Integrable structure of melting crystal model with two q-parameters
نویسنده
چکیده
This paper explores integrable structures of a generalized melting crystal model that has two q-parameters q1, q2. This model, like the ordinary one with a single q-parameter, is formulated as a model of random plane partitions (or, equivalently, random 3D Young diagrams). The Boltzmann weight contains an infinite number of external potentials that depend on the shape of the diagonal slice of plane partitions. The partition function is thereby a function of an infinite number of coupling constants t1, t2, . . . and an extra one Q. There is a compact expression of this partition function in the language of a 2D complex free fermion system, from which one can see the presence of a quantum torus algebra behind this model. The partition function turns out to be a tau function (times a simple factor) of two integrable structures simultaneously. The first integrable structure is the bigraded Toda hierarchy, which determine the dependence on t1, t2, . . .. This integrable structure emerges when the q-parameters q1, q2 take special values. The second integrable structure is a q-difference analogue of the 1D Toda equation. The partition function satisfies this q-difference equation with respect to Q. Unlike the bigraded Toda hierarchy, this integrable structure exists for any values of q1, q2. 2000 Mathematics Subject Classification: 35Q58, 81R12, 82B99
منابع مشابه
Integrable structure of modified melting crystal model
Our previous work on a hidden integrable structure of the melting crystal model (the U(1) Nekrasov function) is extended to a modified crystal model. As in the previous case, “shift symmetries” of a quantum torus algebra plays a central role. With the aid of these algebraic relations, the partition function of the modified model is shown to be a tau function of the 2D Toda hierarchy. We conject...
متن کاملSolutions structure of integrable families of Riccati equations and their applications to the perturbed nonlinear fractional Schrodinger equation
Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Ri...
متن کاملThe New Method for Optical Channel Drop Filter with High Quality Factor Based on Triangular Photonic Crystal Design
We have designed a new type of optical channel drop filter (CDF) based on two dimensionaltriangular lattice photonic crystals. CDF operation is based on coupling to the photonic crystalwaveguide. The proposed structure is optimized to work as a CDF for obtaining the CDFcharacteristics and band structure of the filter the finite difference time domain (FDTD) method andplane wave expansion (PWE) ...
متن کاملTheoretical investigations on molecular structure, NBO, HOMO-LUMO and MEP analysis of two crystal structures of N-(2-benzoyl-phenyl) oxalyl: A DFT study
The N-(2-benzoyl-phenyl) oxalyl derivatives are important models for studying of three-centered intramolecular hydrogen bonding in organic molecules. The quantum theoretical calculations for two crystal structures of N-(2-benzoyl-phenyl) oxalyl (compounds I and II) were performed by Density Functional Theory (B3LYP method and 6-311+G* basis set). From the optimized structures, geometric paramet...
متن کامل