Phase transition phenomena and the Lippmann—Schwinger variational principle

Brian Albert Robson, D. Robson

Han J.F. Geurdes

Fernando Calamante, Horacio Grinberg

Abstract Using the connection between the evolution operator and the stationary value of the Lippmann–Schwinger functional, approximations to this operator are obtained using diagonal Padé approximants. A harmonic oscillator with a non‐hermitean perturbation proportional to powers of the bosonic creation operator is considered and its evolution operator is evaluated. The poles of the spectral representation obtained by this method are compared to both: the ones of the usual perturbative expansion and those of the exact solution. Extensions to Hermitian Hamiltonians are discussed, involving the necessity of inverting more complex operators in the calculation of the Fourier transform. However, the approximation obtained by this procedure becomes exactly unitary. © 1995 John Wiley & Sons, Inc.

G. Toulouse

Ritesh Kumar Dubey, V Jayaram Menon, Dharmendra Tripathi

Due to the presence of an infinitesimal parameter e in the resolvent, the Lippmann-Schwinger states cannot be strict eigenstates of the Hamiltonian, and their time evolution is very non-trivial (in agreement with Fermi's golden rule). In sharp contrast, strict Schrodinger eigenstates cannot make transitions into free channels. Artefacts such as adiabatic switching, wave packets, or infinite time span are not needed in our analysis.