Dimensional crossover of thermal transport in quantum harmonic lattices coupled to self-consistent reservoirs.,Physical Review E

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Dimensional crossover of thermal transport in quantum harmonic lattices coupled to self-consistent reservoirs.
Physical Review E ( IF 2.2 ) Pub Date : 2020-07-08 , DOI: 10.1103/physreve.102.012121
Kiminori Hattori ₁ , Masaya Sambonchiku ₁

Affiliation

In this study, we investigate thermal transport in

d

-dimensional quantum harmonic lattices coupled to self-consistent reservoirs. The

d

-dimensional system is treated as a set of Klein-Gordon chains by exploiting an orthogonal transformation. For generality, the self-energy that describes the reservoir-system coupling is assumed to be a power function of energy

Σ \propto - i ɛ^{n}

, where

n

is limited to odd integers because of the reality condition. Total momentum conservation is violated for

n = 1

but otherwise preserved. In this approach, we show that for

n = 1

, thermal conductivity remains finite in the thermodynamic limit and normal transport takes place for an arbitrary value of

d

. For

n = 3, 5, 7, \dots

, however, thermal conductivity diverges and thermal transport becomes anomalous as long as

d < n

, whereas normal transport is recovered when

d \geq n

. These criteria derived for quantum-mechanical lattices imply that normal transport emerges in high enough dimensions despite total momentum conservation and reinforce the prevailing conjecture deduced in the classical limit.

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