Bohmian Mechanics, Open Quantum Systems and Continuous Measurements

Enrique Colomés, Guillermo Albareda, Zhen Zhan +4 more

This chapter discusses how Bohmian mechanics can help us to understand and model the behavior of novel electron device prototypes at the nanometer and picosecond scales. It shows that how Bohmian mechanics can help us in the understanding and designing the upcoming electron device prototypes. The chapter also discusses how Bohmian mechanics can help us to study many-particle quantum electron transport phenomena in nanoelectronic devices and an important advantage of Bohmian mechanics: its ability to treat many-particle systems. It explains the birth of the electronics and its evolution towards nanoelectronics. The chapter also shows that the Bohmian perspective provides useful tools when dealing with the continuous measurement of the electrical current in nanodevices. The former appears at nonzero temperature, where the thermal agitation causes the occupation of energy states to fluctuate. The practical expressions for the computation of the current fluctuations within Bohmian mechanics are quite simple.

Antonio Boulhosa Nassar, Salvador Miret-Artés

Sheldon Goldstein

Dieter Schuch, Moise Bonilla–Licea

Abstract In Bohmian mechanics it is assumed that quantum objects are particles that follow real physical paths. These Bohmian trajectories are obtained by integrating the velocity field that occurs in the continuity equation. However, in the course of deriving these trajectories, the independent position variable x, appearing in the velocity field, is arbtirarily replaced by the time-dependent trajectory q(t). We show under which restrictions such a replacement can be justified, leading to a totally different interpretation of the Bohmian trajectories. They are not real paths of physical particles but borders of regions of constant probability, so-called quantiles, and therefore must be seen in the context of descriptive statistics. Thus they provide a tool complementary to the conventional statistical formulation of quantum mechanics. A possible extension to include open dissipative systems is also discussed, showing that the inclusion of an environment does not change our interpretation of the Bohmian trajectories.

Arthur Fine, Sheldon Goldstein, James T. Cushing

Nicolas Gisin

In Bohmian mechanics, particles follow continuous trajectories, so two-time position correlations have been well defined. However, Bohmian mechanics predicts the violation of Bell inequalities. Motivated by this fact, we investigate position measurements in Bohmian mechanics by coupling the particles to macroscopic pointers. This explains the violation of Bell inequalities despite two-time position correlations. We relate this fact to so-called surrealistic trajectories that, in our model, correspond to slowly moving pointers. Next, we emphasize that Bohmian mechanics, which does not distinguish between microscopic and macroscopic systems, implies that the quantum weirdness of quantum physics also shows up at the macro-scale. Finally, we discuss the fact that Bohmian mechanics is attractive to philosophers but not so much to physicists and argue that the Bohmian community is responsible for the latter.