Why are phonons bosons

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Let us know if there is a problem with our content. Your message to the editors. Your email only if you want to be contacted back. Send Feedback. Thank you for taking time to provide your feedback to the editors. E-mail the story Experiment shows phonons mix in such a way to allow classification as 'bosonic' particles.

Your friend's email. Your email. I would like to subscribe to Science X Newsletter. Learn more. Your name. Note Your email address is used only to let the recipient know who sent the email. A classical limit is often associated with large occupation numbers, unavailable here, for each mode.

I have to confess I am out of my depth with topological fermions , however, and to what extent these exotic collective excitations are fermionic. Perhaps a condensed matter person could bring expertise to bear. Sign up to join this community. The best answers are voted up and rise to the top.

Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why does a phonon obey the Bose statistic? Ask Question. Asked 3 years, 11 months ago. Active 3 years, 11 months ago. Viewed 2k times. Improve this question. Akemi Homura. Akemi Homura Akemi Homura 8 8 bronze badges. The Hamiltonian has the form. In the one dimensional model, the atoms were restricted to moving along the line, so all the phonons corresponded to longitudinal waves.

In three dimensions, vibration is not restricted to the direction of propagation, and can also occur in the perpendicular plane, like transverse waves.

This gives rise to the additional normal coordinates, which, as the form of the Hamiltonian indicates, we may view as independent species of phonons. This is known as a dispersion relation. At low values of k i. As a result, packets of phonons with different but long wavelengths can propagate for large distances across the lattice without breaking apart. This is the reason that sound propagates through solids without significant distortion.

This behavior fails at large values of k , i. It should be noted that the physics of sound in air is different from the physics of sound in solids, although both are density waves. This is because sound waves in air propagate in a gas of randomly moving molecules rather than a regular crystal lattice. In real solids, there are two types of phonons: "acoustic" phonons and "optical" phonons.

Longitudinal and transverse acoustic phonons are often abbreviated as LA and TA phonons, respectively. They are called "optical" because in ionic crystals like sodium chloride they are excited very easily by light in fact, infrared radiation. This is because they correspond to a mode of vibration where positive and negative ions at adjacent lattice sites swing against each other, creating a time-varying electrical dipole moment.

Optical phonons that interact in this way with light are called infrared active. Optical phonons which are Raman active can also interact indirectly with light, through Raman scattering. Optical phonons are often abbreviated as LO and TO phonons, for the longitudinal and transverse varieties respectively. This is because k is only determined up to multiples of constant vectors, known as reciprocal lattice vectors. Physically, the reciprocal lattice vectors act as additional "chunks" of momentum which the lattice can impart to the phonon.

Bloch electrons obey a similar set of restrictions. It is usually convenient to consider phonon wave vectors k which have the smallest magnitude k in their "family". The set of all such wave vectors defines the first Brillouin zone.

Additional Brillouin zones may be defined as copies of the first zone, shifted by some reciprocal lattice vector. A crystal lattice at zero temperature lies in its ground state , and contains no phonons. According to thermodynamics, when the lattice is held at a non-zero temperature its energy is not constant, but fluctuates randomly about some mean value. These energy fluctuations are caused by random lattice vibrations, which can be viewed as a gas of phonons.

Note: the random motion of the atoms in the lattice is what we usually think of as heat. Because these phonons are generated by the temperature of the lattice, they are sometimes referred to as thermal phonons.

Unlike the atoms which make up an ordinary gas, thermal phonons can be created or destroyed by random energy fluctuations. Their behavior is similar to the photon gas produced by an electromagnetic cavity, wherein photons may be emitted or absorbed by the cavity walls. This similarity is not coincidental, for it turns out that the electromagnetic field behaves like a set of harmonic oscillators; see Black-body radiation. Both gases obey the Bose-Einstein statistics: in thermal equilibrium, the average number of phonons or photons in a given state is.