# What is Statistical phyisics: Definition and 27 Discussions

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1. ### Spectral Intensity Formula by Using Frequency

I found there is kind of solution in Pointon's book: An Introduction to Statistical Physics for Students. But I don't know how to find intensity by using frequency.
2. ### A Fourier transform and Cosmic variance - a few precisions

I cite an original report of a colleague : 1) I can't manage to proove that the statistical error is formulated like : ##\dfrac{\sigma (P (k))}{P(k)} = \sqrt{\dfrac {2}{N_{k} -1}}_{\text{with}} N_{k} \approx 4\pi \left(\dfrac{k}{dk}\right)^{2}## and why it is considered like a relative error ...
3. ### 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...
4. ### How to compute a mean square average

Homework Statement We know that $$< (x_1 - x_2)^2 > = \frac{K_bT}{K}$$ $$< (x_2 - x_3)^2 > = \frac{K_bT}{\gamma}$$ What's ##< (x_3 - x_1)^2 >## equal to? Homework EquationsThe Attempt at a Solution I have tried: ##< (x_2 - x_3)^2 > - < (x_1 - x_2)^2 >## but did not get ##< (x_3 - x_1)^2...
5. ### Expectation Value of a Stochastic Quantity

Homework Statement I'm working on a process similar to geometric brownian motion (a process with multiplicative noise), and I need to calculate the following expectation/mean; \langle y \rangle=\langle e^{\int_{0}^{x}\xi(t)dt}\rangle Where \xi(t) is delta-correlated so that...
6. ### Canonical ensemble of a simplified DNA representation

Question Form the canoncial partition using the following conditions: 2 N-particles long strands can join each other at the i-th particle to form a double helix chain. Otherwise, the i-th particle of each strand can also be left unattached, leaving the chain "open" An "open" link gives the...
7. ### A The Future of "Soft Matter Physics"

Hi all, I am trying to learn more about this field. Whether you work or have worked in this area or not, I would like to know where Soft Matter is going in terms of theory and applications. Thanks, A.D. *I apologize in advance if there are already many threads specifically addressing this...
8. ### I Is there a frequency cutoff for Debye theory of capillary waves?

I calculated the energy density of capillary waves with Debye method (pretty much Debye model in 2D), and I assumed there is a frequency cutoff for capillary waves as well. However, when I checked my work with solution I was quite surprised that the solution suggests there is no such a cuttoff...

18. ### A Where does statistical physics/mechanics fit in with QFT,GR?

We have two theories namely,Quantum Field Theory which works very well at sub-atomic scales, and the General Relativity which works very well at very large scales.So, my question is where does statistical physics/mechanics fit in? What role statistical physics/mechanics play in today's modern...
19. ### Heat capacity under constant pressure or volume question

HOMEWORK POSTED IN WRONG FORUM, SO NO TEMPLATE I have encountered a problem at the university in which there is a thermally isolated container of constant volume in which the number of particles and temperature change with time(the temperature increases). The change in particle number ensures...
20. ### Show interparticle spacing is much greater than wavelength

I have a past paper question from statistical physics: By assuming that ##\hbar^2 k^2=p^2##, I arrived at the result: The interparticle spacing, ##a^3 =\frac{V}{N}## is $$a^3 >> e^{-\frac{p^2}{2mk_B T}} \lambda_{deB}^3$$ Is my assumption correct? and does the result complete the purpose of...
21. ### Understanding the Uniform Probability Distribution in Statistical Ensembles

Homework Statement Confused about what a statistical ensemble actually means. Why does the ensemble have to have a uniform probability distribution at equilibrium? [If my definition of an ensemble is correct] The Attempt at a Solution This is what I understand so far: [/B] For any given...
22. ### Other Research topics in Statistical Physics

Currently I'm in the last year of the Physics course and I've been thinking about working in a project of undergraduate research, specifically in Statistical Physics. Two years ago I've already done a project like that in Fluid Mechanics combined with Gauge Theories and in that project I've...
23. ### Relationship between density and probability in diffusion

Homework Statement Consider the diffusion of a drop of ink in a water vase. The density of the ink is ## \rho (\vec{r}, t) ##, and the probability ##P(\vec{r}, t)## obeys the diffusion equation. What is the relationship between ##\rho (\vec{r}, t)## and ##P(\vec{r}, t)##? Homework...
24. ### Probability that a magnetic dipole is oriented with theta

1. the problem goes like this : The energy of interaction of a classical magnetic dipole with the magnetic field B is given by E = −μ·B. The sum over microstates becomes an integral over all directions of μ. The direction of μ in three dimensions is given by the angles θ and φ of a spherical...
25. ### A Normalization constant of Fermi Dirac distribution function

Fermi-Dirac distribution function is given by f(E)=(1)/(Aexp{E/k_{B}T}+1) here A is the normalization constant? How we can get A? E is the energy, k_{B} is the Boltzmann constant and T is the temperature. thank you
26. ### Probability density function of simple Mass-Spring system.

Homework Statement We know that after long run of simple mass-spring system, there should be a probability of finding the mass at certain points between -A and A.. Obviously in probability of finding the particle near A or -A is higher than finding the particle at 0, because the speed is the...
27. ### Magnetic moment of paramagnetic crystal

Hello, I've been having some trouble with a paramagnetism problem from my Statistical Mechanics class textbook (F. Mandl, Statistical Physics, 2nd edition, p. 25). The problem is as follows 1. Homework Statement 2. Homework Equations 1. The temperature parameter \displaystyle{ \beta =...