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Transport through interacting defects and lack of thermalisation
by Giuseppe Del Vecchio Del Vecchio, Andrea De Luca, Alvise Bastianello
This is not the latest submitted version.
This Submission thread is now published as SciPost Phys. 12, 060 (2022)
|As Contributors:||Alvise Bastianello|
|Arxiv Link:||https://arxiv.org/abs/2104.13887v2 (pdf)|
|Date submitted:||2021-09-20 12:15|
|Submitted by:||Bastianello, Alvise|
|Submitted to:||SciPost Physics|
We consider 1D integrable systems supporting ballistic propagation of quasiparticles, perturbed by a localised defect that breaks most conservation laws and induces chaotic dynamics. We study an out-of-equilibrium protocol engineered activating the defect in an initially homogeneous and far from the equilibrium state. We find that large enough defects induce full thermalisation at their center, but nonetheless the outgoing flow of carriers emerging from the defect is non-thermal due to a generalization of the celebrated Boundary Thermal Resistance effect, occurring at the edges of the chaotic region. Our results are obtained combining ab-initio numerical simulations for relatively small-sized defects, with the solution of the Boltzmann equation, which becomes exact in the scaling limit of large, but weak defects.
Submission & Refereeing History
Published as SciPost Phys. 12, 060 (2022)
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Reports on this Submission
Anonymous Report 1 on 2021-10-27 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2104.13887v2, delivered 2021-10-27, doi: 10.21468/SciPost.Report.3746
1- Nice trick to treat infinite systems numerically
2- Nice results on the effects of interaction on the thermalization properties
1- Lack of clarity on the characteristics of the model studied and the implications of the results on the field
This is a nice and original work on a classical 1-d model written as if it were a paper on a quantum model, which makes reading it quite confusing. It considers a *classical* system of quadratic oscillators with a non-linear potential confined in a region of size L.
The authors observe how thermalization is achieved in such a system as a function of the size L and the non-linearity strength $\lambda$. They open the system via dissipative-driven boundaries, which are supposed to mimic infinite systems in the numerics, which is the classical analog of having a Lindbladian superoperator on the extreme left and right sites of a quantum spin chain. They observe remnants of integrability in transport properties even when the bulk of the system is instead described by a thermal statistics. This is interpreted as a generalized boundary thermal resistance effect. I am not an expert on this last phenomenon but the interpretation seems correct. The paper deserves publication, however the authors need to rewrite big chunks of the paper to make it clear the characteristics of the system they are considering. If one were to read the abstract and skip to Eq.(1), one would think this is a work on an integrable *quantum* model (as I did after a first glance!). They even use the notation $\psi^\dagger$ in Eq.(1) and they talk about Wigner function shortly after. They also talk about "quasiparticles" while these are just the modes of the unperturbed, classical, quadratic oscillators. Written like this, the paper is not honest to its readers. I understand the authors speak the lingo of integrable quantum systems but they are abusing it, making it seem like they have solved the relative quantum problem, which they have not.
As they say at the beginning of Section 2: "Extended quantum systems in very excited states are prohibitively challenging to be simulated for long times ..." So I think the paper deserves publication, and it is also reasonably well written, but the writing requires fine tuning to avoid making the reader wonder if the authors have solved a"prohibitively challenging" problem, which they have not.
Another point: while in the quantum transport set-up driven-dissipative boundaries (which lead to the Lindblad equation) are used to mimic the leads attached to a mesoscopic object (in the markovian limit etc.), in classical mechanics I am not sure this can be easily justified nor I have seen it used before (no reference is quoted here, so I assume this is an invention of the authors). The authors should justify this set-up more convincingly.
1- Make it clear this is a paper about a classical problem.
2- Make more connections with other classical systems works, going outside the realm of quantum integrable systems.
3- Justifications of the driven-dissipative setup.