scholarly journals QUANTUM GROUP APPROACH TO A SOLUBLE VERTEX MODEL WITH GENERALIZED ICE RULE

1996 ◽  
Vol 11 (10) ◽  
pp. 1747-1761
Author(s):  
C.L. SOW ◽  
T.T. TRUONG
Keyword(s):  
Free Energy ◽  
Quantum Mechanics ◽  
Positive Integer ◽  
Quantum Group ◽  
Algebraic Structure ◽  
Square Lattice ◽  
Free Fermion ◽  
Vertex Model ◽  
Group Approach ◽  
Operator Structure

Using the representation of the quantum group SL q(2) by the Weyl operators of the canonical commutation relations in quantum mechanics, we construct and solve a new vertex model on a square lattice. Random variables on horizontal bonds are Ising variables, and those on the vertical bonds take half positive integer values. The vertex is subjected to a generalized form of the so-called “ice rule,” its property is studied in detail and its free energy calculated with the method of quantum inverse scattering. Remarkably, in analogy with the usual six-vertex model, there exists a “free-fermion” limit with a novel rich operator structure. The existing algebraic structure suggests a possible connection with a lattice neutral plasma of charges, via the fermion-boson correspondence.

scholarly journals Arctic Curve of the Free-Fermion Six-Vertex Model in an L-Shaped Domain

2018 ◽  
Vol 174 (1) ◽  
pp. 1-27 ◽  
Author(s):  
F. Colomo ◽  
A. G. Pronko ◽  
A. Sportiello
Keyword(s):  
Free Fermion ◽  
Vertex Model ◽  
Arctic Curve ◽  
Shaped Domain

scholarly journals Mechanism and kinetics for both thermal and electrochemical reduction of N2 catalysed by Ru(0001) based on quantum mechanics

2019 ◽  
Vol 21 (32) ◽  
pp. 17605-17612 ◽  
Author(s):  
Liang-Yu Chen ◽  
Tung-Chun Kuo ◽  
Zih-Siang Hong ◽  
Mu-Jeng Cheng ◽  
William A. Goddard
Keyword(s):  
Free Energy ◽  
Quantum Mechanics ◽  
Electrochemical Reduction ◽  
Mechanism And Kinetics ◽  
Energy Surfaces

QM calculations were used to predict the free energy surfaces for N2 thermal and electrochemical reduction (N2TR and N2ER) on Ru(0001), to find the detailed atomistic mechanism and kinetics, and provide the basis for improving the efficiency of N2ER.

scholarly journals Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Z. E. Musielak ◽  
N. Davachi ◽  
M. Rosario-Franco
Keyword(s):  
Differential Equations ◽  
Lie Groups ◽  
Lie Group ◽  
Algebraic Structure ◽  
Second Order ◽  
Lagrangian Formalism ◽  
Group Approach ◽  
Second Order Differential Equations ◽  
Gauge Functions ◽  
The Relationship

A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate novel equations. The Lagrangian formalism based on standard, null, and nonstandard Lagrangians is established for all members of the semigroup. For the null Lagrangians, their corresponding gauge functions are derived. The obtained Lagrangians are either new or generalization of those previously known. The previously developed Lie group approach to derive some equations of the semigroup is also described. It is shown that certain equations of the semigroup cannot be factorized, and therefore, their Lie groups cannot be determined. A possible solution of this problem is proposed, and the relationship between the Lagrangian formalism and the Lie group approach is discussed.

ON THE ALGEBRAIC STRUCTURE of QUANTUM GRAVITY IN TWO DIMENSIONS

1991 ◽  
Vol 06 (16) ◽  
pp. 2805-2827 ◽  
Author(s):  
Jean-Loup Gervais
Keyword(s):  
Quantum Gravity ◽  
Quantum Group ◽  
Algebraic Structure ◽  
Group Structure ◽  
Two Dimensions ◽  
Conformal Gauge

Current progresses in understanding quantum gravity from the operator viewpoint are reviewed. They are based on the Uq(sl(2))-quantum-group structure recently put forward1,2, for the chiral components of the metric in the conformal gauge.

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