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- W1642381609 abstract "1.1 1925: Einstein’s prediction for the ideal Bose gas Einstein considered N non-interacting bosonic and non-relativistic particles in a cubic box of volume L3 with periodic boundary conditions. In the thermodynamic limit, defined as (1.1) $$ N,L to infty {text{ }}with{text{ }}frac{N} {{L^3 }} = rho = constant, $$ a phase transition occurs at a temperature Tc defined by: (1.2) $$ rho lambda _{{text{dB}}}^3 (T_c ) = zeta (3/2) = 2.612... $$ > where we have defined the thermal de Broglie wavelength of the gas as function of the temperature T: (1.3) $$ lambda _{{text{dB}}} (T) = left( {frac{{2pi hbar ^2 }} {{mk_B T}}} right)^{{1 mathord{left/ {vphantom {1 2}} right. kern-nulldelimiterspace} 2}} $$ and where $$ zeta (alpha ) = sumnolimits_{k = 1}^infty {1/k^alpha } $$ is the Riemann Zeta function." @default.
- W1642381609 created "2016-06-24" @default.
- W1642381609 creator A5031838262 @default.
- W1642381609 date "2007-07-03" @default.
- W1642381609 modified "2023-10-18" @default.
- W1642381609 title "Bose-Einstein Condensates in Atomic Gases: Simple Theoretical Results" @default.
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- W1642381609 doi "https://doi.org/10.1007/3-540-45338-5_1" @default.
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