Lattice vibrations bosons

At low temperatures (well below 100 /iK) the density-density fluctuations (DDF) depend on whether the atoms in the lattice are bosons or fermions. For bosonic atoms in the lowest vibrational state we obtain [Reichl 1998]... 

At a finite temperature the atoms that form a crystalline lattice vibrate about their equilibrium positions, with an amplitude that depends on the temperature. Because a crystalline solid has symmetries, these thermal vibrations can be analyzed in terms of collective modes of motion of the ions. These modes correspond to collective excitations, which can be excited and populated just like electronic states. These excitations are called phonons. Unlike electrons, phonons are bosons their total number is not fixed, nor is there a Pauli exclusion principle governing the occupation of any particular phonon state. This is easily rationalized, if we consider the real nature of phonons, that is, collective vibrations of the atoms in a crystalline solid which can be excited arbitrarily by heating (or hitting) the solid. In this chapter we discuss phonons and how they can be used to describe thermal properties of solids. 

The conventional macroscopic Fourier conduction model violates this non-local feature of microscale heat transfer, and alternative approaches are necessary for analysis. The most suitable model to date is the concept of phonon. The thermal energy in a uniform solid material can be jntetpreied as the vibrations of a regular lattice of closely bound atoms inside. These atoms exhibit collective modes of sound waves (phonons) wliich transports energy at tlie speed of sound in a material. Following quantum mechanical principles, phonons exhibit paiticle-like properties of bosons with zero spin (wave-particle duality). Phonons play an important role in many of the physical properties of solids, such as the thermal and the electrical conductivities. In insulating solids, phonons are also (he primary mechanism by which heal conduction takes place. 

Winkler, K., Lang, R, Thalhammer, G., Straten, P.v.d., Grimm, R., and Hecker Den-schlag, J., Coherent optical transfer of Feshbach molecules to a lower vibrational state, Phys. Rev. Lett., 98, 043201, 2007. In this experiment the presence of an optical lattice suppressed inelastic collisions between molecules of bosonic Rb atoms, which provided a highly efficient transfer of these molecules to a less excited ro-vibrational state and a long molecular lifetime of about 1 second. 

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