Bose–Einstein phase transition

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1: 25.17 Physical Applications

… ►See Armitage (1989), Berry and Keating (1998, 1999), Keating (1993, 1999), and Sarnak (1999). ►The zeta function arises in the calculation of the partition function of ideal quantum gases (both Bose–Einstein and Fermi–Dirac cases), and it determines the critical gas temperature and density for the Bose–Einstein condensation phase transition in a dilute gas (Lifshitz and Pitaevskiĭ (1980)). …

2: Sidebar 22.SB1: Decay of a Soliton in a Bose–Einstein Condensate

Sidebar 22.SB1: Decay of a Soliton in a Bose–Einstein Condensate

… ►Among these are the formation of vortex rings in Bose Einstein condensates. …For details see the NIST news item Decay of a dark soliton into vortex rings in a Bose–Einstein condensate. … ►Cornell, Watching Dark Solitons Decay into Vortex Rings in a Bose–Einstein Condensate, Phys. Rev. Lett. 86, 2926–2929 (2001)

3: 29.19 Physical Applications

… ►Bronski et al. (2001) uses Lamé functions in the theory of Bose–Einstein condensates. …

4: 25.12 Polylogarithms

… ►When $z={\mathrm{e}}^{\mathrm{i}\theta }$, $0\le \theta \le 2\pi$, (25.12.1) becomes … ►valid when $\mathrm{\Re }s>0$ and , or $\mathrm{\Re }s>1$ and $z=1$. … ►

§25.12(iii) Fermi–Dirac and Bose–Einstein Integrals

►The Fermi–Dirac and Bose–Einstein integrals are defined by … ►In terms of polylogarithms …

5: 25.18 Methods of Computation

… ►For dilogarithms and polylogarithms see Jacobs and Lambert (1972), Osácar et al. (1995), Spanier and Oldham (1987, pp. 231–232), and Zudilin (2007). ►For Fermi–Dirac and Bose–Einstein integrals see Cloutman (1989), Gautschi (1993), Mohankumar and Natarajan (1997), Natarajan and Mohankumar (1993), Paszkowski (1988, 1991), Pichon (1989), and Sagar (1991a, b). …

6: Bernard Deconinck

… ►He has worked on integrable systems, algorithms for computations with Riemann surfaces, Bose-Einstein condensates, and methods to investigate the stability of solutions of nonlinear wave equations. …

7: 25.21 Software

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§25.21(vii) Fermi–Dirac and Bose–Einstein Integrals

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8: William P. Reinhardt

… ►He has recently carried out research on non-linear dynamics of Bose–Einstein condensates that served to motivate his interest in elliptic functions. …

9: 4.44 Other Applications

… ►The Einstein functions and Planck’s radiation function are elementary combinations of exponentials, or exponentials and logarithms. …

10: Bibliography J

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Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent. Phys. D 1 (1), pp. 80–158.

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External Links:

ISSN 0167-2789, Document, MathReview, ZentralBlatt

Referenced by:

§32.16.

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Derivation of Green-type, transitional and uniform asymptotic expansions from differential equations. V. Angular oblate spheroidal wavefunctions ${\overline{ps}}_n^r(\eta ,h)$ and ${\overline{qs}}_n^r(\eta ,h)$ for large $h$ . Proc. Roy. Soc. London Ser. A 321, pp. 545–555.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§30.9(ii).

Encodings:

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