 08194 Marco Merkli and Shannon Starr
 A resonance theory for open quantum systems with timedependent dynamics
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Oct 20, 08

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Abstract. We develop a resonance theory to describe the evolution of open systems with timedependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed dynamical resonance theory, and we piece them together to obtain the total evolution. The initial state corresponding to one timeinterval with constant Hamiltonian is the final state of the system corresponding to the interval before. This results in a nonmarkovian dynamics.
We find a representation of the dynamics in terms of resonance energies and resonance states associated to the Hamiltonians, valid for all times $t\geq 0$ and for small (but fixed) interaction strengths. The representation has the form of a path integral over resonances.
We present applications to a spinfermion system, where the energy levels of the spin may undergo rather arbitrary crossings in the course of time. In particular, we find the probability for transition between ground and excited state at all times.
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