scholarly journals Lax Pair for a Novel Two-Dimensional Lattice

2021 ◽  
Author(s):  
Maria N. Kuznetsova ◽  
Keyword(s):  
Lax Pair ◽  
Two Dimensional ◽  
Dimensional Lattice

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

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.

Deposition of particles in a two-dimensional lattice gas flow

1992 ◽  
Vol 68 (13) ◽  
pp. 2027-2030 ◽  
Author(s):  
Jean-Christophe Toussaint ◽  
Jean-Marc Debierre ◽  
Loïc Turban
Keyword(s):  
Gas Flow ◽  
Lattice Gas ◽  
Two Dimensional ◽  
Dimensional Lattice

Phase diagram of a two-dimensional lattice-gas model of oxygen ordering inYBa2Cu3Ozwith realistic interactions

1995 ◽  
Vol 52 (13) ◽  
pp. 9784-9792 ◽  
Author(s):  
D. J. Liu ◽  
T. L. Einstein ◽  
P. A. Sterne ◽  
L. T. Wille
Keyword(s):  
Phase Diagram ◽  
Lattice Gas ◽  
Lattice Gas Model ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Oxygen Ordering
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