In a course on nonrelativistic quantum mechanics you learned about the Pauli exclusion principle2 and its later generalization stating that particles… - Anthony Zee
" "In a course on nonrelativistic quantum mechanics you learned about the Pauli exclusion principle2 and its later generalization stating that particles with half integer spins, such as electrons, obey Fermi-Dirac statistics and want to stay apart, while in contrast particles with integer spins, such as photons or pairs of electrons, obey Bose-Einstein statistics and love to stick together. From the microscopic structure of atoms to the macroscopic structure of neutron stars, a dazzling wealth of physical phenomena would be incomprehensible without this spin-statistics rule. Many elements of condensed matter physics, for instance, band structure, Fermi liquid theory, superfluidity, superconductivity, quantum Hall effect, and so on and so forth, are consequences of this rule.
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About Anthony Zee
Anthony Zee (, b. 1945) (Zee comes from the Shanghainese pronunciation of 徐) is a Chinese-American physicist and author.
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Alternative Names:
Xu Yihong
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The goal of condensed matter physics is to understand the various states of matter. States of matter are characterized by the presence (or absence) of order: a ferromagnet becomes ordered below the transition temperature. In the Landau-Ginzburg theory ... , order is associated with spontaneous symmetry breaking, described naturally with group theory. Girvin and MacDonald first noted that the order in Hall fluids does not really fit into the Landau-Ginzburg scheme: We have not broken any obvious symmetry. The topological property of the Hall fluids provides a clue to what is going on. As explained in the preceding chapter, the ground state degeneracy of a Hall fluid depends on the topology of the manifold it lives on, a dependence group theory is incapable of accounting for. Wen has forcefully emphasized that the study of topological order, or more generally quantum order, may open up a vast new vista on the possible states of matter.
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Normally, the entropy of a system is extensive, that is, proportional to its volume. Somehow, a black hole has an entropy proportional to its surface rather than to its volume. This fact has led to the so-called holographic principle. Many fundamental physicists believe that this mysterious property of black holes holds the key to quantum gravity.
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