The partition-function tag has no wiki summary.
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About deriving the multi-trace index in terms of the single-trace index
This question is in reference to this paper
Combining their equations 5.2, 5.3, 5.6 and 5.7 one seems to be looking at the integral/partition function,
$Z(x) = \prod_{n=1}^{n =\infty}\left [ \int ...
2
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1answer
84 views
Accessible microstates of harmonic oscillator in microcanonical enemble
While reading up on statistical physics, I am going through the calculation of the partition function of the harmonic oscillator in the microcanonical ensemble. The result for the partition function ...
2
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1answer
152 views
Canonical partition of a boson gas
I have a 1D gas made of $N$ particles placed in a harmonic potential well, so the Hamiltonian is:
$$ \mathcal H = \sum_{j=1}^N \left ( \frac{p_j^2}{2m} + \frac{1}{2}m\omega^2 x_j^2 \right )$$
The ...
3
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0answers
108 views
Is there a physical motivation to study finite fields?
Clearly finite groups are of immense value in physics and these are also substructures of fields. However I never came across any computations involving finite fields at university and so I never ...
2
votes
1answer
376 views
Helmholtz Free Energy, Partition Function
I'm trying to develop some basic intuition here, so this comes mostly as a jumble of commentary/questions. Hope its acceptable.
Helmholtz Free Energy: $A = -{\beta ^{-1}}lnZ$. I find this statement ...
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1answer
581 views
Partition function of bosons vs fermions
I have two atoms, both of which are either bosons or fermions, with four allowed energy states: $E_1 = 0$, $E_2 = E$, $E_3 = 2E$, with degeneracies 1, 1, 2 respectively.
What's the difference between ...
0
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1answer
206 views
Expressions for canonical partition function and probabilities $p(E_i)$
Given an atom with 4 allowed states corresponding to the energy levels
$E_1 = 0$, $E_2 = E$, and $E_3 = 2E$ with degeneracies 1, 1, and 2 respectively.
How do I find the expressions for the ...
4
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1answer
125 views
How do I calculate the probability that the oscillator is in a certain state using partition function?
So let's say I have a single ($N=1$) quantum harmonic oscillator and the energy is determined by $E_n = (n + 1/2) \cdot \hbar \omega$ (where $n$ is the quantum number and $n$ = $0, 1, 2, \ldots$)
...
2
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1answer
361 views
Calculating partition function of ultra-relativistic 1D gas
This is a problem (Problem 3.16) from the book Statistical Mechanics 2nd Ed. by Pathria.
In the problem I have to calculate the partition function of an ultra-relativistic 1D gas ($E_i=cp_i$) ...
5
votes
1answer
305 views
Taking the continuum limit of $U(N)$ gauge theories
I would like to draw your attention to appendix $C$ on page 38 of this paper.
The equation $C.2$ there seems to be evaluating the sum $\sum_R \chi _R (U^m)$ in equation 3.16 of this paper. I ...
4
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1answer
208 views
Integration of partition-function over many momentum variables
My integral looks like
$$Z(\beta)
= \frac{1}{h^3}\int d^3p\ \exp{\left(-\frac{\beta}{2m}\sum^{3N}_{i=1}p_i^2\right)}.$$
I'm confused about how to integrate over seemingly 3N variables in only a ...
2
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1answer
163 views
Partition function of an interacting gas
By reading an article, I found a partition function that, according to the author, describes an interacting with random variables as coupling constant.
$$Z =\int \mathrm{d} \lambda_i ...
0
votes
2answers
58 views
What is the minimal set of expectation values I need in a statistical model?
At least if $\vec v$ is really only a one dimensional parameter, measuring all the moments $\langle v^n \rangle_f$ seems to give me all the information to compute $\langle A \rangle_f$ with $A(v)$ ...
2
votes
0answers
29 views
Voros onde dimensional zeta function
in the paper http://arxiv.org/pdf/math-ph/0005029v2.pdf formula 23 Voros evaluate and get the following spectral theta /(semiclassical) function
$ \sum (E_{n}+\lambda )^{-s}= \frac{\Gamma ...
5
votes
2answers
196 views
Branch-point twist fields and operator insertions on a Riemann manifold
I am having trouble understanding how Eq (2.6) in this paper (PDF)
$$Z[\mathcal{L},\mathcal{M}_{n}]\propto\langle\Phi(u,0)\tilde{\Phi}(v,0)\rangle_{\mathcal{L}^{(n)},\mathbb{R}^{2}}$$
generalizes to ...
1
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1answer
284 views
Density of classical states in quantum theory
Let's first treat electrons as classical objects. I can evaluate the classical energy of each state in a configurational space (3N real numbers and, say, spins) using just Coulomb's law.
Then I ...
1
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1answer
68 views
semiclassical exact expression (in one dimension only)
let be $ N(x)= \sum_{n} H(x-E_{n}) $ the eingenvalue 'staircase' function
and let be a system so $ V(x)=V(-x)$ and $ V^{-1}(x)=\sqrt \pi \frac{d^{1/2}}{dx^{1/2}} N(x) $
then would it be true that ...
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0answers
98 views
Measure of Lee-Yang zeros
Consider a statistical mechanical system (say the 1D Ising model) on a finite lattice of size $N$, and call the corresponding partition function (as a function of, say, real temperature and real ...
1
vote
1answer
129 views
Quantum Stat-Mech Proof of an Inequality for the Partition Function
I have the following problem that I was unable to solve for class, but I had a couple first steps that I started with that I am unable to finish. I know I can't get this since it's already been ...
2
votes
1answer
147 views
Negative energies and a partition function
I'm writing down the partition function for a system, for which I know the dispersion relation
$$E \left( \mathbf{k} \right) = \sqrt{ \left| \mathbf{k} \right|^2 + m^2 + \cdots }$$
The exact form is ...
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4answers
598 views
What does third law of thermodynamics tell us?
I just have a question concerning the third law of thermodynamics.
The third law describes that the entropy should be a well defined constant if the system reaches the ground state which depends ...
-2
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1answer
68 views
To what extent `should` raw `data` from `publicly funded` research be made `available for download` `?` [closed]
When taxpayers pay money for expensive research (irrespective of the partition-function ...
3
votes
1answer
124 views
From spectrum/dispersion relation to the partition function
I know the spectrum/dispersion relation for a bosonic system.
$$E \left( \mathbf{k} \right) = \cdots$$
Is there a general method for writing down the partition function when the spectrum of the ...
5
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0answers
115 views
Partition Functions in (A)dS/CFT
I'm trying to understand some aspects of dS/CFT, and I'm running into a little trouble. Any help would be much appreciated.
In arXix:1104.2621, Harlow and Stanford showed that the late-time ...
