板違い

エネルギー板向けだな
https://www.nature.com/nature/journal/v546/n7658/full/nature22404.html

>乱雑さを決める時間の対称性を発見　

こっちは大分前の話だな

ネーターの定理から、非保存量であるエントロピーが保存するケースでは、時間対称性が成立していないといけないという、ある意味、直観的には明らかな話を数学的に導出できたのがポイント

https://arxiv.org/pdf/1509.08943.pdf
We study a classical many-particle system with an external control represented by a timedependent
extensive parameter in a Lagrangian. We show that thermodynamic entropy of the
system is uniquely characterized as the Noether invariant associated with a symmetry for an in-
finitesimal non-uniform time translation t → t + η~β, where η is a small parameter, ~ is the Planck
constant, β is the inverse temperature that depends on the energy and control parameter, and
trajectories in the phase space are restricted to those consistent with quasi-static processes in thermodynamics.

＞ 量子物理学の概念であるパリティ-時間対称性の原理を用いて電気回路を作製

これが何なのか、知りたいけれども、じぇんじぇん分かりません。

むねんざんねん、糸口さえつかめない…

だから、「時間の対称性」で検索したおもろいものを貼り付けただけです。

さっそくのご指摘、さすがです。投稿記事とはあまり？関係なかったのですね。

うん、量子力学って、がっこで習った覚えはないんやけど、これ、おもろい。

パリティ-時間対称性原理の元になる対称性に関しては↓が参考になるかも

https://ja.wikipedia.org/wiki/%E5%AF%BE%E7%A7%B0%E6%80%A7_(%E7%89%A9%E7%90%86%E5%AD%A6)
https://ja.wikipedia.org/wiki/CPT%E5%AF%BE%E7%A7%B0%E6%80%A7

全体は、natureの論文を読めば書いてあるが、
応用した電気回路については下の模式図などがポイントだな

赤い点線がPTのスキームで、これまでの調和振動子的なスキームより距離に対してロスが少なくなっている

理論
https://www.nature.com/nature/journal/v546/n7658/images/nature22404-f1.jpg
Nature 546, 387–390 (15 June 2017) doi:10.1038/nature22404
Comparison between conventional and PT-symmetry-based wireless power transfer schemes as the source–receiver resonant coupling rate κ varies as a function of transfer distance d.

a, Conventional scheme. A harmonic wave at a frequency ω is generated, coupled to the source resonator at a rate γ1, transferred across distance d before being delivered to the load at the receiver resonator at a rate γ2.

b, PT-symmetric scheme. Power is generated at the source resonator via a gain element with a gain rate g1, transferred to and taken out at the receiver resonator by a load with a loss rate γ2. c, Transfer efficiency as a function of the separation distance between source and receiver for a conventional scheme without frequency tuning (black line), a conventional scheme with adaptive frequency tuning (blue dashed line) and a PT-symmetry-based scheme (red dotted line).

https://www.nature.com/nature/journal/v546/n7658/images_article/nature22404-f2.jpg

a, Coupled-mode theory model of a pair of coupled gain–loss resonators. Triangle indicates gain; resistor symbol indicates loss. b, c,
Steady-state mode frequencies and their saturated gain rates as a function of coupling rate.
The mode frequencies are obtained by solving equation (3) for a loss rate γ2 = 0.01 and the gain rates from equation (4). When computed at matched resonance

(b), ω1 = ω2 = 1, we can recover the solutions to the exact PT-symmetric phase in the strong coupling region ( ) with balanced gain and loss (g1 = γ2) and mode frequency splitting of .
In the weak coupling region ( ), gain saturation reduces the steady-state gain ( ), and the steady state has a frequency of ω1. Similar mode frequency behaviour survives with a small detuning

(c): ω1 = 1, ω2 = 0.999; here the lower-frequency branch in the strong coupling requires a higher gain rate (dashed lines). In all these cases the steady-state frequencies are real.

回路図と検証
https://www.nature.com/nature/journal/v546/n7658/images_article/nature22404-f3.jpg

Figure 3: Experimental verification of PT-symmetry-based wireless power transfer.
Experimental verification of PT-symmetry-based wireless power transfer.
a, Circuit theory model for PT-symmetric wireless power transfer, showing inductor (L), capacitor (C), resistor (R) and amplifier (A); the triangle marked ‘×1’ is a voltage buffer. b, Photo of our experiment. S is the source resonator; R is the receiver. c–e, Coupled-mode theory (cmt), circuit simulation (sim) and experimental (exp) results showing voltage ratio (c), frequency (d) and phase (e). The two sets of simulations (red and magenta) use slightly different C2 and R1 values to make the frequency bifurcation visible. The parameters for the circuit simulations are provided in Extended Data Table 1.

その理論式が１〜４式、その原理がP-T対称性にあるということ

そして対称性自体は元々の世界に備わった性質だから、それを、こうした回路を使うことで上手く利用できたということだな

いろいろありがとうございます。参考にします。

しかし、おーよそ、ちんぷんかんぷんです。

まるで洞窟の中、壁に映る影を見ているようです。

とりあえず、物理のブックマークフォルダを作りましたｗ

では