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[A theoretical approach to "macroscopic fluctuations" effect].

V A Namiot

Published Sep 1, 2001• 2 citations
OpenAlex

Abstract

At present there is no generally accepted theory of the effect of macroscopic fluctuations. It the article, an attempt is made to relate this effect to some basic properties of quantum systems, in particular, to the formal absence of dynamic chaos in these systems. Based on this approach, it was shown why the level of the effect must be of the same order of magnitude as the level of noise and cannot exceed this level as the number of experiments increases. It was shown qualitatively what is the cause of the similarity of histograms observed in different experiments.

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At present there is no generally accepted theory of the effect of macroscopic fluctuations. It the article, an attempt is made to relate this effect to some basic properties of quantum systems, in particular, to the formal absence of dynamic chaos in these systems. Based on this approach, it was shown why the level of the effect must be of the same order of magnitude as the level of noise and cannot exceed this level as the number of experiments increases. It was shown qualitatively what is the cause of the similarity of histograms observed in different experiments.
Abstract Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging classicality is expected. This behaviour hinges on collective observables, named quantum fluctuations , that retain a quantum character even in the thermodynamic limit: they provide useful tools for studying properties of many-body systems at the mesoscopic level, in-between the quantum microscopic scale and the classical macroscopic one. We herein present the general theory of quantum fluctuations in mesoscopic systems, and study their dynamics in a quantum open system setting, taking into account the unavoidable effects of dissipation and noise induced by the external environment. As in the case of microscopic systems, decoherence is not always the only dominating effect at the mesoscopic scale: certain types of environment can provide means for entangling collective fluctuations through a purely noisy mechanism.
The relation between determinism and predictability is the central issue in the study of 'deterministic chaos'. Much knowledge has been accumulated in the past 10 years about the chaotic dynamics of macroscopic (classical) systems. Our intention is to examine the implications of chaos in the microscopic quantum world – in other words, how to reconcile the correspondence principle with the inherent uncertainties which reflect the wave nature of quantum dynamics. Some rather surprising and counterintuitive results emerge from this effort which bear an intriguing similarity to a phenomenon associated with electric conductivity in disordered solids, namely 'Anderson localisation'. It is very rewarding that these developments do not remain in the lofty realms of abstract theoretical physics. Indeed, recent atomic physics experiments demonstrate clearly that chaos is relevant to the microscopic world. In particular, such experiments emphasise the urgent need to clarify the genuine quantum mechanism which imposes severe limitations on quantum dynamics, and renders it so very different from its classical counterpart.
The best energy sensitivity expected for a squid operating conventionally in the linear detector mode is believed, on both experimental and theoretical grounds, to be ~ ℏ /2 J Hz −1 (see section 4.3.1 ). As we have already stressed, in almost all real applications environmental noise actually limits the sensitivity at a level several orders of magnitude greater than this. However there are a number of fundamental experiments being carried on at the time of writing which are able to use the full capabilities of a quantum noise-limited squid. These investigations involve tests of general relativity, searches for fundamental particles and high-precision tests of some basic physical laws. In this section a variety of different experiments will be discussed in some detail, both because of the challenging nature of the effects which they are intended to investigate and because they provide classic examples of the type of high-precision measurement which is only possible using the unique properties of superconducting electronics.
Macroscopic realism is a set of assumptions about how we experience the world at a classical level. While the Leggett-Garg inequalities are temporal correlations that are violated by quantum systems not obeying such macrorealism, the no-signaling in time condition is also a necessary condition. This compares measurement outcomes with and without prior measurements. As dynamics and correlations play a central role in these measures, this paper explores the effects of regular versus chaotic dynamics on the violations of macroscopic realism. We observe a close connection between a 3 point out-of-time-order correlator and the conditional probabilities of measurement, and we find unmistakable imprints of chaos on the violations of macrorealism. We provide qualitative semiclassical reasoning for the numerical results involving a kicked top, and for two important initial states that behave very differently.