An Introduction To The Theory Of Superfluidity

Isaac M. Khalatnikov

• Editorial: CRC Press
• Año: 2018
• ISBN:
  9780429982521
• Edición: 1
• Categoría: Ciencias físicas
• Categoría: Física

This book covers main properties of the excitation spectrum in superfluid 4He and the thermodynamics determined by the spectrum. It deals with hydrodynamics and describes that quantitative results should be insignificantly modified with processes of phonon decay taken into account.

PART I

ELEMENTARY EXCITATIONS

1

THE ENERGY SPECTRUM OF A QUANTUM LIQUID AND SUPERFLUIDITY^1,2,3

At a temperature of 2.18° K, liquid helium undergoes a second-order phase transition. Below the λ-point, liquid helium (helium II) has a number of unusual properties, of which the most remarkable is superfluidity, discovered by P. Kapitza. This is the ability of liquid helium to flow without friction through narrow capillaries. It is easy to convince oneself that at temperatures of the order of 1 or 2° K, the de Broglie wavelength of helium atoms is comparable to the interatomic distance. It follows that helium II has quantum properties; it is therefore not a classical liquid, but a quantum liquid. As is well known, there are two stable isotopes of helium, He³ and He⁴, of mass 3 and 4, respectively, in atomic units. The liquid which exhibits superfluidity is the one formed from atoms of He⁴—that is, from particles obeying Bose statistics. He³ atoms also form a quantum liquid which, however, does not exhibit superfluidity in the above-mentioned temperature region. A quantum liquid made up of Fermi particles is usually called a Fermi liquid. We may therefore say that only liquids made up of Bose particles possess the property of superfluidity.

In recent years, however, it has become clear that in a Fermi liquid consisting of atoms of He³, at sufficiently low temperatures (probably around 0.001° K), pairing should occur — that is, the formation of particles of Bose type. Th...