arXiv subjects

H. Akaike

Publications and source records attributed to H. Akaike.

4 recordsLinked to original sources

arXiv2005

Note on the Time Dependent Variational Approach with Quasi-Spin Squeezed State for Pairing Model

A simple many-fermion system in which there exists N identical fermions in a single spherical orbit with pairing interaction is treated by means of the time-dependent variational approach with a quasi-spin squeezed state with the aim of going beyond the time-dependent Hartree-Fock or Bogoliubov theory. It is shown that the ground state energy is reproduced well analytically in this approach.

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arXiv2004

A Possible Extension of a Trial State in the TDHF Theory with Canonical Form in the Lipkin Model

With the aim of the extension of the TDHF theory in the canonical form in the Lipkin model, the trial state for the variation is constructed, which is an extension of the Slater determinant. The canonicity condition is imposed to formulate the variational approach in the canonical form. A possible solution of the canonicity condition is given and the zero-point fluctuation induced by the uncertainty principle is investigated. As an application, the ground state energy is evaluated.

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arXiv2004

Fermionic Squeezed State for Simple Algebraic Models in Many-Fermion Systems

It is shown that a variational approach with fermionic squeezed states to many-fermion systems such as pairing model is one of useful methods beyond the usual Hartree-Fock-Bogoliubov approximation. A pairing-type quasi-spin squeezed state is constructed and adopted as a trial state in the variational method. By using this state, quantum fluctuations are taken into account. In pairing model, dynamical and static approaches are discussed in the context of comparing with the Hartree-Fock-Bogoliubov approximation about ground state energy. As a possible extension to the O(4) model, prospective squeezed states are investigated and the usefulness is discussed.

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arXiv2001

Utility of su(1,1)-Algebra in a Schematic Nuclear su(2)-Model

The su(2)-algebraic model interacting with an environment is investigated from a viewpoint of treating the dissipative system. By using the time-dependent variational approach with a coherent state and with the help of the canonicity condition, the time-evolution of this quantum many-body system is described in terms of the canonical equations of motion in the classical mechanics. Then, it is shown that the su(1,1)-algebra plays an essential role to deal with this model. An exact solution with appropriate initial conditions is obtained by means of Jacobi's elliptic function. The implication to the dissipative process is discussed.

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