Monodromy matrices for Harper equation

Author(s):  
A. Fedotov ◽  
E. Shchetka
2000 ◽  
Vol 14 (11) ◽  
pp. 373-376
Author(s):  
E. PAPP

The 1/N approach to the Harper equation proposed previously is generalized towards performing the pertinent band-energy description. Leading forms and corrections proceeding to first order in the magnetic field are written down. The energy reflection symmetry has also been discussed.


2003 ◽  
Vol 03 (02) ◽  
pp. L251-L258 ◽  
Author(s):  
A. H. OSBALDESTIN ◽  
B. D. MESTEL

We review our recent rigorous results on renormalization in a variety of quasiperiodically forced systems. Our results include a description of (i) self-similar fluctuations of localized states in the Harper equation, including the renormalization strange set (known as the orchid) in the generalized Harper equation; and (ii) self-similarities in the correlations of strange nonchaotic attractors, barrier billiards, and quantum two-level systems.


1997 ◽  
Vol 12 (13) ◽  
pp. 905-911
Author(s):  
G. P. Pronko

We consider the classical KdV theory as an example of non-ultralocal mechanical system (i.e. where fundamental Poisson brackets contain the derivative of δ-function). We show that by an appropriate gauge transformation, the Poisson brackets of the associated monodromy matrices may be transformed into those of the classical Heisenberg magnetic.


2005 ◽  
Vol 02 (06) ◽  
pp. 1063-1080
Author(s):  
S. GRILLO ◽  
H. MONTANI

Given a couple of Yang–Baxter operators 𝖱[k] and 𝖱[l] corresponding to integrable anisotropic vertex models of Ak-1 and Al-1 type, respectively, we construct and study a class of related lattice models whose monodromy matrices alternate between the mentioned operators. In order to do that, we use a natural generalization of the idea of coproduct in a bialgebra, that appears in the scenario of non-commutative algebraic geometry, related to the notion of internal homomorphisms of quantum spaces. We build up all eigenstates and eigenvalues of the transfer matrix by means of algebraic Bethe ansatz technics, where not only one vector, but a pseudovacuum subspace is needed for the process of diagonalization.


2009 ◽  
Vol 116 (4) ◽  
pp. 486-488
Author(s):  
E. Papp ◽  
C. Micu ◽  
I. Bica

Author(s):  
V. V. Amel’kin ◽  
M. N. Vasilevich

One inverse problem of the analytic theory of linear differential equations is considered. Namely, the completely integrable Fuchs equation with four given finite critical points and a given reducible monodromy group of rank 2 on the complex projective line is constructed. Reducibility of the monodromy group of rank 2 means that 2×2-monodromy matrices (the generators of the monodromy group) can be simultaneously reduced by a linear nonsingular transformation to an upper triangular form. In so doing we study the case when the eigenvalue ξj of the diagonal matrix of the monodromy formal exponent at a corresponding Fuchs critical point is equal to an integer different from zero (resonance takes place).


1997 ◽  
Vol 11 (18) ◽  
pp. 773-778 ◽  
Author(s):  
C. Micu ◽  
E. Papp

This paper deals with the derivation of concrete polynomial solutions to the q-difference form of the Harper equation proposed recently [P. B. Wiegmann and A. V. Zabrodin, Phys. Rev. Lett.72, 1890 (1994)], now by using the q-calculus in conjunction with quite directly solvable recurrence relations. Regularity patterns and the onset of level-structures with increasing complexity are discussed.


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