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

Spectral representation

Aloïs Würger

Springer tracts in modern physicsJan 1, 19971 citation

Zeros Of Bargmann Analytic Representation In The Complex Plane

Muna Tabuni

The paper contains an investigation of zeros Of Bargmann analytic representation. A brief introduction to Harmonic oscillator formalism is given. The Bargmann analytic representation has been studied. The zeros of Bargmann analytic function are considered. The Q or Husimi functions are introduced. The The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros μn are discussed. Various examples have been given.The paper contains an investigation of zeros Of Bargmann analytic representation. A brief introduction to Harmonic oscillator formalism is given. The Bargmann analytic representation has been studied. The zeros of Bargmann analytic function are considered. The Q or Husimi functions are introduced. The The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros μn are discussed. Various examples have been given.

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer EngineeringAug 22, 20130 citations

Relative to the interpretation of terms of the Schr�dinger perturbation theory series

R. Kh. Sabirov

Russian Physics JournalFeb 1, 19820 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.