What is a Phonon?

Dear Anjaly,

phonons are a way to describe the vibrational degrees of freedom in periodic structures (lattices): the vibrational motions can be modelled as harmonic oscillators, so they can be quantized nearly in the same way. The result of the quantization (among other consequences) is the appearence of "quanta" of oscillations: the phonons. In this sense, the phonon is the quantum of structural vibrations much in the same way as a photon is a quantum of oscillation of electromagnetic field.

Phonon is considered a quasi-particle, beacuse it can exist only in solids as a consequence of vibrational motions: they cannot propagate in vacuum.

Regards,

Giovanni

Giovanni Acquaviva wrote:

> Phonon is considered a quasi-particle, beacuse it can exist only in solids

> as a consequence of vibrational motions: they cannot propagate in vacuum.

There's a new way of heat transport which the discoverers

call phonon tunneling.

Regards,

Joachim

Thank you all...

A lattice vibration.....!!!!

Similarly like light quanta-photon, phonon is the quanta in lattice vibration.

Dear Joachim,

that's interesting! As explained in the link you provided, phonons seem able to tunnel across a vacuum gap.

If I've understood well, this is due to the strong coupling between phonons and electric field. Indeed, if you have a region of space where more than one field are present, they will in general also interact with each other (we can see it as an interaction term between fields in the Lagrangean), so that some degrees of freedom can be exchanged between the two fields.

Maybe in this case, a phononic vibration (a "phonon") supplies to the electric field (a "photon") some energy; the "photon" in turn can tunnel through vacuum; after the tunneling, the "photon" excites another "phonon" on the other side and the overall effect is seen as a tunnelling of a "phonon" with the support of an electric field.

Maybe also this article published on Nature could enlighten on the topic:

Thanks for the question and the interesting contributions!

Regards,

Giovanni

Thank you for your reply

Here is an equivalent way of understanding phonons. Imagine a crystal at room temperature. The "units" at the lattice sites vibrate due to thermal energy. Their vibrations are coupled. Let us further assume that the vibrations are small enough that the oscillators are linear. By a suitable coordinate transformation, we can transform the hamiltonian so that it looks like a hamiltonian for an ensemble of independent harmonic oscillators. Since the time evolution of a hamiltonian is invariant under a unitary transformation, the hamiltonians before and after the transformation are equivalent. We can therefore treat the coupled oscillators in a real crystal as an ensemble of independent oscillators. A phonon is a quantum of energy of the independent oscillators in the ensemble.

Can you please tell how these vibrations become coupled?

Thank you for your interest. A "unit" in a lattice is bonded with all its neighbours. Therefore a change in the bond length of any one of them tends to affect the bond length with others. Let's see that in a simple 1-dimensional example. If I were to represent a "unit" by the letter 'U' and the bond between then by the letter 'b' then a 1-dimensional lattice would look like ... -b-U-b-U-b-U-b-U-b-.... . A change in position of any 'U' will immediately affects its neighbours on either side. This is what I mean by "vibrations being coupled". Vibrations in a solid are thus a collective motion of all "units" in the lattice. The best way to see the coupling is in the hamiltonian. You may want to look into chapter 4 of Kittel's "Introduction to Solid State Physics" or Appendix L of Ashcroft and Mermin's "Solid State Physics" for the form of the hamiltonian. If you have had a course in Quantum Mechanics, the first few pages of G. D. Mahan's "Many-particle Physics" has the most elegant treatment I have read.

Thank you...

what is the effect of phonon on thermal conductivity

Phonons can carry heat energy away. It is possible to do a kind of optics with phonons. Here are some new results:

Regards,

Joachim

Simplest answer to this question is

"Quantized elastic waves in solids are known as phonons"

The phonon is a vibration of the atomic lattice.This single-frequency wave has a defined momentum and energy and can be considered to be a quantum unit or a packet of mechanical vibrational energy, just as a photon is considered to be a packet of electromagnetic energy. Like photons, phonons exist with discrete amounts of energy: they can only accept or lose energy in accordance with the Planck relation: ΔE = hν where ΔE is energy change, h is Planck's constant, and ν is frequency of vibration. Phonons, like other waves defined quantum mechanically, can be considered as matter waves: therefore, depending on circumstances, phonons can behave like particles or waves, just as electrons can. Interactions between phonons and electrons play significant roles in electrical resistance.

best regard

What type of boson is a phonon? Is it a gauge boson?