2,271 research outputs found
Hamiltonian Formulation of Quantum Hall Skyrmions with Hopf Term
We study the nonrelativistic nonlinear sigma model with Hopf term in this
paper. This is an important issue beacuse of its relation to the currently
interesting studies in skyrmions in quantum Hall systems. We perform the
Hamiltonian analysis of this system in variables. When the coefficient
of the Hopf term becomes zero we get the Landau-Lifshitz description of the
ferromagnets. The addition of Hopf term dramatically alters the Hamiltonian
analysis. The spin algebra is modified giving a new structure and
interpretation to the system. We point out momentum and angular momentum
generators and new features they bring in to the system.Comment: 16pages, Latex file, typos correcte
Fermionic edge states and new physics
We investigate the properties of the Dirac operator on manifolds with
boundaries in presence of the Atiyah-Patodi-Singer boundary condition. An exact
counting of the number of edge states for boundaries with isometry of a sphere
is given. We show that the problem with the above boundary condition can be
mapped to one where the manifold is extended beyond the boundary and the
boundary condition is replaced by a delta function potential of suitable
strength. We also briefly highlight how the problem of the self-adjointness of
the operators in the presence of moving boundaries can be simplified by
suitable transformations which render the boundary fixed and modify the
Hamiltonian and the boundary condition to reflect the effect of moving
boundary.Comment: 24 pages, 3 figures. Title changed, additional material in the
Introduction section, the Application section and in the Discussion section
highlighting some recent work on singular potentials, several references
added. Conclusions remain unchanged. Version matches the version to appear in
PR
Representations of Composite Braids and Invariants for Mutant Knots and Links in Chern-Simons Field Theories
We show that any of the new knot invariants obtained from Chern-Simons theory
based on an arbitrary non-abelian gauge group do not distinguish isotopically
inequivalent mutant knots and links. In an attempt to distinguish these knots
and links, we study Murakami (symmetrized version) -strand composite braids.
Salient features of the theory of such composite braids are presented.
Representations of generators for these braids are obtained by exploiting
properties of Hilbert spaces associated with the correlators of Wess-Zumino
conformal field theories. The -composite invariants for the knots are given
by the sum of elementary Chern-Simons invariants associated with the
irreducible representations in the product of representations (allowed by
the fusion rules of the corresponding Wess-Zumino conformal field theory)
placed on the individual strands of the composite braid. On the other hand,
composite invariants for links are given by a weighted sum of elementary
multicoloured Chern-Simons invariants. Some mutant links can be distinguished
through the composite invariants, but mutant knots do not share this property.
The results, though developed in detail within the framework of
Chern-Simons theory are valid for any other non-abelian gauge group.Comment: Latex, 25pages + 16 diagrams available on reques
Chirality of Knots and and Chern-Simons Theory
Upto ten crossing number, there are two knots, and whose
chirality is not detected by any of the known polynomials, namely, Jones
invariants and their two variable generalisations, HOMFLY and Kauffman
invariants. We show that the generalised knot invariants, obtained through
Chern-Simons topological field theory, which give the known polynomials
as special cases, are indeed sensitive to the chirality of these knots.Comment: 15 pages + 7 diagrams (available on request
Preemptive Thread Block Scheduling with Online Structural Runtime Prediction for Concurrent GPGPU Kernels
Recent NVIDIA Graphics Processing Units (GPUs) can execute multiple kernels
concurrently. On these GPUs, the thread block scheduler (TBS) uses the FIFO
policy to schedule their thread blocks. We show that FIFO leaves performance to
chance, resulting in significant loss of performance and fairness. To improve
performance and fairness, we propose use of the preemptive Shortest Remaining
Time First (SRTF) policy instead. Although SRTF requires an estimate of runtime
of GPU kernels, we show that such an estimate of the runtime can be easily
obtained using online profiling and exploiting a simple observation on GPU
kernels' grid structure. Specifically, we propose a novel Structural Runtime
Predictor. Using a simple Staircase model of GPU kernel execution, we show that
the runtime of a kernel can be predicted by profiling only the first few thread
blocks. We evaluate an online predictor based on this model on benchmarks from
ERCBench, and find that it can estimate the actual runtime reasonably well
after the execution of only a single thread block. Next, we design a thread
block scheduler that is both concurrent kernel-aware and uses this predictor.
We implement the SRTF policy and evaluate it on two-program workloads from
ERCBench. SRTF improves STP by 1.18x and ANTT by 2.25x over FIFO. When compared
to MPMax, a state-of-the-art resource allocation policy for concurrent kernels,
SRTF improves STP by 1.16x and ANTT by 1.3x. To improve fairness, we also
propose SRTF/Adaptive which controls resource usage of concurrently executing
kernels to maximize fairness. SRTF/Adaptive improves STP by 1.12x, ANTT by
2.23x and Fairness by 2.95x compared to FIFO. Overall, our implementation of
SRTF achieves system throughput to within 12.64% of Shortest Job First (SJF, an
oracle optimal scheduling policy), bridging 49% of the gap between FIFO and
SJF.Comment: 14 pages, full pre-review version of PACT 2014 poste
Information from quantum blackhole physics
The study of BTZ blackhole physics and the cosmological horizon of 3D de
Sitter spaces are carried out in unified way using the connections to the Chern
Simons theory on three manifolds with boundary. The relations to CFT on the
boundary is exploited to construct exact partition functions and obtain
logarithmic corrections to Bekenstein formula in the asymptotic regime.
Comments are made on the dS/CFT correspondence frising from these studies.Comment: 11 pages; 1 figure(eps file);Talk presented at the conference
Space-time and Fundamental Interactions: Quantum Aspects'' in honour of A.P.
Balachandran's 65th birthday, Vietri sul Mare, Salerno, Italy 26th-31st May,
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