Modeling and Prediction of Spatial Deterioration of Airport Runway

Tasaki, Yosuke; Yoshida, Ikumasa; Akimoto, Hirohito; Suemasa, Naoaki

doi:10.2472/jsms.67.190

Cited by 36 publications

(79 citation statements)

References 2 publications

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“…On one side, the study of energy transport through mesoscopic or atomic systems has found applications in disparate systems: from solid state devices [1,2] to light harvesting complexes [3][4][5][6]; from ultra-cold atomic systems [7][8][9] to trapped ions [10][11][12]. On the other side, coherent manipulation of energy is at the core of quantum thermodynamics, whose aims include the understanding of the emergence of thermodynamic laws from quantum mechanics [13][14][15][16][17][18][19][20][21] and the design of thermal machines made with quantum devices [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Reconciliation of quantum local master equations with thermodynamics

et al. 2018

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The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially in the modeling of transport in mesoscopic systems, consists in using local master equations (LMEs) containing Lindblad operators acting locally only on the corresponding subsystem. It has been shown that this approach however generates inconsistencies with the laws of thermodynamics. In this paper we demonstrate that using a microscopic model of LMEs based on repeated collisions all thermodynamic inconsistencies can be resolved by correctly taking into account the breaking of global detailed balance related to the work cost of maintaining the collisions. We provide examples based on a chain of quantum harmonic oscillators whose ends are connected to thermal reservoirs at different temperatures. We prove that this system behaves precisely as a quantum heat engine or refrigerator, with properties that are fully consistent with basic thermodynamics. derivations are in general quite involved since they require knowledge of the full set of eigenvalues and eigenvectors of the system's Hamiltonian, something which quickly becomes prohibitive when the number of subsystems increases. Moreover, depending on the approximations employed, one may also arrive at equations which do not generate completely positive maps (the so-called Redfield equations [50]), or equations which contain unphysical heat currents [54]. For these reasons, microscopic derivations of master equations for systems connected to multiple environments still continues, nowadays, to be a topic of great interest.An alternative, more heuristic, approach consists in deriving a master equation for the individual subsystems, neglecting the interaction with the remaining subsystems. The resulting master equation will then contain only local jump operators describing exchanges between the environment E i and its corresponding subsystem S i . Such equations, which we shall henceforth refer to as LMEs (also frequently called boundarydriven master equations), are typically accurate when the dissipation rates are larger than the interaction between subsystems. Due to their computational simplicity, they have been extensively employed over the last two decades in the study of transport in non-equilibrium quantum systems [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73].It turns out, however, that the nonlocal terms neglected in the LME may still lead to non-thermal steadystates [74] and play a significant role if the heat exchanges are small, even for weakly interacting parts. As a consequence, it has been found that LMEs may lead to apparent thermodynamic inconsistencies, as pointed out recently by Levy and Kosloff [75]. They have shown that the LME for two coupled quantum harmonic oscillators (QHO) may predict currents from a cold to a hot ther...

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Section: Introductionmentioning

confidence: 99%

Reconciliation of quantum local master equations with thermodynamics

et al. 2018

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“…Equation(21) shows that the counter-diabatic field vanishes at the initial and final moments, i.e., | ( ) }is identical to the adiabatic eigenbasis s s 0 , 0 ñ ñ   {| ( ) | ( ) }, which satisfies the presumption of the two-point measurement scheme[25,[39][40][41]. In figures 2(c) and (d), the evolution of B t ( ) with the operation time T=25 ns is plotted explicitly.…”

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confidence: 77%

“…. Based on the two-point measurement scheme [25,[39][40][41], the probability distribution function of a quantum work at time t is written as…”

Section: Statistics Of Sta Workmentioning

confidence: 99%

“…To avoid the distinction between two basic thermodynamic variables, work and heat, many theoretical proposals and experimental implementations have been restricted in closed systems without quantum heat transfer between the system and the bath [28][29][30][31][32][33][34][35][36][37][38]. To account the remaining two sources of uncertainty, the two-point measurement scheme has been proposed for the distribution of quantum work cost [24,25,[39][40][41]. The probability of an accessible work is a product of the probability of a certain initial eigenstate and the conditional probability from this initial eigenstate to an instantaneous eigenstate at the measurement time.…”

Section: Introductionmentioning

confidence: 99%

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Experimental demonstration of work fluctuations along a shortcut to adiabaticity with a superconducting Xmon qubit

et al. 2018

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In a 'shortcut to adiabaticity' (STA) protocol, the counter-diabatic Hamiltonian, which suppresses the non-adiabatic transition of a reference 'adiabatic' trajectory, induces a quantum uncertainty of the work cost in the framework of quantum thermodynamics. Following a theory derived recently (Funo et al 2017 Phys. Rev. Lett. 118 100602), we perform an experimental measurement of the STA work statistics in a high-quality superconducting Xmon qubit. Through the frozen-Hamiltonian and frozen-population techniques, we experimentally realize the two-point measurement of the work distribution for given initial eigenstates. Our experimental statistics verify (i) the conservation of the average STA work and (ii) the equality between the STA excess of work fluctuations and the quantum geometric tensor.

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“…(24), we need to perform Gaussian path integrals over each bath variable q n (z) in Eq. (20) which are in general of the form,…”

Section: Summary and Discussionmentioning

confidence: 99%

Symmetry and its breaking in a path-integral approach to quantum Brownian motion

Yeo

2019

Phys. Rev. E

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We study the Caldeira-Leggett model where a quantum Brownian particle interacts with an environment or a bath consisting of a collection of harmonic oscillators in the path integral formalism. Compared to the contours that the paths take in the conventional Schwinger-Keldysh formalism, the paths in our study are deformed in the complex time plane as suggested by the recent study [C. Aron, G. Biroli and L. F. Cugliandolo, SciPost Phys. 4, 008 (2018)]. This is done to investigate the connection between the symmetry properties in the Schwinger-Keldysh action and the equilibrium or non-equilibrium nature of the dynamics in an open quantum system. We derive the influence functional explicitly in this setting, which captures the effect of the coupling to the bath. We show that in equilibrium the action and the influence functional are invariant under a set of transformations of path integral variables. The fluctuation-dissipation relation is obtained as a consequence of this symmetry. When the system is driven by an external time-dependent protocol, the symmetry is broken. From the terms that break the symmetry, we derive a quantum Jarzynski-like equality for a quantum mechanical work-like quantity given as a function of fluctuating quantum trajectory. In the classical limit, the transformations becomes those used in the functional integral formalism of the classical stochastic thermodynamics to derive the classical fluctuation theorem.arXiv:1909.08212v2 [cond-mat.stat-mech]

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Modeling and Prediction of Spatial Deterioration of Airport Runway

Cited by 36 publications

References 2 publications

Reconciliation of quantum local master equations with thermodynamics

Reconciliation of quantum local master equations with thermodynamics

Experimental demonstration of work fluctuations along a shortcut to adiabaticity with a superconducting Xmon qubit

Symmetry and its breaking in a path-integral approach to quantum Brownian motion

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