8 votes

What does it mean if the Fermi level crosses into the valence band? How about into the conduction band?

The terms "conduction band" and "valence band" sort of lose their usefulness if you are not talking about a standard band insulator where you have a filled valence band and the ...
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  • 695
5 votes

What does it mean if the Fermi level crosses into the valence band? How about into the conduction band?

In the book by Naeman, Semiconductor Physics, the equation $$E_F -E_{Fi}=kT\ln{\frac{n_0}{n_i}}$$ is derived and relates the change in the Fermi level due to doping. $E_F$ is the Fermi level after ...
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  • 24.8k
1 vote

How to derive the Lagrangian for a system of first order equations of motion?

I am not sure if this is your problem ?. with the non holonomic constraint equations $$\left[ \begin {array}{c} {\dot x}-f \left( x \right) \\ {\dot y}-g \left( y \right) \\ {\dot m}-h \left( m,x,y \...
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  • 8,379
1 vote

For an arbitrary Ising model, is there any numerical method to calculate its free energy with polynomial cost?

It has been shown that finding the free energy, or equivalently, the partition function, of an arbitrary Ising model is an NP-hard problem. For instance, "On the computational complexity of Ising ...
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1 vote

Computing the partition function from a Metropolis Monte Carlo sample

Metropolis Monte Carlo is a method for calculating averages, like $$ \langle f(x)\rangle = \frac{\int f(x)p(x)dx}{\int p(x)dx}. $$ One cannot however calculate the normalization constant, $Z=\int p(x)...
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  • 37.1k

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