Heat Transport in an Ordered Harmonic Chain in Presence of a Uniform Magnetic Field

Bhat, Junaid Majeed; Cane, Gaëtan; Bernardin, Cédric; Dhar, Abhishek

doi:10.1007/s10955-021-02848-5

Cited by 2 publications

(4 citation statements)

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“…T ∞ (ω) is sensitive to boundary conditions and could be determined by considering the chain in a uniform magnetic field given by B . In [21], we proved that for B = 0, T ∞ (ω) ∼ ω 3/2 and ∼ ω 1/2 for fixed and free boundaries respectively, while for B = 0 it goes as ω 2 and ω 0 for the two boundary conditions respectively. Hence we need to determine the small ω behaviour of λ(ω).…”

Section: Effect Of Localization Due To Random Magnetic Field On the N...mentioning

confidence: 82%

“…The behaviour of T ∞ (ω) was obtained in our previous paper [21] by using the Non-Equilibrium Green Function approach. It was found there that its behaviour depends strongly on the presence or not of the magnetic field but also on the boundary conditions imposed.…”

Section: Discussionmentioning

confidence: 99%

“…In [21], by using the non-equilibrium Green function formalism, we obtained an exact expression for the heat current, J N , in the steady state of the chain. More exactly, let us define the processes (f ± n ) n≥0 and (g ± n ) n≥0 as…”

Section: Heat Currentmentioning

confidence: 99%

“…In this paper we consider an ordered (constant masses) one-dimensional chain of twodimensional oscillators subject to a constant transverse magnetic field when the oscillators are disorderly charged (or equivalently a chain of oscillators with the same charge but subject to a random magnetic field on the lattice). In [21], by using the Non-Equlibrium Greens's Function (NEGF) formalism we obtained an explicit expression of the heat current in the steady state and investigated then the transport properties of such a system when all the charges are the same. We established that transport is ballistic like for ordered harmonic chains.…”

Section: Introductionmentioning

confidence: 99%

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Localization effects due to a random magnetic field on heat transport in a harmonic chain

Cane¹,

Bhat²,

Dhar³

et al. 2021

J. Stat. Mech.

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We consider a harmonic chain of N oscillators in the presence of a disordered magnetic field. The ends of the chain are connected to heat baths and we study the effects of the magnetic field randomness on heat transport. The disorder, in general, causes localization of the normal modes, due to which a system becomes insulating. However, for this system, the localization length diverges as the normal mode frequency approaches zero. Therefore, the low frequency modes contribute to the transmission, T N ( ω ) , and the heat current goes down as a power law with the system size, N. This power law is determined by the small frequency behaviour of some Lyapunov exponents, λ(ω), and the transmission in the thermodynamic limit, T ∞ ( ω ) . While it is known that in the presence of a constant magnetic field T ∞ ( ω ) ∼ ω 3 / 2 , ω 1 / 2 depending on the boundary conditions, we find that the Lyapunov exponent for the system behaves as λ(ω) ∼ ω for B ≠ 0 and λ(ω) ∼ ω 2/3 for B = 0 . Therefore, we obtain different power laws for current vs N depending on B and the boundary conditions.

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Section: Effect Of Localization Due To Random Magnetic Field On the N...mentioning

confidence: 82%

Section: Discussionmentioning

confidence: 99%

Section: Heat Currentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations