Thermal conductivity for coupled charged harmonic oscillators with noise in a magnetic field

Keiji Saitou, Makiko Sasada

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We introduce a d-dimensional system of charged harmonic oscillators in a magnetic field perturbed by a stochastic dynamics which conserves energy but not momentum. We study the thermal conductivity via the Green–Kubo formula, focusing on the asymptotic behavior of the Green–Kubo integral up to time t (i.e., the integral of the correlation function of the total energy current). We employ the microcanonical measure to calculate the Green–Kubo formula in general dimension d for uniformly charged oscillators. We also develop amethod to calculate the Green–Kubo formulawith the canonical measure for uniformly and alternately charged oscillators in dimension 1. We prove that the thermal conductivity diverges in dimension 1 and 2 while it remains finite in dimension 3. The Green–Kubo integral calculated with the microcanonical ensemble diverges as t1/4 for uniformly charged oscillators in dimension 1, while it is known to diverge as t1/2 without magnetic field. This is the first rigorous example of the new exponent 1/4 in the asymptotic behavior for the Green–Kubo integral. We also demonstrate that our result provides the first rigorous example of a diverging thermal conductivity with vanishing sound speed. In addition, employing the canonical measure in the Green–Kubo formula, we prove that the Green–Kubo integral for uniformly and alternately charged oscillators respectively diverges as t1/4 and t1/2. This means that the exponent depends not only on a non-zero magnetic field but also on the charge structure of oscillators.

Original languageEnglish
Pages (from-to)951-995
Number of pages45
JournalCommunications in Mathematical Physics
Volume361
Issue number3
DOIs
Publication statusPublished - 2018 Jan 1

Fingerprint

Coupled Oscillators
Thermal Conductivity
Harmonic Oscillator
harmonic oscillators
Diverge
thermal conductivity
Magnetic Field
oscillators
magnetic fields
Asymptotic Behavior
Exponent
exponents
Microcanonical Ensemble
Calculate
Conserve
Stochastic Dynamics
Energy
Correlation Function
Momentum
Charge

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Thermal conductivity for coupled charged harmonic oscillators with noise in a magnetic field. / Saitou, Keiji; Sasada, Makiko.

In: Communications in Mathematical Physics, Vol. 361, No. 3, 01.01.2018, p. 951-995.

Research output: Contribution to journalArticle

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