Possible quantum eigenstates in a given system

Kurt A. Jacobs, Pavel Lougovski, M. P. Blencowe

We show that it is possible to perform a continuous measurement that continually projects a nanoresonator into its energy eigenstates by employing a linear coupling with a two-state system. This technique makes it possible to perform a measurement that exposes the quantum nature of the resonator by coupling it to a Cooper-pair box and a superconducting transmission line resonator.

Mario Belloni, Wolfgang Christian

Yoshiwo Okamoto, Katsumi Sugita, Matsuo Sekine

In the path integral representation, the Hamiltonian in a quantum system is associated with the Hamiltonian in a classical system through the Weyl transformation. From this, it is possible to describe the time evolution in a quantum system by the Hamiltonian in a classical system. In a Bose system, the Weyl transformation is defined by the eigenstates of the canonical operators, since the Hamiltonian is given by a function of the canonical operators. On the other hand, in a Fermi system, the Hamiltonian is usually described by a function of the creation and annihilation operators, and hence the Weyl transformation is defined by the coherent states which are the eigenstate of an annihilation operator. Here, we formulate the Weyl transformation in Fermi systems in terms of the eigenstates of the canonical operators so as to clarify the correspondence between both systems. Using this, we can derive the path integral representation in Fermi systems.

W. D. Heiss, A. A. Kotz�

Giovanni Costa

Yoshiwo Okamoto, Katsumi Sugita, Matsuo Sekine

Abstract In the path integral representation, the Hamiltonian in a quantum system is associated with the Hamiltonian in a classical system through the Weyl transformation. From this, it is possible to describe the time evolution in a quantum system by the Hamiltonian in a classical system. In a Bose system, the Weyl transformation is defined by the eigenstates of the canonical operators, since the Hamiltonian is given by a function of the canonical operators. On the other hand, in a Fermi system, the Hamiltonian is usually described by a function of the creation and annihilation operators, and hence the Weyl transformation is defined by the coherent states which are the eigenstate of an annihilation operator. Here, we formulate the Weyl transformation in Fermi systems in terms of the eigenstates of the canonical operators so as to clarify the correspondence between both systems. Using this, we can derive the path integral representation in Fermi systems.