Universal Scaling Bounds on a Quantum Heat Current

• URL: http://arxiv.org/abs/2209.05789v2
• Date: Sat, 16 Sep 2023 19:34:12 GMT
• Title: Universal Scaling Bounds on a Quantum Heat Current
• Authors: Shunsuke Kamimura, Kyo Yoshida, Yasuhiro Tokura, and Yuichiro Matsuzaki
• Abstract summary: We derive new bounds on a heat current flowing into a quantum $L$-particle system coupled with a Markovian environment. We show that the absolute value of the heat current scales at most as $Theta (L3)$ in a limit of large $L$. Our results are useful to evaluate the best achievable performance of quantum-enhanced thermodynamic devices.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive new bounds on a heat current flowing into a quantum $L$-particle system coupled with a Markovian environment. By assuming that a system Hamiltonian and a system-environment interaction Hamiltonian are extensive in $L$, we show that the absolute value of the heat current scales at most as $\Theta (L^3)$ in a limit of large $L$. Also, we present an example that saturates this bound in terms of scaling: non-interacting particles globally coupled with a thermal bath. However, the construction of such system requires many-body interactions induced by the environment, which may be difficult to realize with the current technology. To consider more feasible cases, we focus on a class of system where any non-diagonal elements of the noise operator (derived from the system-environment interaction Hamiltonian) become zero in the system energy basis, if the energy difference is beyond a certain value $\Delta E$. Then, for $\Delta E = \Theta (L^0)$, we derive another scaling bound $\Theta (L^2)$ on the absolute value of the heat current, and the so-called superradiance belongs to a class to saturate this bound. Our results are useful to evaluate the best achievable performance of quantum-enhanced thermodynamic devices, which contain far-reaching applications for such as quantum heat engines, quantum refrigerators and quantum batteries.

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