### Abstract

The phase transition between ordered and disordered states is discussed within the framework of non-equilibrium Thermo Field Dynamics (TFD), in which the time-dependent thermal Bogoliubov transformation takes care of the temporal change of quasi-particles. Thus, the system, which is closed, passes through a continuum of out of equilibrium states in going from one phase to another. The formalism is presented for the superfluid model. The time evolution of the system is determined by the self-consistent renormalization conditions which give us equations for the order parameter, number distributions, dissipative coefficients and renormalized energies. A differential Ward-Takahashi relation, rather than an integral one, is combined with the renormalization condition to study the zero momentum mode.

Original language | English |
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Pages (from-to) | 326-335 |

Number of pages | 10 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 158 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1989 May 15 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*158*(1), 326-335. https://doi.org/10.1016/0378-4371(89)90532-3

**Phase transition in non-equilibrium thermo field dynamics.** / Hardman, I.; Umezawa, H.; Yamanaka, Yoshiya.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 158, no. 1, pp. 326-335. https://doi.org/10.1016/0378-4371(89)90532-3

}

TY - JOUR

T1 - Phase transition in non-equilibrium thermo field dynamics

AU - Hardman, I.

AU - Umezawa, H.

AU - Yamanaka, Yoshiya

PY - 1989/5/15

Y1 - 1989/5/15

N2 - The phase transition between ordered and disordered states is discussed within the framework of non-equilibrium Thermo Field Dynamics (TFD), in which the time-dependent thermal Bogoliubov transformation takes care of the temporal change of quasi-particles. Thus, the system, which is closed, passes through a continuum of out of equilibrium states in going from one phase to another. The formalism is presented for the superfluid model. The time evolution of the system is determined by the self-consistent renormalization conditions which give us equations for the order parameter, number distributions, dissipative coefficients and renormalized energies. A differential Ward-Takahashi relation, rather than an integral one, is combined with the renormalization condition to study the zero momentum mode.

AB - The phase transition between ordered and disordered states is discussed within the framework of non-equilibrium Thermo Field Dynamics (TFD), in which the time-dependent thermal Bogoliubov transformation takes care of the temporal change of quasi-particles. Thus, the system, which is closed, passes through a continuum of out of equilibrium states in going from one phase to another. The formalism is presented for the superfluid model. The time evolution of the system is determined by the self-consistent renormalization conditions which give us equations for the order parameter, number distributions, dissipative coefficients and renormalized energies. A differential Ward-Takahashi relation, rather than an integral one, is combined with the renormalization condition to study the zero momentum mode.

UR - http://www.scopus.com/inward/record.url?scp=4243652112&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243652112&partnerID=8YFLogxK

U2 - 10.1016/0378-4371(89)90532-3

DO - 10.1016/0378-4371(89)90532-3

M3 - Article

AN - SCOPUS:4243652112

VL - 158

SP - 326

EP - 335

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1

ER -