The Valuation of Private Firms

Feldman, Stanley

doi:10.1002/9780470404324.hof003035

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…One can also use a more elementary argument briefly explained in [11]: the first Chern class of E {n Γ } is the same as the first Chern class of the line bundle Λ r E {n Γ } , where r is the rank of E {n Γ } and the latter bundle is necessarily trivial because the ring of regular algebraic functions on C * × C * is a Unique Factorization Domain. Or one can use an even more elementary deformation argument which directly shows that the Chern classes of any algebraic vector bundle on C * × C * are trivial [12].…”

Section: The Vanishing Of the Chern Numbermentioning

confidence: 99%

Local Commuting Projector Hamiltonians and the Quantum Hall Effect

Kapustin

Fidkowski

2019

Commun. Math. Phys.

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Section: The Vanishing Of the Chern Numbermentioning

confidence: 99%

Local Commuting Projector Hamiltonians and the Quantum Hall Effect

Kapustin

Fidkowski

2019

Commun. Math. Phys.

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“…While the compressed PH-Pfaffian state blows a life to the PH-Pfaffian topological order numerically, a question was raised if the finite size result will survive in the thermal dynamic limit as one would think two quasiparticles in the ground state would make no difference in the thermal dynamic limit [20] [21]. It is the main purpose of this brief report to address this apparent "two quasiparticles" thermal dynamic shortcoming with a more elegant resolution.…”

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confidence: 97%

A Hafnian PH-Pfaffian State for 5/2 Quantum Hall Effect

Yang¹

2022

Preprint

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The PH-Pfaffian state having 1/2 central charge is consistent with the thermal Hall conductance measurement of ν = 5/2 fractional quantum Hall system, but lacks support from the existing numerical results. In this report we propose a new state described by the wave function(zi − zj) 2 , with P f (A) being the Pfaffian of an antisymmetric matrix A. We call this new state the incompressible PH-Pfaffian state, as it is formed by increasing the relative angular momentum by two for each of the paired composite fermions of the PH-Pfaffian state (as seen from the numerator (zi − zj ) 2 inside the Pfaffian symbol P f ), making the PH-Pfaffian state from possibly compressible to incompressible. We argue that while the incompressible PH-Pfaffian state is distinct, it has the same central charge as the PH-Pfaffian state, and is therefore consistent with the thermal Hall conductance measurement. In spherical geometry, the incompressible PH-Pfaffian state has the same magnetic flux number N φ = 2N + 1 as the anti-Pfaffian state, allowing a direct numerical comparison between the two states. Results of exact diagonalization of finite systems in the second Landau level show that, by increasing the short range component of the Coulomb interaction, the ground state undergoes a phase transition from the anti-Pfaffian state to the incompressible PH-Pfaffian state, thus providing the numerical support to the latter.

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The Valuation of Private Firms

Cited by 2 publications

References 9 publications

Local Commuting Projector Hamiltonians and the Quantum Hall Effect

Local Commuting Projector Hamiltonians and the Quantum Hall Effect

A Hafnian PH-Pfaffian State for 5/2 Quantum Hall Effect

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