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Quantum Correlations and Topological Quantum Numbers in the Fractional Quantum Hall Effect [PDF]

Berichte der Bunsengesellschaft für physikalische Chemie, 1993
AbstractIt is demonstrated that the fractional Hall plateaux, experimentally observed in some nearly ideal samples at very low temperatures, are manifestations of strongly correlated objects explicitly connected with Coleman's extreme case and Yang's concept of off‐diagonal long‐range order (ODLRO). This interpretation yields (n – 1)/(2n – 1), n = 2,3,…
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CONSERVATION OF TOPOLOGICAL QUANTUM NUMBERS IN ENERGY BANDS

Modern Physics Letters A, 1988
Quantum systems described by parametrized Hamiltonians are studied in a general context. Within this context, the classification scheme of Avron-Seiler-Simon for non-degenerate energy bands is extended to cover general parameter spaces, while their sum rule is generalized to cover cases with degenerate bands as well.
Yi-gao Liang, Lay Nam Chang
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Topological Quantum Numbers in Nonrelativistic Physics

International Journal of Modern Physics B, 1997
Voltage measurements using the ac Josephson effect and electrical resistance measurements using the quantum Hall effect are capable of very high precision, despite the relatively poor control of details of the devices. Such measurements rely on topological quantum numbers, which, unlike symmetry-based quantum numbers, are insensitive to deviations of ...
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Introduction to Topological Quantum Numbers

2007
These lecture notes were prepared rather soon after I completed my book on Topological quantum numbers in nonrelativistic physics, which was published by World Scientific Publishing Co. Pte. Ltd., Singapore, in early 1998. I have not attempted to make a completely fresh presentation, but have cannibalized the text of my book to produce something ...
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Shift and Spin Vector: New Topological Quantum Numbers for the Hall Fluids

Physical Review Letters, 1992
We discuss some new quantum numbers (spin vector) for the Hall fluid, representing orbital spin degrees of freedom. We show that the spin vectors are quantized. In the absence of impurites, two Hall fluids with different spin vectors cannot change into each other without a phase transition and closing of the energy gap. In principle the spin vector can
A. Zee, X. G. Wen
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Topological Quantum Numbers of m-Particle Systems

1998
The category of topological spaces and continuous maps is an important conception in theoretical physics. Topological spaces appear in many situations, e. g. as a configuration space or as a state space of a classical or quantum mechanical system, and the elements of these spaces carry information about observable properties of the system.
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Quantum Jacobi forms in number theory, topology, and mathematical physics

Research in the Mathematical Sciences, 2019
We establish three infinite families of quantum Jacobi forms, arising in the diverse areas of number theory, topology, and mathematical physics, and unified by partial Jacobi theta functions.
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How Topological Concepts Lead to Quantum Numbers for Baryons

1985
Strong interaction physics is currently believed to be determined by quantum chromodynamics. If this is correct, then it follows that all of nuclear physics must, somehow, be a consequence. Unravelling these consequences will be a daunting task, for nuclear physics is the regime of longdistances (on the scale of ΛQCD) and it is precisely here that the ...
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High winding number of topological phase in non-unitary periodic quantum walk*

, 2021
Yali Jia, Zhi-Jian Li
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Gravity as Topological Charge Leakage: A Prime Number Approach to Quantum Spacetime

We propose a unified model where gravity emerges from topological charge leakagebetween real and complex sectors of a CY7 manifold (”hourglass spacetime”).Particles correspond to prime-numbered topological defects (p ∈ P), with massesmp ∼ ln p. The Riemann zeta zeros γn quantize gravitational couplings.
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