with various divergences that
appear in such computations we take a point-split definition of the same EM
tensor. The final results are shown not to suffer from the ordering ambiguity
as noticed in the previous work provided the coincidence limit is taken before
sending the regularization parameter to zero at the end of the computation.Comment: 18 pages, Appendix B replaced by shorter argument in text (section
2.1), one reference adde
All order covariant tubular expansion
We consider tubular neighborhood of an arbitrary submanifold embedded in a
(pseudo-)Riemannian manifold. This can be described by Fermi normal coordinates
(FNC) satisfying certain conditions as described by Florides and Synge in
\cite{FS}. By generalizing the work of Muller {\it et al} in \cite{muller} on
Riemann normal coordinate expansion, we derive all order FNC expansion of
vielbein in this neighborhood with closed form expressions for the curvature
expansion coefficients. Our result is shown to be consistent with certain
integral theorem for the metric proved in \cite{FS}.Comment: 27 pages. Corrected an error in a class of coefficients resulting
from a typo. Integral theorem and all other results remain unchange
DeWitt-Virasoro construction
We study a particular approach for analyzing worldsheet conformal invariance
for bosonic string propagating in a curved background using hamiltonian
formalism. We work in the Schrodinger picture of a single particle description
of the problem where the particle moves in an infinite-dimensional space.
Background independence is maintained in this approach by adopting DeWitt's
(Phys.Rev.85:653-661,1952) coordinate independent formulation of quantum
mechanics. This enables us to construct certain background independent notion
of Virasoro generators, called DeWitt-Virasoro (DWV) generators, and invariant
matrix elements of an arbitrary operator constructed out of them in spin-zero
representation. We show that the DWV algebra is given by the Witt algebra with
additional anomalous terms that vanish for Ricci-flat backgrounds. The actual
quantum Virasoro generators should be obtained by first introducing the vacuum
state and then normal ordering the DWV generators with respect to that. We
demonstrate the procedure in the simple cases of flat and pp-wave backgrounds.
This is a shorter version of arXiv:0912.3987 [hep-th] with many technical
derivations omitted.Comment: 18 pages, shorter version of arXiv:0912.3987 [hep-th] accepted for
publication in Pramana - Journal of Physic
Superstrings in type IIB R-R plane-wave in semi-light-cone gauge and conformal invariance
We reconsider the analysis done by Kazama and Yokoi in arXiv:0801.1561
(hep-th). We find that although the right vacuum of the theory is the one
associated to massless normal ordering (MNO), phase space normal ordering (PNO)
plays crucial role in the analysis in the following way. While defining the
quantum energy-momentum (EM) tensor one needs to take into account the field
redefinition relating the space-time field and the corresponding world-sheet
coupling. We argue that for a simple off-shell ansatz for the background this
field redefinition can be taken to be identity if the interaction term is
ordered according to PNO. This definition reproduces the correct physical
spectrum when the background is on-shell. We further show that the right way to
extract the effective equation of motion from the Virasoro anomaly is to first
order the anomaly terms according to PNO at a finite regularization parameter
\eps and then take the \eps \to 0 limit. This prescription fixes an
ambiguity in taking the limit for certain bosonic and fermionic contributions
to the Virasoro anomaly and is the natural one to consider given the above
definition of the EM tensor.Comment: 22 page
The Fractional Quantum Hall effect in an array of quantum wires
We demonstrate the emergence of the quantum Hall (QH) hierarchy in a 2D model
of coupled quantum wires in a perpendicular magnetic field. At commensurate
values of the magnetic field, the system can develop instabilities to
appropriate inter-wire electron hopping processes that drive the system into a
variety of QH states. Some of the QH states are not included in the
Haldane-Halperin hierarchy. In addition, we find operators allowed at any field
that lead to novel crystals of Laughlin quasiparticles. We demonstrate that any
QH state is the groundstate of a Hamiltonian that we explicitly construct.Comment: Revtex, 4 pages, 2 figure
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