Heisenberg Hamiltonian

Claudio Albanese

M Meragi, N. Majd

Jamila Douari

The anyonic Hamiltonian is quantum mechanically given and the bosonic and the fermionic Hamiltonians are found as extremes by discussing the cases of the statistical parameter $ν$ and the dimension of space. The anyonic algebra \cite{upa} is recalled as a deformed Heisenberg algebra and a deformed $C_λ$-extended Heisenberg algebra.

Harry A. Mavromatis

Giancarlo Calvanese Strinati

In the Schrödinger and Heisenberg representations, the time-evolution operator depends on the full time-dependent Hamiltonian, which includes an external time-dependent potential. Out of this full-time dependence, it is useful to isolate the time dependences due to either the full system Hamiltonian or its noninteracting part. These two cases, referred to as the Heisenberg and interaction pictures, respectively, are considered separately.

Dmitry A. Garanin, K. Kladko, Peter Fulde

We propose a method for obtaining effective classical Hamiltonians \cal H for many-body quantum spin systems with large spins. This method uses the coherent-state representation of the partition function Z and the cumulant expansion in powers of 1/S. For the quantum Hamiltonian \hat H of a Heisenberg form, the 1/S corrections in \cal H have a non-Heisenberg many-spin form. The effective Hamiltonian \cal H can be treated by methods familiar for classical systems. The non-Heisenberg terms in \cal H may be responsible for such effects as spin-Peierls transition and uplifting of the classical degeneracy by quantum fluctuations.