Boson Hamiltonians

Ching‐Teh Li

A new method based on a maximal-decoupling variational principle is proposed to treat the Pauli-principle constraints for calculations of nuclear collective motion in a truncated boson space. The viability of the method is demonstrated through an application to the multipole form of boson Hamiltonians for the single-j and nondegenerate multi-j pairing interactions. While these boson Hamiltonians are Hermitian and contain only one- and two-boson terms, they are also the worst case for truncated boson-space calculations because they are not amenable to any boson truncations at all. By using auxiliary Hamiltonians optimally determined by the maximal-decoupling variational principle, however, truncations in the boson space become feasible and even yield reasonably accurate results. The method proposed here may thus be useful for doing realistic calculations of nuclear collective motion as well as for obtaining a viable interacting-boson-model type of boson Hamiltonian from the shell model.

Abraham Klein

Dimitra Karabali A, Alexios P. Polychronakos

We derive the exact form of the bosonized Hamiltonian for a many-body fermion system in one spatial dimension with arbitrary dispersion relations, using the droplet bosonization method. For a single-particle Hamiltonian polynomial in the momentum, the bosonized Hamiltonian is a polynomial of one degree higher in the bosonic ``boundary'' field and includes subleading lower-order and derivative terms. This generalizes the known results for massless relativistic and nonrelativistic fermions (quadratic and cubic bosonic Hamiltonians, respectively). We also consider two-body interactions and demonstrate that they lead to interesting collective behavior and phase transitions in the Fermi sea.

Fumio Hiroshima

Fabrizio Palumb

We derive a boson Hamiltonian from a Nuclear Hamiltonian whose potential is expanded in pairing multipoles and determine the fermion-boson mapping of operators. We use a new method of bosonization based on the evaluation of the partition function restricted to the bosonic composites of interest. By rewriting the partition function so obtained in functional form we get the euclidean action of the composite bosons from which we can derive the Hamiltonian. Such a procedure respects all the fermion symmetries.