Coherent states on horospheric three-dimensional Lobachevsky space

2016 ◽  
Vol 57 (8) ◽  
pp. 082111 ◽  
Author(s):  
Yu. Kurochkin ◽  
I. Rybak ◽  
Dz. Shoukavy
Keyword(s):  
Coherent States ◽  
Three Dimensional ◽  
Lobachevsky Space

Two- and three-dimensional polarons with extended coherent states

1996 ◽  
Vol 53 (17) ◽  
pp. 11296-11299 ◽  
Author(s):  
Chen Qinghu ◽  
Fang Minghu ◽  
Zhang Qirui ◽  
Wang Kelin ◽  
Wan Shaolong
Keyword(s):  
Coherent States ◽  
Three Dimensional

scholarly journals ON RELATION BETWEEN GEOMETRIC MOMENTUM AND ANNIHILATION OPERATORS ON A TWO-DIMENSIONAL SPHERE

2013 ◽  
Vol 10 (06) ◽  
pp. 1320007 ◽  
Author(s):  
Q. H. LIU ◽  
Y. SHEN ◽  
D. M. XUN ◽  
X. WANG
Keyword(s):  
Angular Momentum ◽  
Coherent States ◽  
Three Dimensional ◽  
Extrinsic Curvature ◽  
Flat Space ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Intrinsic Geometry

With a recently introduced geometric momentum that depends on the extrinsic curvature and offers a proper description of momentum on two-dimensional sphere, we show that the annihilation operators whose eigenstates are coherent states on the sphere take the expected form αx + iβp, where α and β are two operators that depend on the angular momentum and x and p are the position and the geometric momentum, respectively. Since the geometric momentum is manifestly a consequence of embedding the two-dimensional sphere in the three-dimensional flat space, the coherent states reflects some aspects beyond the intrinsic geometry of the surfaces.

scholarly journals On the classification of stably reflective hyperbolic Z[√2]-lattices of rank 4

2019 ◽  
Vol 486 (1) ◽  
pp. 7-11
Author(s):  
N. V. Bogachev
Keyword(s):  
Three Dimensional ◽  
Reflection Group ◽  
Lobachevsky Space ◽  
Fundamental Polyhedron

In this paper we prove that the fundamental polyhedron of a ℤ2-arithmetic reflection group in the three-dimensional Lobachevsky space contains an edge such that the distance between its framing faces is small enough. Using this fact we obtain a classification of stably reflective hyperbolic ℤ2-lattices of rank 4.

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