2
votes
1answer
66 views

Statistical count

I am reading the book"Heat and Thermodynamics" by Mark Waldo Zemansky and Richard Dittman. In the chapter "Statistical Mechanics" it says if I have $N_{i}$ distinguishable particles in any of $g_{i}$ ...
2
votes
0answers
33 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf ...
2
votes
2answers
67 views

How to deal with mean field method in antiferromagnetism?

There are lots of ways to apply the mean field method to deal with the Ising model whose ground state is a ferromagnetic state. Hence, it is easy to find the order parameter named magnetization to ...
3
votes
1answer
94 views

Fermi-Dirac distribution derivation?

I am trying to derive the Fermi-Dirac statistics using density matrix formalism. I know that $$<A>= Tr \rho A.$$ So I started from $$<n(\epsilon_i)>= Tr \rho n(\epsilon_i)=\frac {1}{Z} ...
0
votes
0answers
159 views

Ultra-Relativistic Fermi Gas - Chemical Potential and Energy

I tried deriving the expression for chemical potential of a Relativistic Fermi Gas using asymptotic expansion (for large z) in : $$ N = \frac{V}{h^3}4\pi (KT)^3g_s \int \frac{p^2 dp}{e^{p-\nu}+1} $$ ...
0
votes
2answers
215 views

Planck's distribution and Bose-Einstein distribution?

If the application of the Bose-Einstein distribution is in blackbody radiation, then what is Planck's distribution? Are they same? How did Planck know that he should use a Bose-Einstein distribution ...
1
vote
1answer
215 views

Partition function for classical particle and quantum particle are the same?

Permutation for classical particle $$\Omega=\frac{N!}{\Pi n_i!}$$ By using Lagrange method of undetermined multiplier, we get $$n_i=Ae^{\frac{-E}{kT}}$$ Probability, $$p=\frac{n_i} {Z}$$ where we ...
8
votes
3answers
274 views

What is the relationship between Maxwell–Boltzmann statistics and the grand canonical ensemble?

In the grand canonical ensemble one derives the expectation value $\langle \hat n_r\rangle^{\pm}$ for fermions and bosons of sort $r$: $$ \langle \hat n_r\rangle^{\pm} \ \propto \ ...
1
vote
0answers
47 views

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 ...
1
vote
1answer
143 views

Bose–Einstein statistics exercise

I've a basic Bose–Einstein statistics exercise. I've tried to solve it in two ways, but each way gives a different result. We have $n$ identical bosons without interactions at temperature $T$. There ...
2
votes
1answer
187 views

Energy density of a quantum mechanical ensemble

How do we determine the energy density of a given system? I have seen that the density operator $$\rho~=~\frac{\exp(-\beta \hat{H})}{\text{tr}(\exp(-\beta \hat{H}))}.$$ What does this mean exactly ...
7
votes
0answers
314 views

Is the “particle number” of “electrons” well defined in Wen's string-net theory of elementary particles?

According to professor Wen's string-net theory, electrons can be viewed as the elementary excitations of string-net objects. Just like the phonons and magnons are the elementary excitations of ...
5
votes
1answer
320 views

Why is (von Neumann) entropy maximized for an ensemble in thermal equilibrium?

Consider a quantum system in thermal equilibrium with a heat bath. In determining the density operator of the system, the usual procedure is to maximize the von Neumann entropy subject to the ...
7
votes
1answer
98 views

Canonical averages in a Fermi gas aka generalized Fermi-Dirac distribution

I am in the process of applying Beenakker's tunneling master equation theory of quantum dots (with some generalizations) to some problems of non-adiabatic charge pumping. As a part of this work I ...