# Tagged Questions

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### Thermal wavelength and critical temperature for Bose-Einstein condensate

I'm stuck with derivation of critical temperature and thermal wavelength for Bose-Einstein condensate - all sources describe equations very briefly. Suppose we have a system described by Bose-Einstein ...
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### Magnetisation of a degenerate electron gas in a weak field?

So I am looking at Landau's and Lifshitz's "Statistical Physics, Part I" chapter on degenerate fermi gases and specifically at chapter on Pauli's Mangetism or magnetism of degenerate electron gases, §...
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### What fugacity actually is and how it's plays an important role on Bose gas?

We know that the average occupation number cannot be negative for all systems and chemical potential must be negative in Ideal Bose Gas. This fact leads us to arrive a conclusion for fugacity which is ...
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### What are the instances of usage of four color theorem in the theory of fractional statistics?

How important is four-color theorem (Hypothesis) in theory of Fractional Statistics?
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### The symmetry normalization factor of wave functions in quantum statitics

Now I am studying statistical mechanics by R.K.Pathria & Paul D.Beale's Statistical Mechanics(3rd Edition). In page 134, the book claims that the wave function $\psi$ of a system composed of N ...
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### Exploiting Resonance to Make a Bound State with Gamma Rays (and other Very High Energy Particles)

One obvious consequence of any finite potential is that a high enough energy wave-function will not form a bound state, either they are high enough energy they will generally just bypass the barrier ...
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### grand-canonical ensemble

I was wondering if the following reasoning is correct for example for electrons in the classical or qm grand-canonical ensemble? Is it always valid in the grandcanonical ensemble to calculate the ...
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### Chemical potential related with quantum and classical limit in ideal gas

For ideal gas we have chemical potential $\mu = \tau \ln \left(\frac{n}{n_Q}\right)$ where $n = N/V$ number density and $n_Q = \left(\frac{M\tau}{2\pi \hbar^2}\right)^{\frac{3}{2}}$ Note we call ...
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### Diamagnetism of a degenerate electron gas for weak fields

In the book "Statistical Physics, Part I ($3^{{\rm rd}}$ edition)" by Landau and Lifshitz, at $\S59$ when he treats the diamagnetic part of the magnetisation of a degenerate electron gas for weak ...
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### Is there a systematic way to determine the relevant variables needed to describe a nonequilibrium system?

In strong nonequilirium, the statistical operator describing the system depends on an infinite number of variables (BBGKY-hierarchy), contains information about all the previous states starting from ...
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### How to interpret two distinguishable particles with N possible states?

NOTE: Please do not provide an answer to the questions. If I am incorrect, please explain why, and if I am correct, please try to further my understanding. I think that this is a constructive way to ...
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### Fugacity in Bose-Einstein condensate

Just a simple question, I didn't manage to find out in my books... The fugacity $z = e^{\beta \mu}$ in the case we have condensation in a bose statistics. Is it always 1 or $z \to 1$? In the ...
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### Fermion gas exercise with annihilation and creation operator

The number states in the ground state of fermion gas are, \begin{align} n_l &= 1, \qquad \epsilon_l < \epsilon_F \quad (\epsilon_{F} \text{ is the Fermi energy.}) \\ n_l &= 0 \qquad \text{...
My professor said that the $k_BT$ displacement in the energy levels of the band electrons is due to the space-thermal displacement of the potential of the ion host. I think that this displacement is ...