OperatorTheoretical Research of TwoBody System in NonRelativistic Quantum Field Theory
Project/Area Number 
18540180

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Basic analysis

Research Institution  Okayama University 
Principal Investigator 
HIROKAWA Masao Okayama University, Grad. Sch. Nat. & Tech., Professor (70282788)

CoInvestigator(Kenkyūbuntansha) 
HIROSHIMA Fumio Kyushu Univ., Fac. Math., Associate Professor (00330358)
TAMURA Hideo Okayama Univ., Grad. Sch. Nat. & Tech., Professor (30022734)
OSHITA Yoshihito Okayama Univ., Grad. Sch. Nat. & Tech., Associate Professor (70421998)

Project Period (FY) 
2006 – 2007

Project Status 
Completed (Fiscal Year 2007)

Budget Amount *help 
¥4,010,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥510,000)
Fiscal Year 2007: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2006: ¥1,800,000 (Direct Cost: ¥1,800,000)

Keywords  bipolaron / nonrelativistic nuantum field theory / Nelson model / phonon / twobody system / ground state / binding energy / operator theory / ポーラロン / 場の量子論 
Research Abstract 
We have studied the twobody system in nonrelativistic quantum field theory in the light of operator theory. In particular we have been interested in the problem when the socalled bipolaron forms. Let us consider two electrons coupled with longitudinal optical (LO) phonons in a 3dimensional crystal now. Then, in general, an electron is dressed in a phonon cloud because of the electronphonon interaction. The dressed electron is the socalled polaron. If the Coulomb repulsion between the two electrons is strong enough, the two electrons are so far away from each other that each electron dresses itself in an individual phonon cloud. Thus, there is no exchange of phonons between the two. On the other hand, if the distance between the two electrons is so short that a common phonon cloud grasps both electrons, then the phononexchange takes place. In this case, there is a possibility that attraction appears between them and thus we can expect that they are bound to each other. The bound two polarons is called a bipolaron. We have explored tug of war between the two electrons. We have clarified some mathematical aspects for the bipolaron problem.

Report
(3 results)
Research Products
(6 results)