Dephasing representation of quantum fidelity
Quantum fidelity measures the stability of quantum dynamics under perturbations. Fidelity is useful, e.g., for describing accuracy of quantum dynamics on approximate potential energy surfaces [15], for computing inelastic neutron scattering cross sections, or due to its relation to decoherence.
In a general representation, quantum fidelity can decay both due to interference and due to decay of classical overlaps (classical fidelity). We found a special semiclassical representation (“dephasing representation”, DR) of fidelity that apparently only depends on dephasing; originally for localized position wave packets in a kicked rotor, realized by a cold atom in laser field [4,5] and then for general pure and even mixed states [7,8,11]. This expression is suitable for numerical computations in both integrable and chaotic systems.
The left figure below gives the definition of fidelity. The right figure shows the agreement of dephasing representation (DR1 and DR2) with exact quantum (QM) calculation fidelity in a situation where classical (CL) description completely fails (the example is taken from the photodissociation of CO2 in [15]).
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