Quantum stochastic calculus with integral kernels II: the Wigner-Weisskopf atom

J. Martin Lindsay

Kalyan B. Sinha

David Applebaum

Using techniques of quantum stochastic calculus, a dilation scheme is developed to describe the evolution of a two-level atom, which is initially in a (nontracial) Gibbs state, through a radiation field. The Wigner–Weisskopf approximation is assumed but not the rotating wave approximation, the latter being shown to be equivalent to the requirement that the dilation satisfies the quantum detailed balance condition with respect to the initial state.

John Edward Gough, Joachim Kupsch

V. P. Belavkin, M F Brown

We study the continuity property of multiple Q-adapted quantum stochastic integrals with respect to noncommuting integrands given by the non-adapted multiple integral kernels in Fock scale.The noncommutative algebra of relatively (exponentially) bounded nonadapted quantum stochastic processes is studied in the kernel form as introduced in [10].The differential Q-adapted formula generalizing Itô product formula for adapted integrals is presented in both strong and weak sense as a particular case of the quantum stochastic nonadapted Itô formula.

Kalyanapuram Rangachari Parthasarathy