scholarly journals Exponential upper bounds on the spectral gaps and homogeneous spectrum for the non-critical extended Harper's model

2020 ◽  
Vol 40 (8) ◽  
pp. 4777-4800
Author(s):  
Xu Xu ◽  
◽  
Xin Zhao ◽  
Keyword(s):  
Upper Bounds ◽  
Spectral Gaps ◽  
Homogeneous Spectrum

scholarly journals BLOCK-DIAGONALIZATION OF OPERATORS WITH GAPS, WITH APPLICATIONS TO DIRAC OPERATORS

2012 ◽  
Vol 24 (08) ◽  
pp. 1250021 ◽  
Author(s):  
JEAN-CLAUDE CUENIN
Keyword(s):  
Euclidean Space ◽  
Nuclear Charge ◽  
Chemical Elements ◽  
Three Dimensional ◽  
Dirac Operators ◽  
Upper Bounds ◽  
Exact Diagonalization ◽  
Dimensional Euclidean Space ◽  
Spectral Gaps ◽  
Block Diagonalization

We present new results on the block-diagonalization of operators with spectral gaps, based on a method of Langer and Tretter, and apply them to Dirac operators on three-dimensional Euclidean space with unbounded potentials. For the Coulomb potential, we achieve an exact diagonalization up to nuclear charge Z = 124 (which covers all chemical elements) and prove the convergence of an approximate block-diagonalization up to Z = 62, thus considerably improving the upper bounds Z = 93 and Z = 51, respectively, established by Siedentop and Stockmeyer.

scholarly journals Sequences of information backflow in local dephasing channels with spectral gaps

2017 ◽  
Vol 15 (07) ◽  
pp. 1750050 ◽  
Author(s):  
Filippo Giraldi
Keyword(s):  
Quantum Information ◽  
Spectral Gap ◽  
Infinite Sequence ◽  
Low Frequency ◽  
Upper Bounds ◽  
Spectral Gaps ◽  
Time Intervals ◽  
Low Frequencies ◽  
Regular Sequences ◽  
Long Time

The flow of quantum information in local dephasing channels is analyzed over short and long times in case the structured reservoir of frequency modes exhibits a spectral gap in the density of modes over low frequencies. The presence of the low-frequency gap with upper cut-off frequency [Formula: see text] produces an infinite sequence of long-time intervals over which information backflow appears. Though generally irregular, the time intervals exhibit, under certain conditions, upper bounds: the [Formula: see text]th episode of information backflow has already started at the instant [Formula: see text], and already ended at the instant [Formula: see text], for every [Formula: see text]. The intervals become regular over long times, tend to the asymptotic length [Formula: see text], as the supremum value, and are described analytically in terms of the structure of the spectral density near the upper cut-off frequency of the spectral gap. Consequently, engineering structured reservoirs of frequency modes with a spectral gap over low frequencies produces in local dephasing channels regular sequences of information backflow and recoherence over long times, along with non-Markovian evolution.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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