Moment-expansion-method calculations of phonon line shapes in argon

Temperature-dependent classical phonons from efficient nondynamical simulations

We present a method to calculate classical lattice-dynamical quantities, such as the temperature-dependent vibrational spectrum, from simulations that do not require an explicit solution of the time evolution. We start from the moment expansion of the relevant time-correlation function for a many-body system and show that it can be conveniently rewritten by using a basis in which the low-order moments are diagonal. This allows us to approximate the main spectral features (i.e., position and width of the phonon peaks) from thermal averages available from any statistical simulation. We illustrate our method with an application to a model system that presents a structural transition and strongly temperature-dependent phonons. Our theory also clarifies the status of previous heuristic schemes to estimate phonon frequencies.

Selected topics in lattice dynamics: a critical review (including breathers)

We present a review of lattice dynamics to provide the underpinnings for the study of nonlinear localized modes, the so-called breathers. After a historical survey we address the following topics: harmonic theories, anharmonic perturbation theory, self-consistent theories, classical simulation techniques, path-integral theories, realistic crystal potentials, and intrinsic localized modes. We discuss both static and dynamic properties of crystals, e.g., neutron and x-ray scattering. We do not consider transport properties. Throughout, our emphasis is on discussing the major advances in the field and citing the appropriate references. Our aim is to achieve clarity and simplicity for readers who wish to move on to the study of breathers. We have made a special effort to set up the language and notation that is generally accepted in the field. In order to acquaint the reader with the techniques used in lattice dynamics we have analyzed a number of key problems in detail including a comparison with the available experimental data.