Approximate non-paired spatial orbital approach to a regular one-dimensional lattice structure

1974 ◽  
Vol 70 ◽  
pp. 339
Author(s):  
Brian J. Duke
Keyword(s):  
Lattice Structure ◽  
Dimensional Lattice ◽  
One Dimensional

scholarly journals A Novel Bulk-Optics Scheme for Quantum Walk with High Phase Stability

2019 ◽  
Vol 4 (1) ◽  
pp. 14 ◽  
Author(s):  
Andrea Geraldi ◽  
Luís Bonavena ◽  
Carlo Liorni ◽  
Paolo Mataloni ◽  
Álvaro Cuevas
Keyword(s):  
Phase Stability ◽  
Closed Loop ◽  
Lattice Structure ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Phase Component ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Experimental Implementation ◽  
High Phase

A novel bulk optics scheme for quantum walks is presented. It consists of a one-dimensional lattice built on two concatenated displaced Sagnac interferometers that make it possible to reproduce all the possible trajectories of an optical quantum walk. Because of the closed loop configuration, the interferometric structure is intrinsically stable in phase. Moreover, the lattice structure is highly configurable, as any phase component perceived by the walker is accessible, and finally, all output modes can be measured at any step of the quantum walk evolution. We report here on the experimental implementation of ordered and disordered quantum walks.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

One-Dimensional Lattice Model of Superradiance

1984 ◽  
pp. 503-506
Author(s):  
V. Benza ◽  
E. Montaldi ◽  
M. Ciftan
Keyword(s):  
Lattice Model ◽  
Dimensional Lattice ◽  
One Dimensional
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