Block Lanczos approach combined with matrix continued fraction for the S‐matrix Kohn variational principle in quantum scattering

1989 ◽  
Vol 91 (6) ◽  
pp. 3504-3508 ◽  
Author(s):  
Weitao Yang ◽  
William H. Miller
Keyword(s):  
Variational Principle ◽  
Continued Fraction ◽  
Quantum Scattering ◽  
S Matrix ◽  
Block Lanczos ◽  
Matrix Continued Fraction

scholarly journals Quantum scattering via the S‐matrix version of the Kohn variational principle

1988 ◽  
Vol 88 (10) ◽  
pp. 6233-6239 ◽  
Author(s):  
John Z. H. Zhang ◽  
Shih‐I. Chu ◽  
William H. Miller
Keyword(s):  
Variational Principle ◽  
Quantum Scattering ◽  
Matrix Version ◽  
S Matrix

scholarly journals Flow of S-matrix poles for elementary quantum potentials1This research was supported in part by an NSERC Undergraduate Summer Research Award (SGN) and an NSERC Discovery Grant (MAW).

2011 ◽  
Vol 89 (11) ◽  
pp. 1127-1140 ◽  
Author(s):  
B. Belchev ◽  
S.G. Neale ◽  
M.A. Walton
Keyword(s):  
Bound States ◽  
Scattering Matrix ◽  
Nucl Phys ◽  
Quantum Scattering ◽  
Research Award ◽  
Momentum Plane ◽  
S Matrix ◽  
Potential Depth ◽  
Square Well ◽  
Insight Into

The poles of the quantum scattering matrix (S-matrix) in the complex momentum plane have been studied extensively. Bound states give rise to S-matrix poles, and other poles correspond to non-normalizable antibound, resonance, and antiresonance states. They describe important physics but their locations can be difficult to determine. In pioneering work, Nussenzveig (Nucl. Phys. 11, 499 (1959)) performed the analysis for a square well (wall), and plotted the flow of the poles as the potential depth (height) varied. More than fifty years later, however, little has been done in the way of direct generalization of those results. We point out that today we can find such poles easily and efficiently using numerical techniques and widely available software. We study the poles of the scattering matrix for the simplest piecewise flat potentials, with one and two adjacent (nonzero) pieces. For the finite well (wall) the flow of the poles as a function of the depth (height) recovers the results of Nussenzveig. We then analyze the flow for a potential with two independent parts that can be attractive or repulsive, the two-piece potential. These examples provide some insight into the complicated behavior of the resonance, antiresonance, and antibound poles.

LATTICE DYNAMICS OF AN F-TYPE ICOSAHEDRAL QUASICRYSTAL

1993 ◽  
Vol 07 (06n07) ◽  
pp. 1487-1504 ◽  
Author(s):  
G. KASNER ◽  
H. BÖTTGER
Keyword(s):  
Lattice Dynamics ◽  
Continued Fraction ◽  
Pair Interaction ◽  
Icosahedral Quasicrystal ◽  
Cluster Approach ◽  
Vibrational States ◽  
Lennard Jones ◽  
Cluster Calculations ◽  
Face Centered ◽  
Matrix Continued Fraction

By using a matrix-continued fraction approach we calculate the density of vibrational states (DOS) of a tiling model based on the 6D face centered lattice. Parameters of the Lennard-Jones pair interaction are obtained from relaxation calculations. With a ternary decoration the tiling was found to be stable. The DOS was approximated by weighting the local DOS (LDOS) of the allowed vertex configurations by their relative frequencies in the infinite tiling. These frequencies were obtained by using extended deflation rules. Results of this approach are compared to exact finite cluster calculations and an embedded cluster approach. We find the DOS to consist of a single band (in our resolution) and a rich structure at higher frequencies.

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