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Ultracold Quantum FieldsBose-Einstein Condensation

Ultracold Quantum Fields: Bose-Einstein Condensation [States of matter, such as the familiar gas, liquid and solid phases, are characterized by certain specific correlations between particles. For instance, the solid phase is characterized by the existence of a periodicity in the atomic density n(x) = (Ψ∧†( x)Ψ∧(x)), such that the Fourier transform of n(x) signals the periodic lattice structure of the solid. This kind of order is called diagonal long-range order, because the periodic structure that extends over the whole size of the solid shows itself in the diagonal elements of the one-particle density matrix n(x, x′) = (Ψ∧† (x) Ψ∧(x′)). As we soon see, in the state of matter that is known as a Bose-Einstein condensate the long-range order is actually off-diagonal in the one-particle density matrix, which makes the Bose-Einstein condensed gas behave very differently from the other phases of matter that we have encountered so far. In particular, the intrinsic quantum-mechanical nature of this many-body state results in intriguing properties such as the possibility for the gas to flow without friction, i.e. superfluidity.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Ultracold Quantum FieldsBose-Einstein Condensation

Part of the Theoretical and Mathematical Physics Book Series
Ultracold Quantum Fields — Jan 1, 2009
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References (1)

Publisher
Springer Netherlands
Copyright
© Springer Netherlands 2009
ISBN
978-1-4020-8762-2
Pages
235–272
DOI
10.1007/978-1-4020-8763-9_11
Publisher site
See Chapter on Publisher Site

Abstract

[States of matter, such as the familiar gas, liquid and solid phases, are characterized by certain specific correlations between particles. For instance, the solid phase is characterized by the existence of a periodicity in the atomic density n(x) = (Ψ∧†( x)Ψ∧(x)), such that the Fourier transform of n(x) signals the periodic lattice structure of the solid. This kind of order is called diagonal long-range order, because the periodic structure that extends over the whole size of the solid shows itself in the diagonal elements of the one-particle density matrix n(x, x′) = (Ψ∧† (x) Ψ∧(x′)). As we soon see, in the state of matter that is known as a Bose-Einstein condensate the long-range order is actually off-diagonal in the one-particle density matrix, which makes the Bose-Einstein condensed gas behave very differently from the other phases of matter that we have encountered so far. In particular, the intrinsic quantum-mechanical nature of this many-body state results in intriguing properties such as the possibility for the gas to flow without friction, i.e. superfluidity.]

Published: Jan 1, 2009

Keywords: Condensate Density; Landau Free Energy; Bogoliubov Theory; Bogoliubov Approximation; Landau Criterion

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