Quantum Integrable Models and Discrete Classical Hirota Equations
نویسندگان
چکیده
منابع مشابه
Bethe Ansatz and Classical Hirota Equations 1
A brief non-technical review of the recent study [1] of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's Q-operators, etc) with elements of classical non-linear integrable difference equations (τ-functions, Baker-Akhiezer functions, etc). The nested Bethe ansatz...
متن کاملDiscrete Hirota’s equation in quantum integrable models
The recent progress in revealing classical integrable structures in quantummodels solved by Bethe ansatz is reviewed. Fusion relations for eigenvalues of quantum transfer matrices can be written in the form of classical Hirota’s bilinear difference equation. This equation is also known as the completely discretized version of the 2D Toda lattice. We explain how one obtains the specific quantum ...
متن کاملGeneralized Hirota Equations in Models of 2D Quantum Gravity
We derive a set of bilinear functional equations of Hirota type for the partition functions of the sl(2) related integrable statistical models defined on a random lattice. These equations are obtained as deformations of the Hirota equations for the KP integrable hierarchy , which are satisfied by the partition function of the ensemble of planar graphs.
متن کاملIntegrable Classical and Quantum Gravity
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity [1, 2, 3, 4]. Assuming the presence of commuting Killing symmetries which effectively eliminate the dependence on all but two space-time coordinates allows us to cast the models into the form of 2d non-linear (G/H)-coset space σ-models coupled to gravity and a dilaton. This construction includes a...
متن کاملSolutions of Non-Integrable Equations by the Hirota Direct Method
We show that we can also apply the Hirota method to some nonintegrable equations. For this purpose, we consider the extensions of the Kadomtsev-Petviashvili (KP) and the Boussinesq (Bo) equations. We present several solutions of these equations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1997
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s002200050165