4
votes
1answer
153 views

Strange definition of microcanonical partition function

I always thought that the microcanonical partition function would measure the number of states that correspond to some fixed energy. Despite, I found in this paper (equation 3.4) that we integrate ...
2
votes
0answers
36 views

Energy from the Feynman-Kikuchi Partition Function

The Feynman-Kikuchi Partition function is given as $$Z_{FK}=K_\beta \int dx \eta(x) \exp \left(-\frac{x}{\beta}\right) $$ where $K_\beta$ is a normalization constant and ...
2
votes
1answer
238 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 ...
3
votes
1answer
217 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 ...