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arXiv:1812.08627

Time-energy uncertainty as cause of thermal flicker noise

Yuriy E. Kuzovlev

Published Dec 18, 2018• 0 citations
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Abstract

It is shown that if kinetics of quantum transitions takes account of energy uncertainty of intermediate states, then it creates non-decaying correlations and non-averagable (flicker) fluctuations in the energy as well as in rates of transitions-induced irreversible processes, in particular, flicker noise or maybe suppression of mobility (rate of wandering) of particle interacting with thermally equilibrium medium

DOI
10.48550/arxiv.1812.08627

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It is shown that if kinetics of quantum transitions takes account of energy uncertainty of intermediate states, then it creates non-decaying correlations and non-averagable (flicker) fluctuations in the energy as well as in rates of transitions-induced irreversible processes, in particular, flicker noise or maybe suppression of mobility (rate of wandering) of particle interacting with thermally equilibrium medium
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Low-frequency noise in a hysteric rf superconducting quantum interference device (SQUID) originating from fluctuations of critical current of a weak link is considered. Such noise can be due to trapping-detrapping processes within the tunnel barrier or to the presence of structural defects with internal degrees of freedom in the surrounding of the weak link. The defects can switch between two (or more) metastable states due to interaction with the thermal bath. On the other hand, elastic (and electric) fields created by defects act upon the critical current of the weak link inducing its fluctuations in time. Such noise is most important for high-Tc SQUIDs at high enough temperatures when defects are effectively interacting with the thermal bath. The dependencies of the intensity and statistics of flicker noise on the SQUID’s parameters and operating regime are analyzed. It is shown that higher correlation functions of output voltage at a given driving current can provide some information on the mechanism of 1/f noise in rf SQUIDs.
We study the speed of fluctuations of a quantum system around its equilibrium state, and show that the speed is extremely small at almost all times in typical thermodynamic cases. This suggests an alternative view on the nature of thermal equilibrium and, in particular, of the origin of thermal fluctuations. We argue that instead of equilibrium being a dynamical process in which the system actively fluctuates in time, the fluctuations are due to quantum uncertainties in an essentially static state.
How macroscopic, deterministic order emerges from microscopic systems governed by quantum and thermal fluctuations remains a central problem in non-equilibrium statistical mechanics. While classical reaction theories based on linear energy landscapes describe thermally activated processes, they do not fully account for the extreme state localization observed in complex systems such as molecular recognition. Here, we propose the Information-driven Quantum Geometric (IQG) model, a theoretical framework in which measurement-induced feedback modifies the effective free-energy landscape. By combining coarse-grained quantum dynamics with large deviation theory, we show that nonlinear information feedback induces a sharp geometric crossover—termed the Fidelity Cliff—marking a transition from fluctuation-dominated dynamics to deterministic state locking. Numerical analysis based on a nonlinear Fokker-Planck equation demonstrates the formation of a noise-suppressed metastable subspace (NSMS), where an emergent energy gap provides spectral protection against environmental noise. This mechanism ensures robust state localization despite continuous thermal perturbations. Our results establish a unified physical framework linking quantum measurement dynamics to classical reaction kinetics, providing a quantitatively testable mechanism for the emergence of macroscopic attractors in dissipative systems.
Textbook quantum mechanics treats time as a classical parameter and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\mathrm{\ensuremath{\Delta}}t\mathrm{\ensuremath{\Delta}}E\ensuremath{\gtrsim}\ensuremath{\hbar}$, the term $\mathrm{\ensuremath{\Delta}}t$ must be interpreted as a time interval and not as a time measurement uncertainty due to quantum noise. However, quantum clocks allow for a measurement of the ``time at which an event happens'' by conditioning the system's evolution on an additional quantum degree of freedom. Within this framework we derive here two uncertainty relations that relate the uncertainty in the quantum measurement of the time at which a quantum event happens on a system to its energy uncertainty.