Virtual Potentials in Electric Circuit and Motion of Brownian Gyrator

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姓名

張昕(Hsin Chang) 查詢紙本館藏

畢業系所

物理學系

論文名稱

(Virtual Potentials in Electric Circuit and Motion of Brownian Gyrator)

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摘要(中)

受熱擾動影響的電路，其隨機行為類似於高粘度流體中的微觀粒子。藉由外加回饋控制技術(feedback-controlled technique)，我們通過實驗在電路中產生可調虛擬位能的布朗動力學(Brownian dynamics)。當回饋速度夠快，電路雜訊在虛擬位能井(virtual potential)中的行為與在真實的位能井中沒有區別。實驗結果顯示電路版本的回饋阱對於研究非平衡系統是個簡單、有效且可編程的方案。而這樣的方法理論上可以擴展到多自由度的系統。通過回饋耦合兩組電阻電容電路，便可觀察到布朗旋轉子(Brownian Gyrator)的現象。

布朗旋轉子的製備是二維布朗粒子在諧和位能(harmonic potential)中，並受到來自不同方向且具備不同溫度的隨機力撞擊。我們將諧和位能替換為其他類型的位能，並通過模擬研究其非平衡穩態動力學(non-equilibrium steady state dynamics)。在非諧位能的情況下，我們發現此系統機率流(probability flow)不沿著機率等高線流動。甚至在可線性近似的位能低點附近也存在違反此特徵的情況。此現象意味著機率流的方向不垂直於機率梯度，且粒子的熵隨穩態軌跡而改變。

摘要(英)

Electric circuits affected by thermal agitation are analog to confined Brownian particles in a high-viscosity fluid. Here we experimentally demonstrate an effective technique of generating tunable potentials for the Brownian dynamics in an electric circuit, realized by external controlled feedback. The thermal fluctuation undergoes equivalent Brownian dynamics in the authentic potentials as long as the feedback is fast enough to react for designed potentials. The results show that the electric-circuit version of feedback-trap provides a simple, effective, and programmable scheme to study non-equilibrium system. The generation can in principle be expanded to systems with multi degrees of freedom. The phenomenon of the Brownian gyrator can be observed by coupling two RC circuits with a feedback function instead of a coupling capacitor.

A Brownian gyrator features a two-dimensional random particle under a harmonic potential, while random thermal kicks are of distinct temperatures along the two orthogonal axes. We replace the harmonic potential by other types of potentials, and we investigate the non-equilibrium steady states through simulation studies. In contrast to the Brownian-gyrator case, where the probability flow circulates along the probability contour, the results for the non-harmonic cases do not follow this signature. Moreover, the violation of this feature exists even near the potential minima, where the harmonic approximation work. This implies that the probability flow is not perpendicular to the probability gradient and the entropy of the particle changes along with the steady state trajectory.

關鍵字(中)

★ 隨機過程
★ 虛擬位能井
★ 回饋控制
★ 布朗旋轉子
★ 非平衡穩態動力學

關鍵字(英)

★ Stochastic Process
★ Virtual potential
★ Feedback Control
★ Brownian Gyrator
★ Non-equilibrium Steady State Dynamics

論文目次

Abstract i
Contents ii
List of Figures iv
List of Tables v
Glossary vi
Acronym . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
Symbol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
1 Introduction 1
2 Stochastic Thermodynamics 3
2.1 One-Dimensional Brownian Motion . . . . . . . . . . . . . . . . . . . 4
2.1.1 Langevin Equation . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Overdamped Approximation . . . . . . . . . . . . . . . . . . . 9
2.1.3 Johnson-Nyquist Noise . . . . . . . . . . . . . . . . . . . . . . 12
2.1.4 Analogous Brownian Particle in Electric Circuit . . . . . . . . 12
2.2 Brownian Gyrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Markov Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Fokker-Planck Equation . . . . . . . . . . . . . . . . . . . . . 20
2.3 Virtual Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 Experimental Studies of Virtual Potentials in Electric Circuit 27
3.1 Experimental Setup of Feedback Control . . . . . . . . . . . . . . . . 28
3.2 Virtual Harmonic Potential . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.1 Experimental Result . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.2 Discrete Delay Equation . . . . . . . . . . . . . . . . . . . . . 33
3.2.3 Discrete Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Virtual Double Well . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.1 Static Double Well . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.2 Stochastic Resonance in Time-varying Double Well . . . . . . 41
4 Numerical Studies of Motion of Brownian Gyrator 44
4.1 Simulation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Expression of Probability Flow . . . . . . . . . . . . . . . . . . . . . 47
4.3 Harmonic Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.1 Numerical Result . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.2 Analytical Calculation of Probability Distribution and Flow . 50
4.4 Two-Dimensional Double Well . . . . . . . . . . . . . . . . . . . . . . 52
4.4.1 Numerical Result . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4.2 Entropy Changing Rate . . . . . . . . . . . . . . . . . . . . . 52
4.5 Isotropic Quartic Potential . . . . . . . . . . . . . . . . . . . . . . . . 54
4.5.1 Numerical Result . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5.2 Parity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5 Conclusion 57
Bibliography 58

參考文獻

[1] S Ciliberto. Experiments in stochastic thermodynamics: Short history and
perspectives. Physical Review X, 7(2):021051, 2017.
[2] Dennis V Perepelitsa. Johnson noise and shot noise. Dept. of Physics, MIT,
2006.
[3] Udo Seifert. Stochastic thermodynamics,
uctuation theorems and molecular
machines. Rep. Prog. Phys, 75(126001):58pp, 2012.
[4] Dong Yun Lee, Chulan Kwon, and Hyuk Kyu Pak. Nonequilibrium
situations for a single-particle analog of gas in a soft wall. Physical review letters, 114(6):060603, 2015.
[5] Christopher Jarzynski. Nonequilibrium equality for free energy dierences. Physical Review Letters, 78(14):2690, 1997.
[6] Gavin E Crooks. Nonequilibrium measurements of free energy dierences for microscopically reversible markovian systems. Journal of Statistical Physics, 90(5-6):1481{1487, 1998.
[7] Govind Paneru, Dong Yun Lee, Tsvi Tlusty, and Hyuk Kyu Pak. Lossless brownian information engine. Physical review letters, 120(2):020601, 2018.
[8] Kensaku Chida, Samarth Desai, Katsuhiko Nishiguchi, and Akira Fujiwara. Power generator driven by maxwell′s demon. Nature communications, 8(1):1{1}7, 2017.
[9] Chulan Kwon. Information thermodynamics for feedback processes with the
appearance of overshooting. Physical Review E, 95(4):042103, 2017.
[10] Linda E Reichl. A Modern Course in Statistical Physics. John Wiley & Sons,
2016.
[11] Philip Nelson. Biological physics. WH Freeman New York, 2004.
[12] John Bertrand Johnson. Thermal agitation of electricity in conductors. Physical
review, 32(1):97, 1928.
[13] Harry Nyquist. Thermal agitation of electric charge in conductors. Physical
review, 32(1):110, 1928.
[14] Roger Filliger and Peter Reimann. Brownian gyrator: A minimal heat engine
on the nanoscale. Physical review letters, 99(23):230602, 2007.
[15] H Risken and K Voigtlaender. Solutions of the fokker-planck equation describing
the thermalization of neutrons in a heavy gas moderator. Zeitschrift fur Physik
B Condensed Matter, 54(3):253{262, 1984.
[16] Peter Reimann. Brownian motors: noisy transport far from equilibrium.
Physics reports, 361(2-4):57{265, 2002.
[17] Jong-Min Park, Hyun-Myung Chun, and Jae Dong Noh. Eciency at maximum
power and eciency
uctuations in a linear brownian heat-engine model.
Physical Review E, 94(1):012127, 2016.
[18] Adam E Cohen. Control of nanoparticles with arbitrary two-dimensional force
elds. Physical review letters, 94(11):118102, 2005.
[19] Adam E Cohen and WE Moerner. Method for trapping and manipulating
nanoscale objects in solution. Applied physics letters, 86(9):093109, 2005.
[20] John AC Albay, Govind Paneru, Hyuk Kyu Pak, and Yonggun Jun. Optical
tweezers as a mathematically driven spatio-temporal potential generator. Optics
express, 26(23):29906{29915, 2018.
[21] Yonggun Jun and John Bechhoefer. Virtual potentials for feedback traps. Phys-
ical Review E, 86(6):061106, 2012.
[22] Yonggun Jun, Momcilo Gavrilov, and John Bechhoefer. High-precision test of
landauer′s principle in a feedback trap. Physical review letters, 113(19):190601,
2014.
[23] Avinash Kumar and John Bechhoefer. Nanoscale virtual potentials using optical
tweezers. Applied Physics Letters, 113(18):183702, 2018.
[24] John AC Albay, Sarah R Wulaningrum, Chulan Kwon, Pik-Yin Lai, and Yonggun
Jun. Thermodynamic cost of a shortcuts-to-isothermal transport of a brownian
particle. Physical Review Research, 1(3):033122, 2019.
[25] Ping Ao. Potential in stochastic dierential equations: novel construction.
Journal of physics A: mathematical and general, 37(3):L25, 2004.
[26] Chulan Kwon, Ping Ao, and David J Thouless. Structure of stochastic dynamics
near xed points. Proceedings of the National Academy of Sciences,
102(37):13029{13033, 2005.
[27] K-H Chiang, C-L Lee, P-Y Lai, and Y-F Chen. Electrical autonomous brownian
gyrator. Physical Review E, 96(3):032123, 2017.
[28] Juan Pablo Gonzalez, John C Neu, and Stephen W Teitsworth. Experimental
metrics for detection of detailed balance violation. Physical Review E,
99(2):022143, 2019.

指導教授

陳永富(Yung-Fu Chen)

審核日期

2020-7-20

推文