Program

P.11 -- Poster, NCTP-41

Date: Tuesday, 2 August 2016

Time: 08h30 - 10h00

Invariance of probability density functions and transition between Gaussian and Boltzmann forms of envelope functions problem in the similarity between q-deform harmonic oscillator and Cooper pair

Man Van Ngu (1), Ngo Gia Vinh (2), Tran Ngoc Tu (3), Nguyen Tri Lan (4), Luu Thi Kim Thanh (5), Nguyen Ai Viet (4)

(1) Hung Yen Industrial Colleage; (2) Bac Ninh Department of Education and Training; (3) Hoa Lu University; (4) Institute of Physics, 10 Dao Tan, Ba Dinh, Hanoi; (5) Hanoi Pedagogical University No.2

The similarity of a Cooper pair and q-deform harmonic oscillator was discussed in our previous work, where have shown that the main different is the forms of their envelope functions. The envelope function of a Cooper pair has the Boltzmann-like form, while the envelope function of q-deform harmonic oscillator has the Gaussian-like form. In this work we analyze the invariance of probability density functions by a general transformation. We show that translation invariance corresponds to the Boltzmann-like form, and spherical invariance corresponds to the Gaussian-like form of probability density functions. Following the famous Einstein’s idea about the connection between interaction and geometry of vacuum, we propose a possible transformation envelope function of a q-deform harmonic oscillator from Gaussian-like to Boltzmann-like forms, which correspond to the changing of an effective vacuum symmetrical behavior of a Cooper pair from its normal to superconducting states near the phase transition critical temperature.

Presenter: Mẫn Văn Ngữ