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Decoherence in Condensed Phase Nonadiabatic Dynamics How to include decoherence into a time-domain atomistic simulation? - Why is it an issue? Examples - Simple measures of decoherence How to justify (derive) models used for this purpose? Is there something between system-bath and explicit atomistic models?

Example: Solvated Electron - Cannot get away with a harmonic bath model Without decoherence 600 fs P-S transition time becomes <10fs

Example: Solvated Electron - Cannot get away with a harmonic bath model Without decoherence 600 fs P-S transition time becomes <10fs - Decoherence explains absence of solvent isotope effect

Decoherence and Quantum-Classical Simulation Reduced density matrix: on decoherence time scale, missing in q.-cl. models With decoherence: Without decoherence Decoherence makes transitions less likely (quantum Zeno effect)

Simple Estimates of Decoherence Time Bath (vibrational) wave functions diverge Method 1. Assume is particle is a Gaussian wave packet too simplistic, what width to use? Method 2. Compute the correlation function what if properties change with time?

Another Problem that can be Resolved by Decoherence Single average trajectory is unphysical Instead chemists designed ad hoc surface hopping

Another Problem that can be Resolved by Decoherence Stochastic Schrodinger equation gives branching - decoherence rate, L - system-bath coupling Bath is present twice (in H and L) ??

Separate Classical Variables and Treat Quantum Variables as Bath = q 2 + 3 forming infinite hierarchy Can higher orders in this recursive map be described stochastically?

Spin-Phonon Example classical energy decreases Most energy transfers into quantum variables and spin becomes chaotic

Classical energy fluctuates at some “temperature” ?? Spin-Phonon Example Classical energy fluctuates at some “temperature” ??

Decoherence in Condensed Phase Nonadiabatic Dynamics How to include decoherence into a time-domain atomistic simulation? - Why is it an issue? Examples - Simple measures of decoherence How to justify (derive) models used for this purpose? Is there something between system-bath and explicit atomistic models?