# What is Statisical mechanics: Definition and 28 Discussions

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1. ### Z, <U>, and C for Hagedorn Spectrum

So to get the partition function I do the integral ##\int \alpha E^{3} e^{(B_{0}-B)E} dE##, which substituting in ##/Delta B = B_{0} - B## is ##Z = \frac{ \alpha E^{3} e^{\Delta B E}}{\Delta B} - \frac{3 \alpha E^{2} e^{\Delta B}}{\Delta B^{2}} + \frac{6 \alpha E e^{\Delta B E}}{\Delta B ^{3}} -...
2. ### I Balloon experiment - Classical Physics vs. Statistical Physics

While reading a similar and deservedly closed post a contradiction came to my mind. The supposed contradiction is related to Statistical Physics where my understanding is only conceptual so correct me where I might be wrong. I remember reading that lightweight gasses can escape Earth's...
3. ### A system of independent particles (energy levels)

Hi guys, Can you give me some feedback on whether my calculation is correct? I applied the formula below (Boltzmann Distribution) but I didn‘t know what to use for the variable z. I don‘t even know if I used the correct equation. Can you help me further? The task is: Consider a system of...
4. ### Partition function for a spin i

##Z = \sum_{-i}^{i} = e^{-E_n \beta}## ##Z = \sum_{0}^j e^{nh\beta} + \sum_{0}^j e^{-nh\beta}## Those sums are 2 finites geometric series ##Z = \frac{1- e^{h\beta(i+1)}}{1-e^{h\beta}} + \frac{1-e^{-h\beta(i+1)}}{1-e^{-h\beta}}## I don't think this is ring since from that I can't get 2 sinh...
5. ### A Energy hypersurface in a phase space (statistical physics)

what is the reason for that the energy hypersurfaces in a phase space, which belong to systems with constant energy are closed? ( see picture )

20. ### A What is the functional representation of D(E) for a given energy interval?

Data = np.array([-1.61032636, -1.23577245, -0.50587484, -0.28348457, -0.18748945, 0.4537447, 1.2338455, 2.13535718]) print("Data is: ", Data) print(Data.shape) n,bins,patches = plt.hist(Data,bins=4) print("n: ",n) print("bins: ",bins) plt.savefig("./DOS")
21. ### A Quantum statistical canonical formalism to find ground state at T

For my own understanding, I am trying to computationally solve a simple spinless fermionic Hamiltonian in Quantum Canonical Ensemble formalism . The Hamiltonian is written in the second quantization as $$H = \sum_{i=1}^L c_{i+1}^\dagger c_i + h.c.$$ In the canonical formalism, the density...
22. ### Can we study an odd number sized lattice model at half filling?

So one can numerically study (I am interested in exact diagonalization) any 1D lattice model with ##L## sites and ##N## number of particles. At half filling, ##L/N = 2##. My question to a professor was that can we study a system of size ##L = 31## at half filling? He replied yes, there is a way...
23. ### I Changing Summation to Integral

This is the text from Reif Statistical mechanics. In the screenshot he changes the summation to integral(Eq. 1.5.17) by saying that they are approximately continuous values. However,I don't see how. Can anyone justify this change?
24. ### I What is the relation between chemical potential and the number of particles?

Chemical potential is defined as the change in energy due to change in the number of particles in a system. Let we have a system which is defined by the following Hamiltonian: $$H = -t \sum_i^L c_i^\dagger c_{i+1} + V\sum_i^L n_i n_{i+1} -\mu \sum_i^L n_i$$ where ##c^\dagger (c)## are creation...
25. ### Probability at a temperature T that a system has a particular energy

Salutations, I'm starting in statistical mechanics and reviewing some related studying cases I would like to understand what occurs in small systems with normal modes of vibration, for example, a small system that has 2 normal modes of vibration, with natural frequencies $$\omega_1$$ and...
26. ### Finding a Booklist to Learn Nonequilibrium Thermodynamics/Statistical Mechanics

Hi, guys I have posted this question on StackExchange, but no one seems to care answer. Because I don't think this is a simple textbook question, I start my thread here: I know this is a big question. But as a graduate student, my research is somehow related to nonequilibrium...
27. ### Scattering dynamics and viscosity

I have been studying the statistical mechanics' viewpoint of fluid dynamics by considering the derivation of Navier-Stokes' equations from the Boltzmann equation involving the whole Chapman-Enskog expansion. It is clear that through this process, it is possible to account for the dependence of...
28. ### Looking for a solid Introductory Statisical Mechanics textbook.

Title says it all really, I'm a second year undergraduate from oxford, and currently the textbook I've been using for stat. mech. is "Concepts in Thermal Physics", which was wirtten by my lecturer. I'd like (ideally) something a bit longer to work through suring the holidays, that would provide...