Abstract
We consider some possible thermodynamic equilibrium states of a system of electrons with a broken geometrical symmetry. We give the analytic expression for the (quantum-mechanical) static linear-response function of a system of free electrons moving in a uniform magnetic field. For the case where the energy associated with the cyclotron frequency of the system is negligible compared with the Fermi energy, and the temperature of the system is negligible compared with the Fermi temperature, the expression for the static-response function is extremely simple and can be rigorously derived. We analyze the response function and show that it gives various broken-symmetry states in an electron gas.
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