Statistical Definition and 582 Threads

Is it accurate to say that interference cannot happen in Statistical Mechanics? I know it is considered a wave mechanics phenomenon but aren't waves just highly statistical ensembles, like anything else? I always thought that Fourier says periodic spectra could be summed to create any signal...

How to prove this "if p(a)=p(b)=p then p(ab) ≤ p^2Homework EquationsThe Attempt at a Solution

Can someone recommend me some good textbooks or articles that contain or focus on statistical thermodynamics and/or oscillatory motion (preferably with advanced math, not just stories)?

I want to find photon energy distribution, let's say in a closed cube box,there are 100 photons(suppose 1 photon contains 1 Joule),and there's a mirror on left side and then there's a glass in between and the right side is completely black. I want to find photon energy distribution(like how much...

Hello everybody. I've recently finished work through Weinberg's course in QFT which made my understanding of theoretical physics quite peculiar. For example, I can't understand statistical physics from Landau&Lifshitz book at all as there are a lot of unfounded arguments. I wonder firstly is it...

Consider the quote ''The macrostate which corresponds to the highest number of microstates which result in that macrostate, is the state which will be observed.'' Can someone specify in which context this is correct because I'm quite confused by it. If I have an isolated box with N particles in...

My job requires me to update excel reports and also send out analysis and summaries. My concern is, I don't really have a lot of experience with statistics, numbers analysis, or have enough background to know what type of tools are available for me. For example, let's say I send out a weekly...

Hello! I am a master student, and I am about to start working on my master thesis, which, in my counrty, is a substantial work of 6 months which usually involves original research. I will be supervised by two professors of Statistical Mechanics, who have many research interest. In these days...

There are some applications of thermodynamics in engineering which I don't bother to talk about. What I want to ask is, are there any problems in engineering for which thermodynamics is not enough and people have to use statistical mechanics? Thanks

When dealing with cosmological perturbations, there are a lot of different notions that are thrown around in the literature like statistical homogeneity and isotropy. However, these terms are often not motivated and clearly defined. Could anyone recommend any good references where these notions...

So I have just been reading up on statistical thermodynamics and have no idea why the bose-einstein, fermi dirac and maxwell boltzman are all integers, that makes sense, but then when you make the degenerate correction to the maxwell Boltzmann by dividing by N! we get decimal answers. Why is...

Hi, does anyone know of good places to study masters degree in physics with the main focus on statistical physics ?

Homework Statement A simple model for liquid crystals confined to 2 dimensions is o assume each molecule can only align in one of 2 perpendicular directions. To construct a landau model its convenient to define order parameter, s : s = 2 ( Np - 0.5Nt ) / Nt Np - number molecules...

I'm enjoying Lennard Susskind's lectures on Statistical mechanics. I've briefly studied this material before, but I've learned a lot about more practical calculations from these lectures: he's used the partition function to derive all sorts of fun expressions, and to analyse the ideal gas and a...

Hey guys, I've never studied this subject before (except basic thermal physics in high school), and I have a course on it this semester. I'm in a semi international program, and this course isn't taught in English (but the tutorials are, thankfully), so I will need to study on my own. In...

Hey guys, I've been looking up on the web and couldn't find prerequisites for graduate level statistical mechanics. What would be the mathematics/physics background needed for the course? Would I need undergraduate statistical physics first? As always, thanks in advance!

Homework Statement A mixture of two substances exists on a cubic lattice of N sites, each of which is occupied by either an A molecule or a B molecule. The number of A molecules is NA and the number of B molecules is NB, such that NA + NB = N. The energy of interaction is k_BT\chi_{AA} between...

I should have studies statistics in school. I have been collecting some trip data from you commute to and from work, and I want to determine what factors are influencing trip duration. There are multiple factors, which I cannot easily isolate. The factors I'm most interested in are: - duration...

Hello all! I'm hoping you will be able to direct me to sources of raw income1 / employment data. Hopefully this thread can be a help to others who have similar needs in the future, as well. (I did a quick search for a similar thread and didn't find anything - please correct me if I'm wrong.)...

Fundamental assumtption: "a closed system is equally likely to be in any of its g accessible micro- states, and all accessible micro- states are assumed to be equally probable." There's just a few things I don't understand about this, 1. Isn't saying that a closed system is equally likely to...

Hello, I am wondering if anyone would be able to guide me through a practice question for an upcoming test. I am not feeling very confident at this point and would very much appreciate some help! The question is as follows; Let {X}_{1},{X}_{2}…, {X}_{n}and {Y}_{1},{Y}_{2}…,{Y}_{m} be two...

I don't think I've fully grasped the underlying ideas of this class, so at the moment I'm just sort of flailing for equations to plug stuff into... Homework Statement Show that in the mean field model, M is proportional to H1/3 at T=Tc and that at H=0, M is proportional to (Tc - T)1/2...

Homework Statement Show that the number of photons in equlibrium at tempertaure t in a cavity of volume V is, N=[2.404 V (t/ħc^3]/Pi^2 The total number of photons is the sum of the average number of photons over all modes n->∑<s> Homework Equations n=Sqrt[nx^2+ny^2+nz^2] ωn=(n Pi c)/L...

I have access to this book at my uni's library. I'm considering to learn from it as my main source. Is it severely outdated? How good is it for learning statistical mechanics?

Homework Statement 1.) For N particles in a gravity field, the Hamiltonian has a contribution of external potential only (-mgh). Show that the particle density follows the barometric height equation (1). 2.) For N particles in a open system at constant pressure p and temperature T, let there...

It is well known that quantum mechanics in the path-integral form is formally very similar to equilibrium statistical mechanics formulated in terms of a partition function. In a relatively recent, very readable and straightforward paper http://lanl.arxiv.org/abs/1311.0813 John Baez (a well known...

Hello, This is more a question about history of science in general. During my lectures on statistical physics, I noticed that some of the problems that Bolztmann faced lead to the introduction of: ##h/2\pi## (to introduce the unit of an action leading to a "unitless" partition function) which...

Hello everyone! :) I am studying for an honours course in Statistical Physics. I have stumbled upon the book "Statistical Mechanics of Phase Transitions" by J.M. Yeomans. The layout of the book, as well as information, is exactly what I need. I want to work through the problems and was...

I am planning to take a course on Statistical Physics in my university. The main text to be followed is Statistical Physics by F. Reif. As of now, I have completed university level courses on Calculus, Differential Equations, Linear Algebra. What other knowledge would be required to help me get...

It seems like two main applications of statistical mechanics in academia research include the application to solid mechanics/materials and the application to heat transfer. How do statistical mechanics and thermodynamics differ in these two aspects? Is it basically the same theory applied to...

Dear Physics Forum personnel, I am a undergraduate sophomore with double majors in microbiology and chemistry. I have been involving in two research laboratories: theoretical physical chemistry (focused on inorganic chemistry & solid-state physics) and pathogenic bacteriology. I actually...

See image. I have to present this on Monday and don't really know what I'm doing having missed a couple of lectures through illness. Any help or hints would be very much appreciated. Thanks, TM

Homework Statement Consider a chain with N >> 1 segments of length 1. One end of the chain is at the origin, the other at a point R. In this onedimensional model the segments may face left or right. The number of segments facing right is n. 1: What is the number of possible configurations in...

This is an exercise from an old examination that I am trying to understand by following the given solution to this problem. The exercise is about to calculate the four spin average <SiSjSkSl> and the indices i,j,k and l, given a Hamiltonian H. Solution: The problem is that i can't follow the...

Suppose we have a random service time ##T## with residual service time ##R## observed at some point along the way. What is the correct way to call ##T## (in 1-2 words, without having to introduce ##R##) if: 1) For any observation time, ##\mathbb{E}R\leq\mathbb{E}T##? 2) For any observation...

Hi, I am looking for a reference book in statistical physics which comprising any possible aspect of statistical physics. Can anybody help? Thank you

Homework Statement See: attached imageHow do we get the final equation? I'm obviously missing out on something..

Good day, I'm starting my master in physics, and it's time for me to choose my courses. I've decided that I probably want to pursue the direction of quantum information processing, and I'm trying to pick my courses with that in mind. For my first semester I'll be taking four courses: Quantum...

Hello, I am having trouble understanding collision frequency in following discussion from Kubo, $$collision\ frequency = \frac{1}{\frac{l}{v_{x}}}=\frac{p_{x}}{ml}$$ What am I missing ?

I'm currently in a physics grad program and am interested in doing research where statistical analysis is involved by using R or SAS. What fields of physics research relies on this the most? Should I look into theory, computational, or experimental groups? Or perhaps observational astronomy?

hi pf! so i am going to take the skewness and kurtosis of a sample. however, if i already have a pdf, is there really any reason for doing this? thanks! josh

Consider the following problem: A spring with spring constant ##k## is suspended vertically from a fixed support and the spring is in equilibrium with a heat bath of temperature ##T## and resides in a gravitational field ##g##. A mass ##m## is hung from the other end of the spring. Find the...

Homework Statement If Hamiltonian ##\hat{H}## is hermitian show that operator ##\hat{\rho}=\frac{e^{-\beta\hat{H}}}{Tr(e^{-\beta\hat{H}})}## is statistical.Homework Equations In order to be statistical operator ##\hat{\rho}## must be hermitian and must have trace equal ##1##...

I red griffiths many times but even now there is something I can't understand. It's about statistical interpretation. In his book chapter 3.4 he says "If you measure an observable Q(x,p) on a particle in the state ψ(x,t), you are certain to get one of the eigenvalues of the hermitian operator...

I am considering majoring in statistics. The school (a mediocre state uni, by the way) calls the major "statistics", but the curriculum is that of an "applied statistics" program, in that it requires you to choose an emphasis that you could apply statistics to. I'm going to choose science...

When do these two fields of physics overlap other than when we discuss entropy of supersymmetric black holes? Does statistical mechanics or statistical physics support any aspect in string theory or vice verse? I have read some place that the string theory reduces to the standard model by doing...

Homework Statement Consider a classical one-dimensional nonlinear oscillator whose energy is given by \epsilon=\frac{p^{2}}{2m}+ax^{4} where x,p, and m have their usual meanings; the paramater, a, is a constant a) If the oscillator is in equilibrium with a heat bath at temperature T...

There had been a case in the UK where a woman's two babies died one after the other. Then some apparent statistician concluded 'If the chance of that occurring is 1 in a million, then she must have killed her babies'. Later, a very long court of law had been doing research on it and she appeared...

Homework Statement A cavity contains black body radiation at temperature at T=500K. Consider a optical mode in the cavity with frequency w=2.5x10^(13) Hz. Calculate; (a)the probability of finding 0 photons in the mode. (b)the probability of finding 1 photon in the mode (c)the mean number of...

1. Homework Statement An average value of N measurements is defined as: ravg = 1N ∑ ri where i = 1 and it sums up to N measurements By using this expression in the master formula for a general function z = (x1, x2,...) error propagation, we find the δravg error propagation: (δravg)2 =...