共查询到20条相似文献,搜索用时 31 毫秒
1.
Anjan Kundu 《Chaos, solitons, and fractals》1995,5(12):2329-2344
The basic ideas behind the construction of integrable statistical as well as quantum models are reviewed, showing the connection between the related Yang-Baxter equations and the quantum group algebra structures. Such quantized algebra is shown to play an important role in integrable theories for generating different classes of quantum integrable systems in a rather systematic way. 相似文献
2.
A. Kundu 《Theoretical and Mathematical Physics》1999,118(3):333-340
Integrable inhomogenous or impurity models are usually constructed by either shifting the spectral parameter in the Lax operator or using another representation of the spin algebra. We propose a more involved general method for such construction in which the Lax operator contains generators of a novel quadratic algebra, a generalization of the known quantum algebra. In forming the monodromy matrix, we can replace any number of the local Lax operators with different realizations of the underlying algebra, which can result in spin chains with nonspin impurities causing changed coupling across the impurity sites, as well as with impurities in the form of bosonic operators. Following the same idea, we can also generate integrable inhomogeneous versions of the generalized lattice sine-Gordon model, nonlinear Schrödinger equation, Liouville model, relativistic and nonrelativistic Toda chains, etc. 相似文献
3.
A. Kundu 《Theoretical and Mathematical Physics》1994,99(3):699-704
We effectively translate our earlier quantum constructions to the classical language and, using Yang-Baxterisation of the Faddeev-Reshetikhin-Takhtajan algebra, are able to construct the Lax operators and associated -matrices of classical integrable models. Thus, new as well as known lattice systems of different classes are generated, including new types of collective integrable models and canonical models with nonstandard matrices.Fachbereich 17-Mathematik/Informatik, GH-Universitän Kassel, Holländische Str. 36, 34109 Kassel, Germany. (Permanent address: Saha Institute of Nuclear Physics, AF/1 Bidhan Nagar, Calcutta 700 064, India.) Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 428–434, June, 1994. 相似文献
4.
Dynamic effect algebras 总被引:1,自引:0,他引:1
We introduce the so-called tense operators in lattice effect algebras. Tense operators express the quantifiers “it is always
going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in
the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that every lattice effect
algebra whose underlying lattice is complete can be equipped with tense operators. Such an effect algebra is called dynamic
since it reflects changes of quantum events from past to future. 相似文献
5.
A. V. Smirnov 《Theoretical and Mathematical Physics》2009,158(3):300-312
We show a relation between systems of integrable tops on the algebras sl(N, ℂ) and Calogero-Moser systems of N particles. We construct classical Lax operators corresponding to these systems. We show
that these operators are related to certain new trigonometric and rational solutions of the Yang-Baxter equations for the
algebras sl(N, ℂ) and give explicit formulas for N = 2, 3.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 355–369, March, 2009. 相似文献
6.
Kaoru Ikeda 《Journal of Fourier Analysis and Applications》2009,15(1):80-100
We study the maximal commutative ring of partial differential operators which includes the quantum completely integrable system
defined by the quantum Toda lattice. Kostant shows that the image of the generalized Harish-Chandra homomorphism of the center
of the enveloping algebra is commutative (Kostant in Invent. Math. 48:101–184, 1978). We demonstrate the commutativity of the ring of partial differential operators whose principal symbols are
-invariant. Our commutative ring includes the commutative system of Kostant (Invent. Math. 48:101–184, 1978). The main tools in this paper are Fourier integral operators and Radon transforms.
相似文献
7.
8.
Kenny De Commer 《Journal of Functional Analysis》2018,274(1):152-221
We introduce a notion of I-factorial quantum torsor, which consists of an integrable ergodic action of a locally compact quantum group on a type I-factor such that also the crossed product is a type I-factor. We show that any such I-factorial quantum torsor is at the same time a I-factorial quantum torsor for the dual locally compact quantum group, in such a way that the construction is involutive. As a motivating example, we show that quantized compact semisimple Lie groups, when amplified via a crossed product construction with the function algebra on the associated weight lattice, admit I-factorial quantum torsors, and give an explicit realization of the dual quantum torsor in terms of a deformed Heisenberg algebra for the Borel part of a quantized universal enveloping algebra. 相似文献
9.
It is verified that the long-range interaction integrable chain models with Yangian symmetry can be obtained from RTT relation,
which therefore make this kind of models merge into Yang-Baxter system. A general method for obtaining Hamiltonian from quantum
determinant of transfer matrix satisfying RTT relation is given.
Project supported by the National Natural Science Foundation of China. 相似文献
10.
本文定义了(f,T)-相容对(B,H),利用这样的相容对可以给出一个辫子张量 范畴和一个量子Yang-Baxter方程的解,并且通过扭曲Hopf代数B的乘法,构造 Yetter-Drinfeld范畴中HHyD的Hopf代数. 相似文献
11.
E. T. Akhmedov 《Theoretical and Mathematical Physics》2006,147(1):509-523
We take one more step in formulating the theory of non-Abelian two-tensor fields: we find gauge transformation rules and the
curvature tensor for them. To define the theory, we use the surface exponential. We derive a differential equation for the
exponential and attempt to formulate its definition as a matrix model. We discuss applications of our construction to the
Yang-Baxter equation for integrable models and to string field theory.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 73–91, April, 2006. 相似文献
12.
Misha Feigin 《Selecta Mathematica, New Series》2012,18(1):253-281
We consider ideals of polynomials vanishing on the W-orbits of the intersections of mirrors of a finite reflection group W. We determine all such ideals that are invariant under the action of the corresponding rational Cherednik algebra hence form
submodules in the polynomial module. We show that a quantum integrable system can be defined for every such ideal for a real
reflection group W. This leads to known and new integrable systems of Calogero–Moser type which we explicitly specify. In the case of classical
Coxeter groups, we also obtain generalized Calogero–Moser systems with added quadratic potential. 相似文献
13.
A. V. Tsyganov 《Theoretical and Mathematical Physics》1999,118(2):164-172
Outer automorphisms of infinite-dimensional representations of the Lie algebra sl(2) are used to construct Lax matrices for
integrable Hamiltonian systems and discrete integrable mappings. The known results are reproduced, and new integrable systems
are constructed. Classical r-matrices, corresponding to the Lax representation with the spectral parameter are dynamic. This
scheme is advantageous because quantum systems naturally arise in the framework of the classical r-matrix Lax representation
and the corresponding quantum mechanical problem admits a variable separation.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 2, pp. 205–216, February, 1999. 相似文献
14.
We construct the class of integrable classical and quantum systems on the Hopf algebras describing n interacting particles.
We obtain the general structure of an integrable Hamiltonian system for the Hopf algebra A(g) of a simple Lie algebra g and
prove that the integrals of motion depend only on linear combinations of k coordinates of the phase space, 2·ind g≤k≤g·ind g, whereind g andg are the respective index and Coxeter number of the Lie algebra g. The standard procedure of q-deformation results in the
quantum integrable system. We apply this general scheme to the algebras sl(2), sl(3), and o(3, 1). An exact solution for the
quantum analogue of the N-dimensional Hamiltonian system on the Hopf algebra A(sl(2)) is constructed using the method of noncommutative
integration of linear differential equations.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 3, pp. 373–390, September, 2000 相似文献
15.
16.
T. V. Skrypnyk 《Theoretical and Mathematical Physics》2016,189(1):1509-1527
We construct quantum integrable systems associated with the Lie algebra gl(n) and non-skew-symmetric “shifted and twisted” rational r-matrices. The obtained models include Gaudin-type models with and without an external magnetic field, n-level (n?1)-mode Jaynes–Cummings–Dicke-type models in the Λ-configuration, a vector generalization of Bose–Hubbard dimers, etc. We diagonalize quantum Hamiltonians of the constructed integrable models using a nested Bethe ansatz. 相似文献
17.
A classical integrable Hamiltonian system is defined by an Abelian subalgebra (of suitable dimension) of a Poisson algebra, while a quantum integrable Hamiltonian system is defined by an Abelian subalgebra (of suitable dimension) of a Jordan–Lie algebra of Hermitian operators. We propose a method for obtaining large Abelian subalgebras inside the tensor product of free tensor algebras, and we show that there exist canonical morphisms from these algebras to Poisson algebras and Jordan–Lie algebras of operators. We can thus prove the integrability of some particular Hamiltonian systems simultaneously at both the classical and the quantum level. We propose a particular case of the rational Gaudin magnet as an example. 相似文献
18.
I. G. Korepanov 《Journal of Mathematical Sciences》1997,85(1):1671-1683
A completely integrable dynamical system in discrete time is studied by methods of algebraic geometry. The system is associated
with factorization of a linear operator acting in the direct sum of three linear spaces into a product of three operators,
each acting nontrivially only in the direct sum of two spaces, and subsequently reversing the order of the factors. There
exists a reduction of the system, which can be interpreted as a classical field theory in the 2+1-dimensional space-time,
whose integrals of motion coincide, in essence, with the statistical sum of an inhomogeneous 6-vertex free-fermion model on
the 2-dimensional kagome lattice (here the statistical sum is a function of two parameters). This establishes a connection
with the “local,” or “generalized,” quantum Yang-Baxter equation. Bibliography:10 titles.
Dedicated to L. D. Faddeev on the occasion of his 60th birthday
Published inZapiski Nauchnykh Seminarov POMI, Vol. 215, 1994, pp. 178–196.
Translated by I. G. Korepanov. 相似文献
19.
A. M. Zeitlin 《Theoretical and Mathematical Physics》2006,147(2):698-708
We continue the study of the quantization of supersymmetric integrable KdV hierarchies. We consider the N=2 KdV model based
on the sl(1)(2|1) affine algebra but with a new algebraic construction for the L-operator, different from the standard Drinfeld-Sokolov
reduction. We construct the quantum monodromy matrix satisfying a special version of the reflection equation and show that
in the classical limit, this object precisely gives the monodromy matrix of the N=2 supersymmetric KdV system. We also show
that at both the classical and the quantum levels, the trace of the monodromy matrix (transfer matrix) is invariant under
two supersymmetry transformations and the zero mode of the associated U(1) current.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 303–314, May, 2006. 相似文献
20.
As an analog of the quantum TKK algebra, a twisted quantum toroidal algebra of type A 1 is introduced. Explicit realization of the new quantum TKK algebra is constructed with the help of twisted quantum vertex operators over a Fock space. 相似文献