Some Integrable Quantum Systems on the Lattice
نویسنده
چکیده
The Weyl relations, the harmonic oscillator, the hydrogen atom, the Dirac equation on the lattice are presented with the help of the difference equations and the orthogonal polynomials of discrete variable. This area of research is attracting more interest due to the lattice field theories and the hypothesis of a finite space. 1 Weyl group on finite space We defined the position space of dimension N with orthonormal basis |0〉 =
منابع مشابه
Integrable systems on the lattice and orthogonal polynomials of discrete variable
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
متن کاملIntegrable Quantum Mappings and Quantization Aspects of Integrable Discrete-time Systems
We study a quantum Yang-Baxter structure associated with non-ultralocal lattice models. We discuss the canonical structure of a class of integrable quantum mappings, i.e. canonical transformations preserving the basic commutation relations. As a particular class of solutions we present two examples of quantum mappings associated with the lattice analogues of the KdV and MKdV equations, together...
متن کاملمقدمهای بر سیستمهای اسپینی کوانتمی
This manuscript is the collection of lectures given in the summer school on strongly correlated electron systems held at Isfahan university of technology, June 2007. A short overview on quantum magnetism and spin systems is presented. The numerical exact diagonalization (Lanczos) alghorithm is explained in a pedagogical ground. This is a method to get some ground state properties on finite clus...
متن کاملIntegrable discretizations for lattice systems: local equations of motion and their Hamiltonian properties
We develop the approach to the problem of integrable discretization based on the notion of r–matrix hierarchies. One of its basic features is the coincidence of Lax matrices of discretized systems with the Lax matrices of the underlying continuous time systems. A common feature of the discretizations obtained in this approach is non–locality. We demonstrate how to overcome this drawback. Namely...
متن کاملIntegrable Discrete Geometry: the Quadrilateral Lattice, its Transformations and Reductions
We review recent results on Integrable Discrete Geometry. It turns out that most of the known (continuous and/or discrete) integrable systems are particular symmetries of the quadrilateral lattice, a multidimensional lattice characterized by the planarity of its elementary quadrilaterals. Therefore the linear property of planarity seems to be a basic geometric property underlying integrability....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008