The Partition Function of the Bose-Einstein Condensation in Parabolic Trap
| Autor: | Teguh Budi Prayitno, Sinta Latifa |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Condensed Matter::Quantum Gases
Physics thermodynamic properties partition function quantum oscillator Statistical mechanics Translational partition function Gross–Pitaevskii equation symbols.namesake Nonlinear system Quantum harmonic oscillator Quantum mechanics Helmholtz free energy symbols lcsh:Science (General) Ground state Characteristic state function Gross-Pitaevskii equation lcsh:Q1-390 Mathematical physics |
| Zdroj: | Makara Seri Sains, Vol 16, Iss 2, Pp 83-88 (2012) |
| ISSN: | 1693-6671 |
| DOI: | 10.7454/mss.v16i2.1401 |
| Popis: | We have discussed the partition function of the Bose-Einstein condensation in parabolic trap associated to the one-dimensional Gross-Pitaevskii equation. The partition function itself is constructed by considering all the energy levels of the macroscopic quantum oscillator which is similar to statistical mechanics. The solutions of the energy levels for this case can be derived by pursuing the method that applies the time-independent perturbation theory. In this case, the one-dimensional Gross Pitaevskii equation can be treated as the one-dimensional macroscopic quantum oscillator on condition that the nonlinearity is very small. Moreover, the analytical expression for the ground state energy can be obtained by applying the method. However, the higher level states were not explicitly provided. In this research we followed up on the former work to derive explicitly the other states in order to formulate the partition function. However, we did not find the closed form of the partition function since the results of nonlinear term integral could not form the recursion relation. As a consequence, not only should the partition function but also the Helmholtz free energy and entropy should be reevaluated to check their convergences. |
| Databáze: | OpenAIRE |
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