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Absence of a dissipative quantum phase transition in Josephson junctions: Theory
by Carles Altimiras, Daniel Esteve, Çağlar Girit, Hélène le Sueur, Philippe Joyez
Submission summary
| Authors (as registered SciPost users): | Çağlar Girit · Philippe Joyez |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202406_00019v1 (pdf) |
| Date submitted: | 2024-06-10 21:34 |
| Submitted by: | Joyez, Philippe |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We investigate the resistively shunted Josephson junction (RSJ), using the stochastic Liouville equation method in imaginary time - an exact scheme based on the Feynman-Vernon influence functional. The formulation we use makes it clear that Schmid's superconducting - insulating quantum phase transition long believed to occur in the RSJ is forbidden already at the qualitative level. This confirms theoretically a similar conclusion based on experimental observations drawn in 2020 by Murani et al. For all parameters investigated, we find that shunting a junction makes it more superconducting. We reveal that the UV cutoff of the resistor plays an unforeseen key role in these systems, and show that the erroneous prediction of an insulating state resulted from ill-assuming it would not.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We are pleased that, in this first reviewing round, the referees made no fundamental objection to our exact theoretical approach able to deliver quantitative predictions on the RSJ in a wide range of parameters. This validates some of our essential findings stemming from it (⟨cosφ⟩ always positive, role of the UV cutoff, …). Although our main conclusion is an unavoidable consequence of these results, the referees' reports highlight that they all missed this logical link and we blame ourselves for this. It is true that we were more focused on explaining why previous authors came to predict results inconsistent with ours, which we thought the readers would recognize as rigorously excluding a phase transition.
The referee's report stimulated us to provide better explanations and we realized we could reformulate our demonstration in terms of a qualitative energy argument (hence independent of our numerical results) that makes it much simpler to understand. In the resubmitted manuscript, the discussions could be substantially simplified owing to the early exposition of this argument in Sec․ 2.
In the responses to the referees, we try to answer precisely to their criticism aiming to dismiss our conclusions, detailing several arguments not exposed in the original manuscript. All these arguments are not strictly necessary for our invalidation of the phase transition, but they reveal a more complete picture. We hope the referees will find we bring convincing answers to their criticism, clarifying the points that needed be, and that the resubmitted manuscript now makes our main point crystal-clear.
List of changes
Summary of the changes made (These changes are highlighted in color in the attached pdf).
-the abstract
-the end of the introduction
-expressions for actions and/or Lagrangians were corrected where needed (we thank Dr․ Riwar for spotting our incorrect writing). We also corrected a missing prefactor in the expression for the kernel. All these typo-like errors had no impact on our numerics or reasonings.
-in Sec․ 2 after new Eq․ 12, we explain that the expression we use for the action excludes delocalized states (and hence the phase transition) using qualitative energy arguments.
-the discussions section was modified
-the conclusion was modified
-the second half of Appendix D was simplified.
-in Appendix E, we partially rewrote the discussion of Ref. 23, including input from the added Ref. 44.
-a few very minor corrections were made here and there.