"Finite size effect"의 두 판 사이의 차이
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| 36번째 줄: | 36번째 줄: | ||
* <br> | * <br> | ||
| − | * transformaion<br><math>z \to w=\frac{L}{2\pi}\ln z</math><br> | + | * strip geometry |
| + | |||
| + | * transformaion<br><math>z \to w=\frac{L}{2\pi}\ln z</math><br> maps the entire plane onto a strip of width L<br> | ||
* Schwarzian derivative<br><math>\frac{1}{2z^2}</math><br> | * Schwarzian derivative<br><math>\frac{1}{2z^2}</math><br> | ||
* energy momentum tensor changes<br><math>T_{cyl}(w)=(\frac{2\pi}{L})^2\{T_{pl}(z)z^2-\frac{c}{24}\}</math><br><math>L_0 \to L_0-c/24</math><br> | * energy momentum tensor changes<br><math>T_{cyl}(w)=(\frac{2\pi}{L})^2\{T_{pl}(z)z^2-\frac{c}{24}\}</math><br><math>L_0 \to L_0-c/24</math><br> | ||
| 89번째 줄: | 91번째 줄: | ||
| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;"> | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia</h5> |
* [http://ko.wikipedia.org/wiki/%EC%B9%B4%EC%8B%9C%EB%AF%B8%EB%A5%B4%ED%9A%A8%EA%B3%BC http://ko.wikipedia.org/wiki/카시미르효과] | * [http://ko.wikipedia.org/wiki/%EC%B9%B4%EC%8B%9C%EB%AF%B8%EB%A5%B4%ED%9A%A8%EA%B3%BC http://ko.wikipedia.org/wiki/카시미르효과] | ||
| 103번째 줄: | 105번째 줄: | ||
<h5>articles</h5> | <h5>articles</h5> | ||
| + | * Conformal invariance, the central charge, and universal finite-size amplitudes at criticality H. W. J. Blöte, J. Cardy and M. P. Nightingale, Phys. Rev. Lett. 56, 742–745 (1986) | ||
* [http://prl.aps.org/abstract/PRL/v56/i7/p742_1 Conformal invariance, the central charge, and universal finite-size amplitudes at criticality] | * [http://prl.aps.org/abstract/PRL/v56/i7/p742_1 Conformal invariance, the central charge, and universal finite-size amplitudes at criticality] | ||
2010년 5월 25일 (화) 17:52 판
introduction
- Casimir effect in QED is one example of finite size effect
- the stress on the bounding surfaces when quantum field is confined to finite volume of space
- type of boundaries
- real material media
- interface between two different phases of the vacuum of a field theory such as QCD, in which case colored field may only exist in the interior region
- topology of space
- the boundaries restrict the modes of the quantum fields
- give rise to measurable and important forces
how to compute the Casimir effect
- zero-point energy in the presence of the boundaries
- sum over all modes
- any kind of constraint or boudary conditions on the the zero-point modes of the quantum fields in question, including backgrounds such as gravity
- In a model without boundary conditions, the Hamiltonian value associated wih the vacuum or ground state, called zero-point energy, is usually discarded because, despite being infinite, may be reabsorbed in a suitable redefinition of the energy origin
- there are several ways to put such an adjustment into practice, normal ordering being oneof the most popular
- Green's functions method
- represents the vacuum expectation value of the produc of fields
QFT interpretation of the Casimir effect
conformal transform from the plane to cylinder
-
- strip geometry
- transformaion
\(z \to w=\frac{L}{2\pi}\ln z\)
maps the entire plane onto a strip of width L - Schwarzian derivative
\(\frac{1}{2z^2}\) - energy momentum tensor changes
\(T_{cyl}(w)=(\frac{2\pi}{L})^2\{T_{pl}(z)z^2-\frac{c}{24}\}\)
\(L_0 \to L_0-c/24\) - the central charge emerges
- central charge is proportional to the Casimir energy, the change in the vacuum energy density brought about by the periodicity condition on the cylinder
vacuum energy density
\(<T_{cyl}(w)>=-\frac{c\pi^2}{6L^2}\)
free energy per unit length
- formula
\(F_L=f_{0}L-\frac{c\pi}{6L}\)
where \(f_{0}\) is the free energy per unit area in the thermodynamic \(L\to\infty\) limit
표준적인 도서 및 추천도서
- 찾아볼 수학책
- The Casimir Effect: Physical Manifestations of Zero-Point Energy
- [1]Kimball A. Milton
- Conformal invariance and finite size effects in critical two dimensional statistical models
- Claude Itzykson
- Casimir effect in critical systems
- Michael Krech
- http://gigapedia.info/1/Casimir+effect
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
encyclopedia
- http://ko.wikipedia.org/wiki/카시미르효과
- http://en.wikipedia.org/wiki/finite_size_effect
- http://en.wikipedia.org/wiki/Casimir_effect
- http://en.wikipedia.org/wiki/Vacuum_energy
- http://en.wikipedia.org/wiki/
articles
- Conformal invariance, the central charge, and universal finite-size amplitudes at criticality H. W. J. Blöte, J. Cardy and M. P. Nightingale, Phys. Rev. Lett. 56, 742–745 (1986)
- Conformal invariance, the central charge, and universal finite-size amplitudes at criticality
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