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

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 the 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 (BCWF) allow a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of such single-particle 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 (RTD), where a single photon is interacting with a single electron. Third, we emphasize the importance of interpreting such scattering mechanism as a transition between initial and final single-particle BCWF with well-defined energies (rather than with well-defined momenta).

References in corpus (16)

• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• Open system dynamics with non-Markovian quantum trajectories
• Markovian and non-Markovian dynamics in quantum and classical systems
• Linear Scaling Quantum Transport Methodologies
• Non-Markovian stochastic Schrödinger equations: Generalization to real-valued noise using quantum measurement theory
• Exact closed master equation for Gaussian non-Markovian dynamics
• General Non-Markovian structure of Gaussian Master and Stochastic Schrödinger Equations
• Quantum-transport theory for semiconductor nanostructures: A density-matrix formulation
• The interpretation of non-Markovian stochastic Schrödinger equations as a hidden-variable theory
• Exact solution for a non-Markovian dissipative quantum dynamics
• Quantum dissipation with conditional wave functions: Application to the realistic simulation of nanoscale electron devices
• Time-dependent exchange and tunneling: detection at the same place of two electrons emitted simultaneously from different sources
• Bohmian trajectories in an entangled two-qubit system
• The photoelectric effect in external fields
• Chaos and ergodicity in an entangled two-qubit Bohmian system
• Wave packet approach to transport in mesoscopic systems

Cited by in corpus (2)

• Can Wigner distribution functions with collisions satisfy complete positivity and energy conservation?
• Bohmian Mechanics as a Practical Tool