2007 Fiscal Year Final Research Report Summary
Operator-Theoretical Research of Two-Body System in Non-Relativistic Quantum Field Theory
| Project/Area Number |
18540180
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Okayama University |
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Principal Investigator |
HIROKAWA Masao Okayama University, Grad. Sch. Nat. & Tech., Professor (70282788)
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| Co-Investigator(Kenkyū-buntansha) |
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)
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| Project Period (FY) |
2006 – 2007
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| Keywords | bipolaron / non-relativistic nuantum field theory / Nelson model / phonon / two-body system / ground state / binding energy / operator theory |
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| Research Abstract |
We have studied the two-body system in non-relativistic quantum field theory in the light of operator theory. In particular we have been interested in the problem when the so-called bipolaron forms.
Let us consider two electrons coupled with longitudinal optical (LO) phonons in a 3-dimensional crystal now. Then, in general, an electron is dressed in a phonon cloud because of the electron-phonon interaction. The dressed electron is the so-called 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 phonon-exchange 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.
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