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Comments on the approximating Hamiltonian method for imperfect boson gas

Thomas Jaeck

In the recent paper (Pulé J V and Zagrebnov V A 2004 The approximating Hamiltonian method for the imperfect boson gas J. Phys. A: Math. Gen. 45 3565–83 ) the pressure for the imperfect (mean field) boson gas is derived by a method based on the approximating Hamiltonian argument. We give some comments about this derivation.

Journal of Physics A Mathematical and GeneralJul 19, 20063 citations

The approximating Hamiltonian method for the imperfect boson gas

Joseph V Pulé, Valentin Anatol'evich Zagrebnov

In the denominators of the last terms of (2.16), (2.17), (2.18) and of the line after (2.16), the parameter μ should be replaced by μ-μ 0 .

Journal of Physics A Mathematical and GeneralJun 14, 20060 citations

PROOF OF THE VARIATIONAL PRINCIPLE FOR A PAIR HAMILTONIAN BOSON MODEL

Joseph V. Pulé, Valentin Anatol'evich Zagrebnov

We give a two-parameter variational formula for the grand-canonical pressure of the Pair Boson Hamiltonian model. By using the Approximating Hamiltonian Method we provide a rigorous proof of this variational principle.

arXiv:math-ph/0603061Reviews in Mathematical PhysicsMar 1, 20075 citations

On the pair Hamiltonian for an imperfect boson gas

C. J. Pethick, D. ter Haar

Physics LettersSep 1, 19656 citations

Simple renormalization-group approximation of the ground-state properties of interacting bosonic systems

Roman Werpachowski, Jerzy Kijowski

We present a simple renormalization-group method of investigating ground-state properties of interacting bosonic systems. Our method reduces the number of particles in a system, which makes numerical calculations possible for large systems. It is conceptually simple and easy to implement, and allows investigation of properties unavailable through mean-field approximations, such as one- and two-particle reduced density matrices of the ground state. As an example, we model a weakly interacting one-dimensional Bose gas in a harmonic trap. Compared to the mean-field Gross-Pitaevskii approximation, our method provides a more accurate description of the ground-state one-particle density matrix. We have also obtained the Hall-Post lower bounds for the ground-state energy of the gas. All results have been obtained by straightforward numerical diagonalization of the Hamiltonian matrix.We present a simple renormalization-group method of investigating ground-state properties of interacting bosonic systems. Our method reduces the number of particles in a system, which makes numerical calculations possible for large systems. It is conceptually simple and easy to implement, and allows investigation of properties unavailable through mean-field approximations, such as one- and two-particle reduced density matrices of the ground state. As an example, we model a weakly interacting one-dimensional Bose gas in a harmonic trap. Compared to the mean-field Gross-Pitaevskii approximation, our method provides a more accurate description of the ground-state one-particle density matrix. We have also obtained the Hall-Post lower bounds for the ground-state energy of the gas. All results have been obtained by straightforward numerical diagonalization of the Hamiltonian matrix.

arXiv:cond-mat/0510436Physical Review AJun 21, 20070 citations

An Approximating Hamiltonian Method In The Theory of Imperfect Bose Gases

N. N. Bogolyubov, Дмитрий Петрович Санкович

NATO science for peace and security series. B, Physics and biophysicsOct 7, 20100 citations

The approximating Hamiltonian method for the imperfect boson gas

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The approximating Hamiltonian method for the imperfect boson gas

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