Statistical Definition and 582 Threads

Hi i would like to understand if it is advisable to study statistical mechanics before of the MQ (with the classical stat. mec.), or after the MQ all together ?? Thank you

Homework Statement With the Hamiltonian here: Compute the cananonical ensemble partition function given by ##\frac{1}{h} \int dq dp \exp^{-\beta(H(p,q)}## for 1-d , where ##h## is planks constant Homework EquationsThe Attempt at a Solution I am okay for the ##p^2/2m## term and the...

Phase volume is it the same as the number of total microstates in some physical system? Phase volume= volume of phase space. Or there is some difference?

Normally, I prefer to do my own research, but I'm drawing a blank on this one. Any help would be appreciated. My understanding is that statistical mechanics accounts for all of the heat energy in a gas by the kinetic energy of the molecules. I also understand that atomic orbitals have different...

Hello all, Jackson Ch. 6 (3rd edition) tells the reader to look at de Groot for a statistical mechanical derivation of the macroscopic Maxwell equations. I figure he means "Foundations of Electrodynamics" by S. R. de Groot. I requested that book be sent to my school library on loan, but I was...

Last week I went to a state fair which I saw a game of lucky draw. There is two sealed boxes, contains bunch of 4 different color balls: red, blue, green and white. Here is the game rule. Players make an initial draw on box one, if players get a white ball, lose the game; if getting a red one...

The statistical ensemble interpretation (SEI) is supposed to be a minimal interpretation of QM with the smallest amount of philosophy, vagueness and controversy. Yet it turns out not to be the case. For instance Ballentine, the inventor of SEI, interprets Bell theorem as a strong evidence of...

Homework Statement See attached. to get ##p## I need to differentiate ##F## w.r.t ##V##, but I also have that the upper limit ##T_{D}## depends on ##V##, so I must take this into consideration when doing the differentiation. The solution looks as though it has done this without evaluating...

Homework Statement Two components of a laptop computer have the following joint probability density function for their useful lifetimes X and Y (in years): f(xy)=xe^(−x(1+y)) 0 <= x <= y 0 otherwise Find the marginal probability density function of X, fX(x). Enter a formula below. Use * for...

Hi All, What are the main differences between statistical and dynamics properties in physics? Could you please explain the difference for problems in both classical and quantum mechanics. For instance, path integral molecular dynamics is supposed to give statistical properties of a quantum...

Homework Statement Can someone tell me when testing for independence using chi square tests, why is the expected frequency of a cell is denoted by the formula $$ \frac{\sum row * \sum column}{\sum total } \ $$

Hi community, I have a question about the Bernoulli principle. From statistical mechanics the pressure in the ideal gas is independent of velocity. But in the case of the flow of an ideal gas in a channel, the pressure depends on the velocity. Where can I clarify this misunderstanding...

Homework Statement I look at the distribution ##(Y_1,Y_2,...,Y_n)## where ##Y_i=μ+(1+φ x_i)+ε_i## where ##-1<φ<1## and ##-1<x_i<1## . x's are known numbers. ε's are independent and normally distributed with mean 0 and variance 1. I need to find the the maximum likelihood estimator for μ and...

Homework Statement Hi I am looking at the attached extract from David Tong's lecure notes on statistical phsyics So we have a canonical ensemble system ##S##, and the idea is that we take ##W>>1## copies of the system ##S##, and the copies of ##W## taken together then can be treated as a...

Please translate to English, so that it can be discussed here! I am primarily interested in how the virtual ensemble differs from an ordinary statistical ensemble, i.e., a large collection of actually identically prepared systems. The latter is the usual ensemble on which one can make...

Recently I have had a conversation with one of my professors, and he suggested me to take a graduate statistical mechanics course in the coming Spring semester. Although the various reasons my professor gave for his suggestion sound really appealing to me, I am a little bit worried about whether...

I have two different maps of dots representing locations of settlements of two different populations in the same geographical area. I want to compare both maps to know in which of both maps the dots are more "randomly spread". How can I proceed?

Hi, So I am aiming to derive the continuity equation using the fact that phase space points are not created/destroyed. So I am going to use the Leibiniz rule for integration extended to 3-d: ## d/dt \int\limits_{v(t)} F dv = \int\limits_{v(t)} \frac{\partial F}{\partial t} dV +...

The assumption states that all states (or I shall say micro-states) are equally probable. This is the foundation where we construct our theories on entropy, different kind of distributions, etc. Is there any explanation for this assumption? Or why did the scientists that time take this...

I'm undergrad physics student and I have read some statistical physics like equilibrium statistical physics, Langevin model and Fokker-Planck equation. I have developed interest in application of statistical physics in biology like protein folding. So what are the other research topics that lie...

hello everyone. i need help understanding this statement: d(lnΩ)/dE = 1/kbT so Ω are the posible microstates for energy E, and the derivative of Ω w.r.t E is 1/kbT. why? what i understand so far is: looking at the division of energy of two "connected" systems the energy will divide itself in a...

I'm reading Statistical Mechanics 3rd Edition by Pathria and I found his discussion some very confusing, it's like he discussed a lot of things but I still end up asking, "so what now?" I've looked into Kardar's book but found it too terse. Can anybody recommend some books that fits my situation...

Young's Modulus is usually defined as the intrinsic property of a material indicating it's stiffness, or it's ability to resist deformation. Though, it is measured in Pa, meaning it should have some statistical description. Spring constant, for example, can be define as the stiffness of an item...

Hi everyone. I wasn't sure where to post this thread, so I figured I'll post this under General Physics. Out of interest, I've been perusing online about connections that exist between statistical physics and theoretical computer science. For example, consider the following report by Pietro...

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...

I would like to know if I'm the only one finding Pathria's book not organized and somehow I have an uneasy feeling when reading it. What are other graduate books in statistical mechanics (aside from Kardar's book which is more organized but too concise)? How does Pathria's book compare to others?

How does the equation with partial derivative evolve into the next equation which also involves ln? How do we get the logarithmic part? E(0) = const = E1 +E2 where E1 and E2 are the energies of two separate systems in equilibrium and E(0) is the energy of the conjugate system where the two...

I was given a code that generates the statistical or systematic uncertainty of different sub-backgrounds to the total background... Let's say that the total is N and each sub-background has N_i, \delta N_i number of events and relative uncertainty (=err/Nevt) respectively. What the code does is...

Hi, Although I'll be taking a course on statistical mechanics next term, I'm looking to work through the details of statistical mechanics on my own in the summer. Which textbook would one recommended. I have heard that Schrdoder's and Kerson Huang's books are good. Any suggestions? And how do...

I came across this article, called "Ten Simple Rules for Effective Statistical Practice", and thought it was monumental in its importance for understanding statistics and using it practically, particularly in science. I hope you enjoy it!

Homework Statement A system is subject to Hamiltonian ##\hat{H}=-\gamma B_z \hat{S}_z##. Write down the density matrix.[/B]Homework Equations For canonical ensemble ##\hat{\rho}=\frac{1}{Tr(e^{-\beta \hat{H}})}e^{-\beta \hat{H}}## In general ##\rho=\sum_m |\psi_m\rangle \langle \psi_m|## The...

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...

Hi all, I consider myself a physics self-studier (although I've taken the introductory physics series and more in college), and I'm looking for an introduction to statistical mechanics. My thermal physics class used Schroeder's "Thermal Physics" text, which touches slightly on stat-mech at the...

ok so I am in this class... but my professor is not very helpful. I'm not really caring for the assigned textbook, I want to try a different one. One of the issues is that my professor just threw the textbook away and is doing his own thing, so it is difficult to try and study from the textbook...

Hi everyone. What you see here is er Fourier spectra. If i want to conclude that there is a statistical significance difference between the peak value around 30 hz, and all the other smaller peaks. Should i do as following. Estimate the mean value as 2. Estimate the mean peak value to around...

Is Quantum Statistical Mechanics being the application of Quantum Mechanics on the separate particles of bulk matter or the application of QM on whole agregate matter?

Hi, I was studying about the statistical ensemble theory and facing some problem to understand these concepts , I have understood that the ensemble is a collection of systems which are macroscopically identical but microscopically different . In some books they are called as systems with...

Hi! The following image is taken from my note in Stat Mech. Please excuse my ugly handwriting... I copied this from my professor's note on a whiteboard, and I'm not so sure if it is correct. The equations for Z1 (partition function before mixing) and Z2 (partition function after mixing) seems...

Anyone know where i can get statistical physics by F Mandl? or can recommend any other textbook for a course in statistical mechanics.

Background: I'm just a guy who took some (very old fashioned) undergrad GR course some years ago. I'm only know about the basic stuff and nothing of the more advanced stuff. Question: Is there an statistical mechanics for GR that resembles the one in classical mechanics?, I mean with...

Homework Statement "A model system consists of N identical ”boxes” (e.g. quantum wells, atoms), each box with only two quantum levels, energies E0 = 0 and E1 = ε What is the number of microstates corresponding to the macrostate with total energy Mε?" The Attempt at a Solution I've done...

I have to take a graduate level statistical mech course and a solid state physics course next sem (starting in feb).As I will be dealing with these topics for the first time, I'd like to like to prepare myself for them by learning/revising the math involved in them. What are the mathematical...

Homework Statement The 3 state Potts model is defined by $$-\beta \mathcal H = J \sum_{r,r'} (3 \delta_{\sigma(r), \sigma(r')} - 1) + h\sum_r \delta_{\sigma(r),1},$$ with J > 0 to encourage neighbouring Potts spins to have same value and h orienting field. The spin like variables can take...

Homework Statement Consider a zipper of N links, each of which can either be open or closed with associated energy 0 if closed and ##\epsilon## if open. a) Suppose the N links are independent, compute the partition function of the system and the average number of open links b)Now assume that...

Hello! I'm a student in my 3rd year in physics, and due to low demand for physicits in my country. I'm planning to switch for something else. Right now, I have the opportunity to join a bachelor in Statistical Modelling and Computer Science. I love both majors, and I like how the second one...

Hi friends, I have to do a semester project (analytic, computational, or both) for my second course in Statistical Physics - a graduate level course with great emphasis on phase transitions. It will be graded just 15% of the final grade (so, it is not necessary to elaborate exhaustively) and it...

Suppose that you have N = \left(\frac{\partial U}{\partial \mu}\right)_{S,V} < 0, supposedly the number of particles, even though the actual number of particles is greater than zero. This means that you can have, in a system subjected to a grand canonical ensemble, less than 0 particle for...

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...

I was looking at a research paper the other day. In the paper they described some of the results from an experiment. They looked at two of the variables recorded in the experiment, mass and velocity. They looked at mass independently. First, they took the median of the mass. They then had two...

Hi, I need assistance in performing statistical checks in MCNP5 i.e print table 160. I am not sure where the PRINT card should be placed and the format of it. I am using F4mesh tallies