Additivity principle in high-dimensional deterministic systems

Keiji Saitou, Abhishek Dhar

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The additivity principle (AP), conjectured by Bodineau and Derrida, is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated and compared with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high dimensional. Surprisingly, even in the anomalous regime the CGF is also well fitted by the AP. Lower-dimensional systems are also studied and the importance of three dimensionality for the validity is stressed.

Original languageEnglish
Article number250601
JournalPhysical Review Letters
Volume107
Issue number25
DOIs
Publication statusPublished - 2011 Dec 14
Externally publishedYes

Fingerprint

conductive heat transfer
ballistics
heat transfer
harmonics

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Additivity principle in high-dimensional deterministic systems. / Saitou, Keiji; Dhar, Abhishek.

In: Physical Review Letters, Vol. 107, No. 25, 250601, 14.12.2011.

Research output: Contribution to journalArticle

@article{f49add7cd64f4e7d98a34e7b4c158bec,
title = "Additivity principle in high-dimensional deterministic systems",
abstract = "The additivity principle (AP), conjectured by Bodineau and Derrida, is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated and compared with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high dimensional. Surprisingly, even in the anomalous regime the CGF is also well fitted by the AP. Lower-dimensional systems are also studied and the importance of three dimensionality for the validity is stressed.",
author = "Keiji Saitou and Abhishek Dhar",
year = "2011",
month = "12",
day = "14",
doi = "10.1103/PhysRevLett.107.250601",
language = "English",
volume = "107",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "25",

}

TY - JOUR

T1 - Additivity principle in high-dimensional deterministic systems

AU - Saitou, Keiji

AU - Dhar, Abhishek

PY - 2011/12/14

Y1 - 2011/12/14

N2 - The additivity principle (AP), conjectured by Bodineau and Derrida, is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated and compared with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high dimensional. Surprisingly, even in the anomalous regime the CGF is also well fitted by the AP. Lower-dimensional systems are also studied and the importance of three dimensionality for the validity is stressed.

AB - The additivity principle (AP), conjectured by Bodineau and Derrida, is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated and compared with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high dimensional. Surprisingly, even in the anomalous regime the CGF is also well fitted by the AP. Lower-dimensional systems are also studied and the importance of three dimensionality for the validity is stressed.

UR - http://www.scopus.com/inward/record.url?scp=83655193115&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=83655193115&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.107.250601

DO - 10.1103/PhysRevLett.107.250601

M3 - Article

C2 - 22243060

AN - SCOPUS:83655193115

VL - 107

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 25

M1 - 250601

ER -