bibkey: schnellketzmerickeckardt2018bose
authors: Schnell, Alexander; Ketzmerick, Roland; Eckardt, André
year: 2018
title: "On the number of Bose-selected modes in driven-dissipative ideal Bose gases"
doi: 10.1103/PhysRevE.97.032136
url: "https://arxiv.org/abs/1802.04088v2"
claim: "The paper characterizes the Bose-selected states of driven-dissipative ideal Bose gases by the condition mu = A eta on the rate-asymmetry matrix, shows that two ohmic baths with product coupling select at most three states (M_S <= 2 M_B - 1 for M_B baths), and expects the same bound for non-ohmic spectral densities |epsilon|^d sgn(epsilon)."
strata_touched:
  - D5/S3/StatisticalMechanics/BoseSelectionCubicTwoBathRefutation
license: citation-only
triage: anchor

Schnell, Ketzmerick and Eckardt, On the number of Bose-selected modes in driven-dissipative ideal Bose gases

A. Schnell, R. Ketzmerick and A. Eckardt, Phys. Rev. E 97, 032136 (2018), DOI 10.1103/PhysRevE.97.032136; arXiv:1802.04088v2. Quotations are from the arXiv v2 TeX source main.tex; macros are expanded.

The selected set $S$ of single-particle states is characterized by $\mu =A\eta$ with ${\mu }_i=0$, ${\eta }_i>0$ for $i\in S$ and ${\mu }_i<0$, ${\eta }_i=0$ for $i\notin S$ (l. 373–381), a condition that “has been shown to uniquely determine the set of the selected states” (l. 367). For two baths coupled through $|f⟩⟨f|$ and $|g⟩⟨g|$ with $J_{B_2}=-J_{B_1}=-J$, the rate-asymmetry matrix is $A_{ij}=\frac{2\pi }{\hslash }J({\epsilon }_j-{\epsilon }_i)(f_i{f}_j-g_i{g}_j)$ with $f_i=|⟨i|f⟩{|}^2$, $g_i=|⟨i|g⟩{|}^2$ (l. 1066–1083). For two ohmic baths “the number of Bose-selected states is restricted to a maximum of three” (l. 1145–1146), and $M_B$ baths give $M_S\le 2M_B-1$ (l. 1170). The paper then states (l. 1173–1179):

We expect that there is a generalization of the above arguement also to non-ohmic systems described by arbitrary spectral densities. We have checked functions of the form (remember that $J$ must be odd) $J(\epsilon )\propto |\epsilon {|}^d\mathrm{sgn}(\epsilon )$ with some power $d$ (not necessarily integer) and similarly observe $M_S\le 2M_B-1$.

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• DOI: https://doi.org/10.1103/PhysRevE.97.032136
• Source: https://arxiv.org/abs/1802.04088v2