Thermal conductance of a two-level atom coupled to two quantum harmonic oscillators

Abstract

We have determined the thermal conductance of a system consisting of a two-level atom coupled to two quantum harmonic oscillators in contact with heat reservoirs at distinct temperatures. The calculation of the heat flux as well as the atomic population and the rate of entropy production are obtained by the use of a quantum Fokker-Planck-Kramers equation and by a Lindblad master equation. The calculations are performed for small values of the coupling constant. The results coming from both approaches show that the conductance is proportional to the coupling constant squared and that, at high temperatures, it is proportional to the inverse of temperature.

Effect of coherence of nonthermal reservoirs on heat transport in a microscopic collision model

“…And they have the similar behaviors that κ firstly increases (at low temperatures T 0.45) and then decreases (at high temperatures T 0.45) with the increase of temperatures, and as mentioned above this result is consistent with Ref. [24]. Physically, this can be easily understood as following.…”

“…Note that a similar result has been obtained in Ref. [24] that the conductance firstly increases (low temperatures) and then decreases (high temperatures) with the increase of temperature, and at high temperatures the conductance is proportional to the inverse of temperature. State with coherence.…”

“…For example, Wichterich et al have investigated heat transport in a spin-1/2 Heisenberg chain, locally coupled to independent thermal baths of different temperatures, and they have obtained a stationary energy current by quantum master equation method and provided the way for efficient numerical investigations of heat transport in larger systems [15]; Werlang et al have realized a heat trans- * Electronic address: zoujian@bit.edu.cn port between two pure-dephasing Markovian reservoirs connected through a chain of coupled sites, and quantum coherence between sites is generated in the steady regime and results in the underlying mechanism sustaining the effect of heat transport [19]. Moreover, one of the conceptual pillars in energy transport, Fourier's law of heat conduction, has become an important issue and has been investigated in classical [20,21] and quantum systems [17,[22][23][24]. An important step in understanding how Fourier's law emerges from the quantum domain has been made by Michel et al [22].…”

Fenômenos de transporte em sistemas fora do equilíbrio

“…, onde uma expressão para o fluxo de calor foi obtida analiticamente no regime de acoplamento fraco entre os osciladores da cadeia. Além disso, no limite clássico, foi recuperado o resultado obtido por Rieder et al [17] para a versão clássica do problema.O outro modelo foi estudado pelo autor desta tese e consiste em uma extensão do modelo de Rabi[95], onde consideramos dois modos do campo eletromagnético no interior de uma cavidade ótica interagindo com um único átomo de dois níveis[105]. Esse sistema está representado na Figura 10.1.…”

“…Quando a diferença entre as temperaturas dos reservatórios T 1 − T 2 = ∆T é infinitesimal, obtivemos também a condutância térmica κ = φ /∆T, tanto para dinâmica a FPK quântica, quanto para a dinâmica de Lindblad. Não mostraremos os resultados aqui, porém uma cópia do artigo[105] pode ser encontrada no Apêndice C.A seguir, pretendemos utilizar a dinâmica FPK quântica para estudar sistemas fisicamente mais ricos, como o modelo de Dicke e o modelo de Bose-Hubbard, já que estes apresentam transição de fase quântica.…”