Exact solutions for nonlinear Hamiltonians

Carl M. Bender, Gerald V. Dunne

Mustapha Maamache

By performing unitary transformations on the time-dependent Schrödinger equation, the exact solution for a class of nonlinear Hamiltonian systems is obtained and it is shown that these time-dependent problems are related to the associated time- independent problems. In addition, the evolution operator is derived. Nonadiabatic Berry’s phase is calculated on the basis of the exact solution. The theory is applied to some illustrative examples.

Duger Ulam-Orgikh, Purevdorj Munkhbaatar

In this Paper, we have dealt with two-axis twisting Hamiltonian for spin squeezing, which is experimentally implementable in Bose-Einstein Condensate, and have found an exact solution by two alternative methods. Many other important nonlinear Hamiltonians could also be solved exactly in a similar way.

A. Horzela

Monique Combescure, Didier Robert

Sergio Lerma-Hernández, B. Errea, J. Dukelsky +1 more

The exact solution of the proton-neutron isoscalar-isovector (T=0,1) pairing Hamiltonian with nondegenerate single-particle orbits and equal pairing strengths is presented for the first time. The Hamiltonian is a particular case of a family of integrable SO(8) Richardson-Gaudin models. The exact solution of the T=0,1 pairing Hamiltonian is reduced to a problem of 4 sets of coupled nonlinear equations that determine the spectral parameters of the complete set of eigenstates. The microscopic structure of individual eigenstates is analyzed in terms of evolution of the spectral parameters in the complex plane for a system of A=80 nucleons. The spectroscopic trends of the exact solutions are discussed in terms of generalized rotations in isospace.