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２０２１年７月１３日（火）物 理 学 第 一 分 野

物理学第一分野ＤＣ３回生研究発表会
場所：理学研究科５号館 ５階・第四講義室＋オンライン
発表：２０分（別に質問１０分程度）
２０２１年７月１３日（火）１１：３０～

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１． Pumping current in a non-Markovian N-state model
Ville Matias Mikael Paasonen（１１：３０）・・・・・ １

Pumping current in a non-Markovian N-state model
Advanced Statistical Dynamics Group

Ville Matias Mikael Paasonen

Abstract A periodically modulated N-state model whose dynamics are governed by a timeconvoluted generalized master equation is theoretically analyzed. The non-Markovian masterequation is converted to a larger Markovian model affording easy analysis. The behavior of thismodel is investigated by calculating the cycle-averaged pumping current analytically andnumerically.
© 2021 Department of Physics, Kyoto University− J (Ω)

Cycle averag ed current

Master equations (MEs) are widely used in non-equilibrium statistical mechanics to model the time evolution ofa range of classical and quantum mechanical systems. In their basic form, MEs only describe systems that carry no
memory of their past: this property is referred to as Markovianity. It is known, however, that due to a number ofphysical reasons, real systems do usually possess some degree of memory of their past evolution, and thus obey a
non-Markovian ME (nMME) [1].
Modulating control parameters such as reaction rate coefficients, bath temperatures or gate voltages of a physicalsystem out of equilibrium can lead to net flow of a physical current, known as Thouless pumping [2]. The origin of
the pumping current is the Berry-Sinitsyn-Nemenman (BSN) phase, which was originally discovered in the contextof quantum systems [3]. The BSN phase is a geometrical effect which also exists in classical systems, such as theSinitsyn-Nemenman (SN) model of reaction kinetics, in which some parameters are cyclically modulated by an
external agent [4].
0.01
Motivated by these results, in the present study aw = 0.5
w= 1
generalization of the SN model obeying a nMME
w= 2
is presented as a natural extension of thew= 5
conventional SN model, and mapped onto a larger
Markovian system. We demonstrate that a good0.005agreement is achieved between the pumping
current obtained from the numerical solution, andthe analytically calculated geometrical current in
the adiabatic limit. Furthermore, we employ a0technique based on eigenvalue analysis and0 2 4 6 8 10 12 14 16 18 20
perturbation theory to go beyond the adiabaticΩlimit and show the improvement on the analyticalm easurecalculation that results from accounting for theJ(t)effect of finite modulation speed [5]. Fig. 1111
shows a schematic of the Markovian system used
K L (t)K R (t)WLWRL
R
for the calculations and a plot of the modulation
222
driving at
driving at
speed dependence of the pumping current.
qL (t)p(t)qR (t)

References
Fig. 1. Schematic of the Markovian system used for the[1] H.-P Breuer et al., Rev. Mod. Phys. 88,
calculations (bottom) and a plot of the modulation
021002 (2016).
speed dependence of the pumping current for selected[2] D. J. Thouless, Phys Rev B 27, 6083 (1983).
values of the system parameters (top).
[3] M. V. Berry. Proc. Roy. Soc. London, Series A 392,45 (1984).
[4] N. A. Sinitsyn and I. Nemenman, Europhys. Lett. 77, 58001 (2007).
[5] V. M. M. Paasonen and H. Hayakawa, Phys. Rev. Research 3, 023238 (2021).