Instead of representing quantum states by vectors in the Hilbert space one could represent them as a convergent monomial in the space of holomorphic functions with Gaussian measure using the Bargmann representation of the lowering and raising operators. This strategy simplifies the calculations since for a given quantum system the coordinate representation of any quantum state is always more complicated than its corresponding expression in the Bargmann space. We solve the quantum absorption refrigerator analytically in term of the phase space coordinates $z_{i}$ and their partial derivatives. 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 in all quantum heat engines and refrigerators.Instead of representing quantum states by vectors in the Hilbert space one could represent them as a convergent monomial in the space of holomorphic functions with Gaussian measure using the Bargmann representation of the lowering and raising operators. This strategy simplifies the calculations since for a given quantum system the coordinate representation of any quantum state is always more complicated than its corresponding expression in the Bargmann space. We solve the quantum absorption refrigerator analytically in term of the phase space coordinates $z_{i}$ and their partial derivatives. 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 in all quantum heat engines and refrigerators.

May 6, 20210 citations

z_{i}

and their partial derivatives. 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 in all quantum heat engines and refrigerators.