Let H be the three-dimensional Heisenberg group. We introduce a structure on the Heisenberg group which consists of the biregular representation of H×H restricted to some discrete subset of H×H and a free group of automorphisms H singly generated and acting semi-simply on H. Using well-known theorems borrowed from Gabor theory, we are able to construct simple and computable bandlimited discrete...

motivating the perturbations of frames in hilbert and banach spaces, in this paper we introduce the invariance of fr'echet frames under perturbation. also we show that for any fr'echet spaces, there is a fr'echet frame and any element in these spaces  has a series expansion.

The results of a detailed histogram Monte-Carlo study of critical-fluctuation effects on the magnetic-field temperature phase diagram associated with the hexagonal Heisenberg antiferromagnet with weak axial anisotropy are reported. The multiphase point where three lines of continuous transitions merge at the spin-flop boundary exhibits a structure consistent with scaling theory but without the ...

In an interesting note, E.M. Stein observed some 20 years ago that while the Kohn Laplacian b on functions is neither locally solvable nor (analytic) hypoelliptic, the addition of a non-zero complex constant reversed these conclusions at least on the Heisenberg group, and Kwon reproved and generalized this result using the method of concatenations. Recently Hanges and Cordaro have studied this ...

The mapping transformation technique is applied to obtain exact results for the spin-1/2 and spin-S (S = 1/2, 1) Ising-Heisenberg antiferromagnetic chain in the presence of an external magnetic field. Within this scheme, a field-induced first-order metamagnetic phase transition resulting in multiplateau magnetization curves, is investigated in detail. It is found that the scenario of the platea...

The natural explanation of the excitation spectrum of the spin1 antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy spectrum of the latter is calculated with fixed momentum k by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) an...

We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we construct a quantum field theory that creates at any space-time point particles described by a qdeformed Heisenberg algebra and we compute the propagator and a speci...

Tight Weyl–Heisenberg frames in `(Z) are the tool for short-time Fourier analysis in discrete time. They are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory. Good resolution of short-time Fourier analysis in the joint time–frequency plane is not attainable unless some redundancy is introduced. That is the reason for consideri...

The SLAC real-space renormalization group method is used to study one-dimensional antiferromagnetic chains at zero temperature. Calculations using three-site blocks (for the Heisenberg-Ising model) and two-site blocks (for the isotropic Heisenberg model) are compared with exact results. In connection with the two-site calculation a duality transformation is introduced under which the isotropic ...

The Higgs mode is expected to exist in any system with the spontaneous symmetry breaking of the continuous symmetry. We make numerical study about the Higgs mode in the Heisenberg antiferromagnet on the square lattice by the exact diagonalisation approach. Since the Higgs mode can couple with a pair of the Nambu-Goldstone modes, we calculate the dynamical correlation of the two spin operators, ...