Exact mapping from singular value spectrum of a class of fractal images to entanglement spectrum of one-dimensional free fermions

2015 ◽  
Author(s):  
Hiroaki Matsueda ◽  
Ching Hua Lee
Keyword(s):  
Singular Value ◽  
Free Fermions ◽  
One Dimensional ◽  
Entanglement Spectrum ◽  
Fractal Images

Singular value decomposition for cross‐well tomography

Geophysics ◽  
1993 ◽  
Vol 58 (11) ◽  
pp. 1655-1661 ◽  
Author(s):  
Reinaldo J. Michelena
Keyword(s):  
Singular Value Decomposition ◽  
Null Space ◽  
Vertical Component ◽  
Singular Values ◽  
Singular Value ◽  
Velocity Estimation ◽  
One Dimensional ◽  
Anisotropic Models ◽  
Value Decomposition ◽  
Frequency Variations

I perform singular value decomposition (SVD) on the matrices that result in tomographic velocity estimation from cross‐well traveltimes in isotropic and anisotropic media. The slowness model is parameterized in four ways: One‐dimensional (1-D) isotropic, 1-D anisotropic, two‐dimensional (2-D) isotropic, and 2-D anisotropic. The singular value distribution is different for the different parameterizations. One‐dimensional isotropic models can be resolved well but the resolution of the data is poor. One‐dimensional anisotropic models can also be resolved well except for some variations in the vertical component of the slowness that are not sensitive to the data. In 2-D isotropic models, “pure” lateral variations are not sensitive to the data, and when anisotropy is introduced, the result is that the horizontal and vertical component of the slowness cannot be estimated with the same spatial resolution because the null space is mostly related to horizontal and high frequency variations in the vertical component of the slowness. Since the distribution of singular values varies depending on the parametrization used, the effect of conventional regularization procedures in the final solution may also vary. When the model is isotropic, regularization translates into smoothness, and when the model is anisotropic regularization not only smooths but may also alter the anisotropy in the solution.

scholarly journals Casimir effect in a one-dimensional gas of free fermions

2008 ◽  
Vol 78 (2) ◽  
Author(s):  
Eugene B. Kolomeisky ◽  
Joseph P. Straley ◽  
Michael Timmins
Keyword(s):  
Casimir Effect ◽  
Free Fermions ◽  
One Dimensional

scholarly journals Extended Conformal Symmetry of the One-Dimensional Bose Gas

1997 ◽  
Vol 12 (29) ◽  
pp. 2153-2159 ◽  
Author(s):  
Milena Maule ◽  
Stefano Sciuto
Keyword(s):  
Cartan Subalgebra ◽  
Conformal Symmetry ◽  
Hard Core ◽  
Bose Gas ◽  
Effective Hamiltonian ◽  
Coupling Constant ◽  
Free Fermions ◽  
One Dimensional ◽  
First Order ◽  
The One

We show that the low-lying excitations of the one-dimensional Bose gas are described, at all orders in a 1/N expansion and at the first order in the inverse of the coupling constant, by an effective Hamiltonian written in terms of an extended conformal algebra, namely the Cartan subalgebra of the [Formula: see text] algebra. This enables us to construct the first interaction term which corrects the Hamiltonian of the free fermions equivalent to a hard-core boson system.

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