The fermionic ideal gas is an unexpectedly good model for understanding electrons in metals. One would expect that the strong electrostatic forces between electrons, and between electrons and ions in the crystal lattice, would significantly change their behavior compared to a gas without interaction. The success of the ideal gas model in describing real electrons is a consequence of the Pauli principle, which kinematically restricts the possible states of electron motion at low temperature so much that very little phase space remains for dynamical effects. To understand how this is possible, one needs to understand the ground state of the fermionic ideal gas. It is the lowest possible energy state, the only one that remains in the absence of thermal fluctuations at zero temperature.

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Fermions

  • Denis Sunko

摘要

The fermionic ideal gas is an unexpectedly good model for understanding electrons in metals. One would expect that the strong electrostatic forces between electrons, and between electrons and ions in the crystal lattice, would significantly change their behavior compared to a gas without interaction. The success of the ideal gas model in describing real electrons is a consequence of the Pauli principle, which kinematically restricts the possible states of electron motion at low temperature so much that very little phase space remains for dynamical effects. To understand how this is possible, one needs to understand the ground state of the fermionic ideal gas. It is the lowest possible energy state, the only one that remains in the absence of thermal fluctuations at zero temperature.