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5
votes
2answers
189 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 j_{\...
3
votes
1answer
56 views

Quantum versus classical computation of the density of states

If I consider for instance N non interacting particles in a box, I can compute the energy spectrum quantum mechanically, and thus the number of (quantum) microstates corresponding to a total energy ...
1
vote
1answer
309 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 ...
0
votes
1answer
25 views

Why must the separation constant be real in a time dependent wave function?

I'm not sure if I'm asking this right. I'm reading ''Introduction to Quantum Mechanics'' by Griffiths and in the chapter 2 exercises he asks to prove that the separation constant, $E$, must be real. ...
0
votes
1answer
103 views

Quantum Dimer Model (QDM) hamiltonian

The Hamiltonian given by Rokhsar-Kivelson QDM is based on tensor products of the state vectors. Why is this the case?, is it because the lattice model is a mixed state? It'd be great if someone could ...
0
votes
1answer
76 views

Does spin degeneracy affect ideal Fermi gases in any way as T->Infinity?

In other words, given any system comprised of an ideal Fermi gas, in the high-temperature (classical) limit, are there any observable thermodynamic quantities (pressure, volume, energy, density, etc.) ...
16
votes
0answers
235 views

Anyons as particles?

I'm trying to understand the basics of anyons physics. I understand there is neither a Fock space they live in (because Fock is just the space of (anti-)symmetrized tensor product state, see e.g. ...
7
votes
0answers
361 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 ...
3
votes
0answers
39 views

If 2 fermionic atoms form a molecule, will the molecule always behave as a boson?

2 fermionic atoms give a bosonic molecule. 2 bosonic atoms form a bosonic molecule. Is there a energy scale where these two molecules will behave differently? If yes, will it depend on the ...
2
votes
0answers
44 views

dependence of braiding matrix element on the fusion product of anyons

In the case of Majorana fermions (MFs), one knows that if one braids MF $a$ with MF $b,$ then braiding matrix element $R^{c}_{ab}$ depends on the state $c$ which is the fusion outcome of $a$ and $b$. ...
2
votes
0answers
48 views

Bose-Einstein-statistics out of fermionic many body system

ok, let me try this again. How do I get to atoms obeying Bose Einstein statistics from considering the fermionic many body problem of a bunch of electrons, protons and neutrons forming these (bosonic)...
1
vote
0answers
41 views

Link Between the Density Operator and the Partition Function and Boltzmann Distribution in Quantum Statistical Mechanics

I have a very limited knowledge of statistical mechanics, but I seem to running into some related concepts for my background readings for the research project this summer. For example, see the ...
1
vote
0answers
68 views

Some subtleties in quantizing a fermi field

Consider the quantization conditions for a complex Fermi field $\Psi=\Phi_1+i\Phi_2$: $$\{\Psi(x),\Psi(y)\}=\{\Psi^\dagger(x)\Psi^\dagger(y)\}=0,~~~~ \{\Psi^\dagger(x),\Psi(y)\}=\delta(x-y)$$ Compare ...
1
vote
0answers
28 views

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 ...
1
vote
0answers
27 views

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, §...
1
vote
0answers
51 views

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 ...
1
vote
0answers
22 views

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?
1
vote
0answers
42 views

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 ...
1
vote
0answers
74 views

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 ...
1
vote
0answers
73 views

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 ...
1
vote
0answers
245 views

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 ...
1
vote
0answers
93 views

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 ...
1
vote
0answers
125 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 ...
0
votes
0answers
25 views

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 ...
0
votes
0answers
47 views

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 ...
0
votes
0answers
33 views

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{...
0
votes
0answers
74 views

Thermal fluctuations in metals

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 ...
0
votes
0answers
158 views

relative phase/sign in $\Psi$ after exchange of composite particles with angular momenta

I'm reading Quantum Liquids by A.J. Leggett and became confused by the following statement in the first chapter. Consider now a pair of such identical atoms. In the absence of appreciable coupling ...