Modified Hermitian Treatment of Dyson Boson Expansion Theory

On Modified Hermitian and Skew - Hermitian Splitting

Hermitian boson mapping and finite truncation.

Starting from a general, microscopic fermion-to-boson mapping that preserves Hermitian conjugation, we discuss truncations of the boson Fock space basis. We give conditions under which the exact boson images of finite fermion operators are also finite (e.g., a 1+2-body fermion Hamiltonian is mapped to a 1+2-body boson Hamiltonian) in the truncated basis. For the most general case, where the ima...

Boson-fermion Dyson mapping and supersymmetry in fermion systems

We demonstrate that exact supersymmetry can emerge in a purely fermionic system. This “supersymmetry without bosons” is unveiled by constructing a novel boson-fermion Dyson mapping from a fermion space to a space comprised of collective bosons and ideal fermions. In a nuclear structure context the collective spectra of even and odd nuclei can then be unified in a supersymmetric description with...

Large N expansion of the 2 D Dyson gas

We discuss the 1/N expansion of the free energy of N logarithmically interacted charges in the plane in an external field. For some particular values of the inverse temperature β this system is equivalent to the eigenvalue version of certain random matrix models, where it is refered to as the " Dyson gas " of eigenvalues. To find the free energy at large N and the 1/N-corrections, we first use ...

Modified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems

Comparing the lopsided Hermitian/skew-Hermitian splitting (LHSS) method and Hermitian/skewHermitian splitting (HSS) method, a new criterion for choosing the above two methods is presented, which is better than that of Li, Huang and Liu [Modified Hermitian and skew-Hermitian splitting methods for nonHermitian positive-definite linear systems, Numer. Lin. Alg. Appl., 14 (2007): 217-235]. Key-Word...