arXiv:1802.07141 · Scientific Reports

Arrival Time Distributions of Spin-1/2 Particles

Siddhant Das, Detlef Dürr

Published Feb 19, 2019• 67 citations

Abstract

The arrival time statistics of spin-1/2 particles governed by Pauli's equation, and defined by their Bohmian trajectories, show unexpected and very well articulated features. Comparison with other proposed statistics of arrival times that arise from either the usual (convective) quantum flux or from semiclassical considerations suggest testing the notable deviations in an arrival time experiment, thereby probing the predictive power of Bohmian trajectories. The suggested experiment, including the preparation of the wave functions, could be done with present-day experimental technology.

DOI: 10.1038/s41598-018-38261-4

Related papers

Exotic Bohmian arrival times of spin-1/2 particles: An analytical treatment

Siddhant Das, Markus Nöth, Detlef Dürr

It is well known that orthodox quantum mechanics does not make unambiguous predictions for the statistics in arrival time (or time-of-flight) experiments. Bohmian mechanics (or de Broglie--Bohm theory) offers a distinct conceptual advantage in this regard, owing to the well-defined concepts of point particles and trajectories embedded in this theory. We revisit a recently proposed experiment [S. Das and D. D\"urr, Sci. Rep. 9, 2242 (2019)], the numerical analysis of which revealed a striking spin dependence in the (Bohmian) time-of-arrival distributions of a spin-1/2 particle. We present here a mathematically tractable variant of the same experiment, where the predicted effects can be established rigorously. We also obtain some results that can be compared with experiment.

arXiv:1901.08672Physical Review AMay 28, 201932 citations

Arrival Times Versus Detection Times

Sheldon Goldstein, Roderich Tumulka, Nino Zanghı̀

Abstract How to compute the probability distribution of a detection time, i.e., of the time which a detector registers as the arrival time of a quantum particle, is a long-debated problem. In this regard, Bohmian mechanics provides in a straightforward way the distribution of the time at which the particle actually does arrive at a given surface in 3-space in the absence of detectors. However, as we discuss here, since the presence of detectors can change the evolution of the wave function and thus the particle trajectories, it cannot be taken for granted that the arrival time of the Bohmian trajectories in the absence of detectors agrees with the one in the presence of detectors, and even less with the detection time. In particular, we explain why certain distributions that Das and Dürr (Sci. Rep. 9: 2242, 2019) presented as the distribution of the detection time in a case with spin, based on assuming that all three times mentioned coincide, are actually not what Bohmian mechanics predicts.

arXiv:2405.04607Foundations of PhysicsSep 14, 202413 citations

What Does One Measure When One Measures the Arrival Time of a Quantum Particle?

Nicola Vona, Günter Hinrichs, Detlef Dürr

What is the right statistics for the measurements of arrival times of a quantum particle? Although this question is very old, it is still open. The usual experiments are performed in the far-field regime and this question becomes unimportant, as a semiclassical analysis suffices. Nevertheless, the development in the detector technology will soon allow for near-field investigations; thus, a better understanding of arrival time measurements is needed. Since outcomes of quantum measurements are always described by positive-operator-valued measures (POVMs), various arrival time POVMs have been proposed. On the other hand, many physicists would agree that the arrival time statistics is given by the quantum flux. This urges the question whether a POVM exists, which agrees approximately with the quantum flux values on a reasonable set of wave functions. We answer this question negatively for a very natural set of wave functions, but we remark that the answer is very sensitive to the choice of the set and provide evidence for the existence of a POVM that agrees with the quantum flux on a more restrictive set.

arXiv:1307.4366Physical Review LettersNov 26, 201335 citations

Inequivalence of stochastic and Bohmian arrival times in time-of-flight experiments

Pascal Naidon

Motivated by a recent prediction [Commun. Phys. 6, 195 (2023).] that time-of-flight experiments with ultracold atoms could test different interpretations of quantum mechanics, this work investigates the arrival times predicted by the stochastic interpretation, whereby quantum particles follow definite but nondeterministic and nondifferentiable trajectories. The distribution of arrival times is obtained from a Fokker-Planck equation and confirmed by direct simulation of trajectories. It is found to be, in general, different from the distribution predicted by the Bohmian interpretation, in which quantum particles follow definite deterministic and differentiable trajectories. This result suggests that trajectory-based interpretations of quantum mechanics could be experimentally discriminated.

arXiv:2405.06324Physical Review AJun 6, 20243 citations

On the possibility of empirically probing the Bohmian model in terms of the testability of quantum arrival/transit time distribution

Dipankar Home, A. K. Pan

The present article focuses on studying the extent to which the nonuniqueness that is inherent in the standard quantum mechanical calculation of arrival/transit time distribution can be exploited to enable an empirical scrutiny of any causal trajectory model such as the Bohmian scheme. For this purpose, we consider the example of spin-1/2 neutral particles corresponding to a wave packet which passes through a spin rotator(SR) that contains constant magnetic field confined within a region - in such a case, the transit time distribution can be measured in terms of the spin distribution of particles emerging from the SR. In particular, we investigate the way one can compare the Bohmian predictions obtained for this example with that using one of the quantum approaches, say, the probability current density based scheme. Here the Bohmian calculational procedure involves a couple of critical subtleties that lead to some specific directions for further studies.

arXiv:1007.0699Jul 5, 20101 citation

On the Possibility of Empirically Probing the Bohmian Model in Terms of the Testability of Quantum Arrival/Transit Time Distribution

Born’s interpretation of the squared modulus of a wave function (|ψ|2) as the probability density of finding a particle within a specified region of space is a key ingredient of the standard framework of quantum mechanics, thereby implying that the standard interpretation of quantum mechanics is inherently epistemological. On the other hand, the possibility of an alternative interpretation of quantum mechanics by interpreting |ψ|2 as the probability density of a particle being actually present within a specified region was first suggested by de Broglie [1]. Later, Bohm [2-4] developed the details of such an ontological model of quantum mechanics by using the notion of an observer-independent spacetime trajectory of an individual particle T&F Cat # K11224, Chapter 8, Page 114, 15-9-2010 that is determined by its wave function through an equation of motion which is formulated in a way consistent with the Schrödinger time evolution. Bohm’s model, thus, explicitly refuted the counterarguments (such as those put forward by Pauli [5] and von Neumann [6]) that claimed to have ruled out the formulation of such a model. Subsequently, much work has been done on various aspects of the Bohmian model [7-10]. That such a model is not unique has been elaborately discussed [11,12] while different versions of the ontological model of quantum mechanics have been proposed [13-21].

CRC Press eBooksApr 19, 20161 citation