An adiabatic theorem for singularly perturbed hamiltonians
Infinite products of random matrices and repeated interaction dynamics
Let be a product of independent, identically distributed random matrices , with the properties that is bounded in , and that has a deterministic (constant) invariant vector. Assume that the probability of having only the simple eigenvalue 1 on the unit circle does not vanish. We show that is the sum of a fluctuating and a decaying process. The latter converges to zero almost surely, exponentially fast as →∞. The fluctuating part converges in...
Landau-Zener transitions through small electronic eigenvalue gaps in the Born-Oppenheimer approximation
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