Are there phonons in a free electron gas?

In summary, the conversation discusses the properties of an electron gas with an equation of state p=p(V) and its behavior in a confined space. The OP's question is whether phonons emit and absorb in this type of electron gas at finite temperature. The responses mention the existence of plasmons in such a gas and their potential to carry thermal energy. However, the energy range of plasmons is typically much higher than the ambient temperature, making their contribution to thermal energy negligible unless the temperature is increased or the plasmon frequency is lowered.
  • #1
bjnartowt
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TL;DR Summary
Is there emission and absorption of phonons within an electron gas lacking an underlying lattice?
It is well-known that the electron gas of volume V has an equation of state p=p(V) and thus has a bulk modulus $$B=-V(dp/dV)$$. Suppose the electron gas had no underlying lattice but was confined. Do phonons emit and absorb in such an electron gas at finite temperature?

The reason I ask is because I have found that if I try to make a Carnot engine with an electron gas as the working fluid, I get above-Carnot efficiencies if I consider the electrons alone to carry thermal energy. I can only conclude that a separate system of phonons exists within the electrons that carry thermal energy.

Comments?
 
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  • #2
My guess is that the light one might see is from traveling photons. I am unaware of photon energy being held in captivity. I may be very wrong but that’s the extent of my knowledge.

I must have bad eyes or a bad brain or both.
 
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  • #3
lsume said:
My guess is that the light one might see is from traveling photons. I am unaware of photon energy being held in captivity. I may be very wrong but that’s the extent of my knowledge.

The OP is asking about PHONONS, not PHOTONS. It is why this is the Condensed Matter forum.

Zz.
 
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  • #4
It would appear that an electron gas would support sound wave, just like an ordinary gas, however, the electron gas is charged. So in addition to gas pressure, you have to include electric field effects. Therefore, the oscillation of electron gas do exist but they are known as plasma oscillation.
bjnartowt said:
Summary: Is there emission and absorption of phonons within an electron gas lacking an underlying lattice?

I get above-Carnot efficiencies
That, according to the sate of thermodynamics, is impossible. You can derive Carnot cycle efficiency without any reference to any physical system. All you need is the concept of energy and entropy.
 
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  • #5
Indeed, a gas of that type would support plasmons (not phonons).
 
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  • #6
f95toli said:
Indeed, a gas of that type would support plasmons (not phonons).

Incidentally, in low-dimensional cases, these plasmons afford us a nice description when the Fermi liquid renormalisation scheme stops working, as a highly correlated 1D electron liquid can be described as a gas of non-interacting plasmons.
 
  • #7
Thank you all for your replies.

My next question is, naturally, if plasmons can carry thermal energy.
 
  • #8
bjnartowt said:
My next question is, naturally, if plasmons can carry thermal energy
In principle yes, however, typical plasmon energies are in a few eV range that is much larger than kT at ambient temperature (~ 0.025 eV), so probability of plasmon excitation at ambient temperature is very low.
To get some contribution you have to either increase the temperature or lower plasmon frequency (this by lowering plasma density).
 
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1. What is a free electron gas?

A free electron gas refers to a system of electrons that are not bound to any particular atom or molecule. This can occur in metals or other conductive materials where the outermost electrons are not tightly bound to the nucleus and are able to move freely.

2. What are phonons?

Phonons are quantized units of vibrational energy in a solid material. They can be thought of as the "building blocks" of sound and heat in a solid. Phonons are responsible for the transfer of heat and sound energy in materials.

3. How do phonons relate to a free electron gas?

In a free electron gas, the electrons are able to move freely and interact with each other. This leads to the creation of phonons as the electrons vibrate and transfer energy to each other. Phonons can also interact with the electrons, affecting their movement and behavior.

4. What is the significance of phonons in a free electron gas?

The presence of phonons in a free electron gas can affect the material's properties, such as its conductivity and thermal conductivity. Phonons can also play a role in the behavior of electrons, leading to phenomena such as superconductivity.

5. How are phonons in a free electron gas studied?

Scientists can study the behavior of phonons in a free electron gas through various experimental techniques, such as neutron scattering and Raman spectroscopy. Theoretical models and simulations can also be used to understand the interactions between phonons and free electrons.

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