Quantum Liquids: Bose Condensation and Cooper Pairing in by Hans J. Leisi

By Hans J. Leisi

Ranging from first rules, this e-book introduces the heavily similar phenomena of Bose condensation and Cooper pairing, within which a truly huge variety of unmarried debris or pairs of debris are pressured to act in precisely a similar approach, and explores their outcomes in condensed topic platforms. Eschewing complex formal equipment, the writer makes use of basic recommendations and arguments to account for a few of the qualitatively new phenomena which happen in Bose-condensed and Cooper-paired platforms, together with yet no longer restricted to the fantastic macroscopic phenomena of superconductivity and superfluidity; the actual platforms mentioned contain liquid 4-He, the BEC alkali gases, "classical" superconductors, superfluid 3-He, "exotic" superconductors and the lately stabilized Fermi alkali gases.The e-book can be available to starting graduate scholars in physics or complicated undergraduates.

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Additional resources for Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems

Example text

G. a path taken around the torus 4 With hindsight it would probably be more logical to call this quantity the “condensate velocity” and to denote it v c . The conventional terminology reflects the history of the subject. 9) The explicit occurrence of h in this formula reminds us that v s is an essentially quantum-mechanical object. It is interesting to contrast the superfluid velocity v s (rt) with two other “velocities” which we can define for a quantum-mechanical system. First, consider a single particle with Schr¨ odinger wave function χ1 (rt).

G. in the case of liquid 4 He). For such a system by far the most useful and generally applicable definition of BEC is, to my mind, one given nearly 50 years ago by Penrose and Onsager (1956). Consider a system consisting of a large number N of bosons characterized by coordinates r i (i = 1, 2, . . , N ). It may have arbitrary interparticle interactions and in addition be subject to an arbitrary single-particle potential, in general time-dependent. Any pure many-body state s of the system at time t can be written in the form ΨsN (t) ≡ Ψs (r 1 , r 2 , .

3 ˚ A. Two 4 He atoms in free space can form a diatomic molecule (dimer), with however a very tiny binding energy (∼1 mK); this would correspond to an enormous s-wave scattering length (see Chapter 4), but this is unlikely to be relevant at liquid-state densities. Because of their lighter mass, two 3 He atoms should not be bound (nor should a 3 He–4 He pair). It is, of course, the combination of weak attraction and small mass which prevents either isotope of helium forming a solid under its own vapor pressure; in fact, the solid phase of 4 He is stable only above ∼26 atm and that of 3 He only above 34 atm.

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