The level of adiabaticity determines many properties of time-dependent quantum systems. However, a reliable and easy-to-apply criterion for checking and tracking it remains an open question, especially for complex many-body systems. Here, we test techniques based on recently proposed metrics to characterize and track adiabaticity quantitatively. We investigate the time evolution of x-ray photoemission in metals, which exhibits a strongly out-of-equilibrium character, a continuum of energies, and the Anderson orthogonality catastrophe—a nightmarish scenario for this type of test. Our results show that the metrics-based methods remain valid. In particular, we demonstrate that the natural local density distance can not only track adiabaticity but also provide information not captured by the corresponding Bures or trace distances regarding the system's dynamics. In the process, we derive a simple analytical solution that accurately describes the evolution of a tight-binding chain with a time-dependent localized scattering potential for an extensive range of parameters, and we establish an explicit upper limit for this local density distance in terms of the trace distance. We also demonstrate that, for x-ray photoemission, the quantum adiabatic criterion, as commonly used, fails to predict and track adiabaticity. The local particle density is typically much more straightforward to compute than the corresponding quantum state and is experimentally measurable; this makes the tested method extremely appealing.

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• Adiabatic quantum optimization
• Fermions
• Nonrelativistic wave equations
• Photoemission
• Quantum simulation
• Dynamical systems
• Nonequilibrium systems
• Quantum many-body systems
• Adiabatic approximation
• Exact solutions for many-body systems
• Finite-difference time-domain method
• Functional analytical methods
• Numerical Renormalization Group
• Renormalization group
• Second quantization
• Tight-binding model