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It is well known that the optical branches of the dispersion curves of ionic crystals exhibit a polaritonic feature, i.e., a splitting about the electromagnetic dispersion line $omega=ck$. This phenomenon is considered to be due to the retardation of the electromagnetic forces among the ions. However, the problem is usually discussed at a phenomenological level, through the introduction of a macroscopic polarization field, so that a microscopic treatment is apparently lacking. A microscopic first principles deduction is given here, in a classical frame, for a model in which the ions are dealt with as point charges. At a qualitative level it is made apparent that retardation is indeed responsible for the splitting. A quantitative comparison with the empirical data for LiF is also given, showing a fairly good agreement over the whole Brillouin zone.
We describe a possible general and simple paradigm in a classical thermal setting for discrete time crystals (DTCs), systems with stable dynamics which is subharmonic to the driving frequency thus breaking discrete time-translational invariance. We c
The problem of finding a microscopic theory of phase transitions across a critical point is a central unsolved problem in theoretical physics. We find a general solution to that problem and present it here for the cases of Bose-Einstein condensation
We present a general approach to describe slowly driven quantum systems both in real and imaginary time. We highlight many similarities, qualitative and quantitative, between real and imaginary time evolution. We discuss how the metric tensor and the
Classical density functional theory for finite temperatures is usually formulated in the grand-canonical ensemble where arbitrary variations of the local density are possible. However, in many cases the systems of interest are closed with respect to
Time crystals are proposed states of matter which spontaneously break time translation symmetry. There is no settled definition of such states. We offer a new definition which follows the traditional recipe for Wigner symmetries and order parameters.