Bohmian Mechanics as a Practical Tool

• URL: http://arxiv.org/abs/2212.09671v3
• Date: Wed, 14 Feb 2024 15:17:49 GMT
• Title: Bohmian Mechanics as a Practical Tool
• Authors: Xabier Oianguren-Asua, Carlos F. Destefani, Matteo Villani, David K. Ferry, Xavier Oriols
• Abstract summary: We will take a trip around several hot-spots where Bohmian mechanics can be harnessed as computational tools. We will see how a Schr"odinger Equation, when used to compute the reduced density matrix of a non-Markovian open quantum system, necessarily seems to employ the Bohmian concept of a conditional wavefunction. We will introduce how a Copenhagen "observable operator" can be derived from numerical properties of the Bohmian trajectories, which within Bohmian mechanics, are well-defined even for an "unmeasured" system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this chapter, we will take a trip around several hot-spots where Bohmian mechanics and its capacity to describe the microscopic reality, even in the absence of measurements, can be harnessed as computational tools, in order to help in the prediction of phenomenologically accessible information (also useful for the followers of the Copenhagen theory). As a first example, we will see how a Stochastic Schr\"odinger Equation, when used to compute the reduced density matrix of a non-Markovian open quantum system, necessarily seems to employ the Bohmian concept of a conditional wavefunction. We will see that by dressing these conditional wavefunctions with an interpretation, the Bohmian theory can prove to be a useful tool to build general quantum frameworks, like a high-frequency electron transport model. As a second example, we will introduce how a Copenhagen "observable operator" can be derived from numerical properties of the Bohmian trajectories, which within Bohmian mechanics, are well-defined even for an "unmeasured" system. Most importantly in practice, even if these numbers are given no ontological meaning, not only we will be able to simulate (thus, predict and talk about) them, but we will see that they can be operationally determined in a weak value experiment. Therefore, they will be practical numbers to characterize a quantum system irrespective of the followed quantum theory.

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