Kinetic energy equipartition: a tool to characterize quantum thermalization

The Orthodox kinetic energy has, in fact, two hidden-variable components: one linked to the current (or Bohmian) velocity, and another linked to the osmotic velocity (or quantum potential), and which are respectively identified with phase and amplitude of the wavefunction. Inspired by Bohmian and Stochastic quantum mechanics, we address what happens to each of these two velocity components when the Orthodox kinetic energy thermalizes in closed systems, and how the pertinent weak values yield experimental information about them. We show that, after thermalization, the expectation values of both the (squared) current and osmotic velocities approach the same stationary value, that is, each of the Bohmian kinetic and quantum potential energies approaches half of the Orthodox kinetic energy. Such a `kinetic energy equipartition' is a novel signature of quantum thermalization that can empirically be tested in the laboratory, following a well-defined operational protocol as given by the expectation values of (squared) real and imaginary parts of the local-in-position weak value of the momentum, which are respectively related to the current and osmotic velocities. Thus, the kinetic energy equipartion presented here is independent on any ontological status given to these hidden variables, and it could be used as a novel element to characterize quantum thermalization in the laboratory, beyond the traditional use of expectation values linked to Hermitian operators. Numerical results for the nonequilibrium dynamics of a few-particle harmonic trap under random disorder are presented as illustration. And the advantages in using the center-of-mass frame of reference for dealing with systems with many indistinguishable particles are also discussed.Comment: submitted on 02/May/2

How weak values illuminate the role of "hidden"-variables as predictive tools

In this chapter we offer an introduction to weak values from a three-fold perspective: first, outlining the protocols that enable their experimental determination; next, deriving their correlates in the quantum formalism and, finally, discussing their ontological significance according to different quantum theories or interpretations. We argue that weak values have predictive power and provide novel ways to characterise quantum systems. We show that this holds true regardless of ongoing ontological disputes. And, still, we contend that certain "hidden" variables theories like Bohmian mechanics constitute very valuable heuristic tools for identifying informative weak values or functions thereof. To illustrate these points, we present a case study concerning quantum thermalization. We show that certain weak values, singled out by Bohmian mechanics as physically relevant, play a crucial role in elucidating the thermalization time of certain systems, whereas standard expectation values are "blind" to the onset of thermalization.Comment: 16 pages, 2 figures, article accepted for publication by Oxford University Press in the forthcoming book "Guiding Waves in Quantum Mechanics", edited by Andrea Oldofredi, due for publication in 202

Bohmian Mechanics as a Practical Tool

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.Comment: 13 pages, 1 figure, to be published as a Chapter in the book "Physics and the Nature of Reality: Essays in Memory of Detlef D\"urr". Accepted version, integrating comments by refere