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Modern Physics Letters B

The role of dissipation in macroscopic quantum tunneling and in near-field propagation

Anedio Ranfagni, Gian Paolo Pazzi, Ilaria Cacciari

Published Mar 27, 2019• 1 citation
Publisher

Abstract

A stochastic model, which demonstrated to be capable of determining dissipative effects in the microwave circuits loading superconducting devices, is found to be suitable also for analyzing near-field microwave propagation when the wave attenuation is interpreted as a dissipative effect. An alternative approach to the problem is offered by Feynman’s transition elements.

DOI
10.1142/s0217984919501318

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A stochastic model, which demonstrated to be capable of determining dissipative effects in the microwave circuits loading superconducting devices, is found to be suitable also for analyzing near-field microwave propagation when the wave attenuation is interpreted as a dissipative effect. An alternative approach to the problem is offered by Feynman’s transition elements.
Delay time results obtained in microwave experiments at frequencies above and below the cutoff frequency of different waveguide sections are interpreted on the basis of wave propagation in the presence of dissipative effects. Kac's original suggestion was the starting point for the formulation of a stochastic model, which has now been substantially improved, also in relation to the transition-elements theory of Feynman-Hibbs. In this way, an approach to the problem is provided, which is completely distinct from the ones formulated elsewhere.
ABSTRACT In this work, we introduce an alternative framework for describing dissipative effects in macroscopic quantum tunnelling (MQT) and microwave modulation transfer. We analyse how environmental dissipation modifies dynamics and observable timescales in these two microwave‐frequency contexts, revisiting transmission‐line and resistive‐load models within the bounce (path‐integral) formalism and introducing a complementary Brownian‐motion (statistical‐trajectory) description for modulation‐transfer phenomena. While remaining consistent with established approaches, such as the transmission‐line model and the Leggett prescription, the proposed formulation provides a unified and operational perspective that facilitates the interpretation of experimental data and the identification of effective dissipation mechanisms. Applied to previously published measurements, the framework shows quantitative agreement while offering a physically transparent and practically accessible tool for modelling dissipation in microwave and quantum devices. Beyond its consistency with existing models, the approach is particularly advantageous in systems where dissipation is effectively distributed or non‐local, providing a simplified and physically transparent description in regimes where standard treatments may be less intuitive. These features suggest its potential relevance for the analysis and design of systems in which environmental coupling plays a critical role.
The problem of evaluating dissipative effects in macroscopic quantum tunneling is re-examined for the case of Josephson junctions, with the adoption of an alternative way with respect to several previously proposed and, in some cases, contradictory approaches. The system, which consists of a junction coupled to a transmission line, is analyzed both analytically and numerically. A test of the theoretical model, as compared to the experimental results available, is performed in accordance with a criterion based on a shortening of the traversal time.
Reviewing macroscopic quantum phenomena and quantum dissipation, from the phenomenology of magnetism and superconductivity to the presentation of alternative models for quantum dissipation, this book develops the basic material necessary to understand the quantum dynamics of macroscopic variables. Macroscopic quantum phenomena are presented through several examples in magnetism and superconductivity, developed from general phenomenological approaches to each area. Dissipation naturally plays an important role in these phenomena, and therefore semi-empirical models for quantum dissipation are introduced and applied to the study of a few important quantum mechanical effects. The book also discusses the relevance of macroscopic quantum phenomena to the control of meso- or nanoscopic devices, particularly those with potential applications in quantum computation or quantum information. It is ideal for graduate students and researchers.
The case of an electron tunnelling through a parabolic repeller and acted upon by a microwave electric field is presently treated taking account of dissipation. Dissipation is introduced using a frictional force and the relevant quantum mechanics stems from an appropriate Lagrangian capable of generating the dissipative force. Considerations are presented for deriving a suitable continuity equation adapted to the dissipative processes involved. Starting with a wavepacket as the particle's initial state, expressions for the probability and current densities, as well as the transmission coefficient, are derived. These are used to see the influence of friction, frequency, amplitude and initial phase of the applied field on the tunnelling effect. Furthermore, the localizing effect of friction is made visible on the reflected portion of the wavepacket, where the main body of the probability resides.
The results relative to macroscopic quantum tunneling rate, out of the metastable state of Josephson junctions, are examined in view of determining the effect of dissipation. We adopt a simple criterion in accordance to which the effect of dissipation can be evaluated by analyzing the shortening of the semiclassical traversal time of the barrier. In almost all the considered cases, especially those with relatively large capacitance values, the relative time shortening turns out to be about 20% and with a corresponding quality factor Q ≃ 5.5. However, beyond the specific cases here considered, still in the regime of moderate dissipation, the method is applicable also to different situations with different values of the quality factor. The method allows, within the error limits, for a reliable determination of the load resistance RL, the less accessible quantity in the framework of the resistively and capacitively shunted junction model, provided that the characteristics of the junction (intrinsic capacitance, critical current, and the ratio of the bias current to the critical one) are known with sufficient accuracy.