Adiabatic and isothermal elastic constants from space- and time-dependent response theory

Abstract

The elastic constants of an anharmonic crystal are studied as an example for discussing the general problem of the static limit in Kubo's linear response theory. By starting from the microscopic theory and by defining wavevector- and frequency-dependent elastic constants it is possible to define adiabatic and isothermal limits. It is shown that phonon transport plays a fundamental role in taking these limits. By summing up the ladder diagrams in the self-energy of the long-wavelength acoustic phonons in a collision-time approximation, the difference between the adiabatic and isothermal elastic constants is obtained in agreement with thermodynamics.