Fermi energy definition and Fermi-Dirac distribution

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Discussion Overview

The discussion revolves around the definition of Fermi energy and its relationship with the Fermi-Dirac distribution, particularly in the context of temperature effects on electron occupancy in a system. Participants explore the implications of temperature on the definition and behavior of Fermi energy, as well as the characteristics of the Fermi-Dirac function at different temperatures.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant states that Fermi energy is defined as the topmost filled level in the ground state of an N electron system, questioning if this definition is valid only at absolute zero.
  • Another participant points out that the definition of Fermi energy does not account for temperature, suggesting that at finite temperatures, the probability of occupancy of energy states follows a Boltzmann distribution.
  • A later reply reiterates the importance of temperature in defining the state of the system, emphasizing that Fermi-Dirac statistics apply to half-integer spin particles and produce a step function at absolute zero.
  • One participant questions whether Fermi energy still represents the topmost filled level at non-absolute temperatures, indicating a potential shift in understanding.
  • Another participant asserts that Fermi energy is defined as the zero temperature result, noting that at finite temperatures, the occupancy of energy levels becomes fluctuating.

Areas of Agreement / Disagreement

Participants express differing views on the definition of Fermi energy in relation to temperature, with some asserting that it is strictly a zero-temperature concept while others suggest it has implications at finite temperatures. The discussion remains unresolved regarding the exact nature of Fermi energy at non-zero temperatures.

Contextual Notes

There are limitations regarding the assumptions made about temperature and the definitions of energy states, as well as the dependence on the specific system being discussed. The implications of quantum effects and statistical mechanics are also noted but not fully resolved.

chikchok
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Fermi energy definition and fermi-dirac distribution
1)In my book , there is a definition of fermi energy as topmost filled level in the ground state of an N electron system. This definition holds only for absolute zero,right? If it is not absolute zero,fermi energy is the energy at which the probability of a state being occupied is 50 percent. Please, tell me if I am understanding this correctly.
2)I was wondering why at low temperatures Fermi-Dirac function goes sharply from 1 to 0 and for higher temperature it goes down smoothly. Is it reasonable to assume that for low temperature, levels below the fermi level are filled and all above are empty? But why it does not happen with higher temperatures. Thank you in advance.
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1) Stating "In the ground state" obviates mention of temperature.
2) Temperature is a measure of average internal energy. An isolated system at lowest energy will be in the ground state. If connected to a thermal reservoir it will have a finite probability of being in an excited state with a probability that is roughly negative exponential in energy e.g. the Boltzmann factor. Careful consideration of quantum effects gives rise to Fermi-Dirac statistics for half integer spin which gives a "step" function for T=0
 
hutchphd said:
1) Stating "In the ground state" obviates mention of temperature.
2) Temperature is a measure of average internal energy. An isolated system at lowest energy will be in the ground state. If connected to a thermal reservoir it will have a finite probability of being in an excited state with a probability that is roughly negative exponential in energy e.g. the Boltzmann factor. Careful consideration of quantum effects gives rise to Fermi-Dirac statistics for half integer spin which gives a "step" function for T=0
so for non-absolute temperature fermi energy is not the energy of topmost filled level anymore?
 
The Fermi Energy is defined as the zero T result. It is "5" for your graphed system. With finite temperature occupation of levels is fluctuating.
 

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