We show that the quantum Heisenberg group Hq(1) can be obtained by means of contraction from quantum SUq(2) group. Its dual Hopf algebra is the quantum Heisenberg algebra Uq(h(1)). We derive left and right regular representations for Uq(h(1)) as acting on its dual Hq(1). Imposing conditions on the right representation the left representation is reduced to an irreducible holomorphic representati...

In the framework of the q-deformed Heisenberg algebra the investigation of qdeformation of Virial theorem explores that q-deformed quantum mechanics possesses better dynamical property. It is clarified that in the case of the zero potential the theoretical framework for the q-deformed Virial theorem is self-consistent. In the selfadjoint states the q-deformed uncertainty relation essentially de...

Introduction. In [14] we began a study of C*-algebras corresponding to projective representations of the discrete Heisenberg group, and classified these C*-algebras up to *-isomorphism. In this sequel to [14] we continue the study of these so-called Heisenberg C*-algebras, first concentrating our study on the strong Morita equivalence classes of these C*-algebras. We recall from [14] that a Hei...

A non-empirical Heisenberg Hamiltonian had been proposed for conjugated 03C0 systems from ab initio calculations on ethylene, and proved to be very efficient. Its theoretical foundation from the full Hamiltonian was evident from the concept of effective Hamiltonian and the use of Quasi-Degenerate-Perturbation Theory (QDPT), as shown by Anderson. When one wants to define a Heisenberg Hamiltonian...

Fractional derivative can be defined as a fractional power of derivative. The commutator (i/h̄)[H, . ], which is used in the Heisenberg equation, is a derivation on a set of observables. A derivation is a map that satisfies the Leibnitz rule. In this paper, we consider a fractional derivative on a set of quantum observables as a fractional power of the commutator (i/h̄)[H, . ]. As a result, we ob...

In its most general formulation a quantum kinematical system is described by a Heisenberg group; the ”configuration space” in this case corresponds to a maximal isotropic subgroup. We study irreducible models for Heisenberg groups based on compact maximal isotropic subgroups. It is shown that if the Heisenberg group is 2-regular, but the subgroup is not, the ”vacuum sector” of the irreducible r...

In agreement with the Harris criterion, asymptotic critical exponents of threedimensional (3d) Heisenberg-like magnets are not influenced by weak quenched dilution of non-magnetic component. However, often in the experimental studies of corresponding systems concentrationand temperature-dependent exponents are found with values differing from those of the 3d Heisenberg model. In our study, we u...