Bargmann representation of quantum absorption refrigerators

In this work, we solve the quantum absorption refrigerator analytically in the space of holomorphic functions with Gaussian measure . Our approach simplifies the calculations since for a given quantum system the coordinate representation of any quantum state is always more complicated than its corresponding expression written with respect to the phase-space coordinate $z_{i}$. We finally discuss the computational complexity of the holomorphic representation and compare it with the computational complexity of the standard operator method and prove the efficiency of the holomorphic representation in computing some tasks. Our treatment is applicable to all quantum heat engines and refrigerators.