اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBacklund transformations for difference Hirota equation and supersymmetric Bethe ansatz
192
0
0.0
(
0
)
تأليف
A. Zabrodin
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider GL(K|M)-invariant integrable supersymmetric spin chains with twisted boundary conditions and elucidate the role of Backlund transformations in solving the difference Hirota equation for eigenvalues of their transfer matrices. The nested Bethe ansatz technique is shown to be equivalent to a chain of successive Backlund transformations undressing the original problem to a trivial one.
قيم البحث
اقرأ أيضاً
Hirotas bilinear approach is a very effective method to construct solutions for soliton systems. In terms of this method, the nonlinear equations can be transformed into linear equations, and can be solved by using perturbation method. In this paper,
we study the bilinear Boussinesq equation and obtain its bilinear B{a}cklund transformation. Starting from this bilinear B{a}cklund transformation, we also derive its Lax pair and test its integrability.
Using the generalized perturbation reduction method the Hirota equation is transformed to the coupled nonlinear Schrodinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is obtained. The component
s of the pulse oscillate with the sum and difference of the frequencies and the wave numbers. Explicit analytical expressions for the shape and parameters of the two-component nonlinear pulse are presented.
We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian $mathrm Y(mathfrak{gl}_{m|n})$. To a solution we associate a rational difference operator $mathcal D$ and a superspace of rational
functions $W$. We show that the set of complete factorizations of $mathcal D$ is in canonical bijection with the variety of superflags in $W$ and that each generic superflag defines a solution of the Bethe ansatz equation. We also give the analogous statements for the quasi-periodic supersymmetric spin chains.
We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation t
o an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators.
We study fluctuations and finite size corrections for the ferromagnetic thermodynamic limit in the Bethe ansatz for the Heisenberg XXX1/2 spin chain, which is the AdS/CFT dual of semiclassical spinning strings. For this system we derive the standard
quantum mechanical formula which expresses the energy shift as a sum over fluctuation energies. As an example we apply our results to the simplest, one-cut solution of this system and derive its spectrum of fluctuations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
