Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with 
Non-Commuting Energy and Momentum Operators

Villani, M.; Albareda Piquer, G.; Destefani, C.; Cartoixà, X.; Oriols, X.

doi:10.3390/e23040408

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Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

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Albareda Piquer, G.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Institute of Theoretical and Computational Chemistry, Universitat de Barcelona;

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Citation

Villani, M., Albareda Piquer, G., Destefani, C., Cartoixà, X., & Oriols, X. (2021). Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators. Entropy, 23(4): 408. doi:10.3390/e23040408.

Cite as: https://hdl.handle.net/21.11116/0000-0008-931C-3

Abstract

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).