Adiabatic theorem for the time-dependent wave operator (12 pages)

Nimrod Moiseyev, Avner Fleischer

Zege Wu, Hang Zhou Yang

H. E. Moses

Tosio Kato

Georges Jolicard, John P. Killingbeck

Time-dependent and stationary wave operators are presented as tools to define active spaces and simplified dynamics for the integration of the time-dependent Schrödinger equation in large quantum spaces. Within this framework a new light is thrown on the duality between time-dependent and time-independent approaches and a generalized version of the adiabatic theorem is given. For the Floquet treatment of photodissociation processes, the choice of the relevant subspaces and the construction of the effective Hamiltonians are carried out using the Bloch wave operator techniques. Iterative solutions of the basic equations associated with these wave operators are given, based on Jacobi, Gauss-Seidel and variational schemes.

Kyu Hwang Yeon, Jeong Ryeol Choi, Shou Zhang +1 more

The unitary operator corresponding to the classical canonical transformation that connects a general closed system to an open system under adiabatic conditions is found. The quantum invariant operator of the adiabatic open system is derived from the unitary transformation of the quantum Hamiltonian of the closed system. On the basis of these results, we investigate the evolution of the general quantum adiabatic system and construct a revised adiabatic theorem. The adiabatic theorem developed here exactly reduces to the well-known Berry adiabatic theorem when the control parameter