Statistical mechanics Definition and 398 Threads

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 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...

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...

Hello, I am trying to work out a mean field theory for an antiferromagnetic Ising model on a square lattice. The Hamiltonian is: ## H = + J \sum_{<i,j>} s_{i} s_{j} - B \sum_{i} s_{i} ## ## J > 0 ## I'm running into issues trying to use ## <s_{i}> = m ## together with the self-consistency...

Homework Statement We have a quantum rotor in two dimensions with a Hamiltonian given by \hat{H}=-\dfrac{\hbar^2}{2I}\dfrac{d^2}{d\theta^2} . Write an expression for the density matrix \rho_ {\theta' \theta}=\langle \theta' | \hat{\rho} | \theta \rangle Homework Equations...

A Monatomic gas passes from state 1 (pressure p1, volume V1) to state 2 (p2, V2). Derive an expression for the change in entropy of a monatomic ideal gas. The required final equation is: ΔS = Cv ln(T2/T1) + nRln(V2/V1) In my attempt, I am retrieving ΔS = Cv ln(T2/T1) + Rln(V2/V1) i.e.; the...

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...

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...

Homework Statement Hello, I tried to solve a problem on my own and then I looked up a solution on the web, and I realize that it seems that I goofed. The problem statement can be found at http://www.hep.fsu.edu/~reina/courses/2012-2013/phy5524/homework/solutions/hw5_sol.pdf (Problem 1, part...

Homework Statement I am trying to solve a problem but I am confused on what's going on with an approximation. I have to find the pressure in function of V, T and N of an ideal gas using the partition function, then obtain the chemical potential in function of T, p and N and I must graph it in...

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 ?

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 ##Z## is homogeneous function with property ##Z(\alpha T,\alpha^{-\frac{3}{\nu}}V,N)## and you calculate Z(T,V,N). Could you calculate directly ##Z(\alpha T,\alpha^{-\frac{3}{\nu}}V,N)##. Homework Equations ##Z(T,V,N)=\frac{1}{h^{3N}N!}(2\pi m k...

I've been reading, in my own time, a first course in thermodynamics and they present a quantum treatment of statistical mechanics (discrete energy levels), but on the article for the partition function on wikipedia, I find out that there is a classical treatment of statistical mechanics as well...

That's the only equation I know on the topic so far. I'm an undergrad physics major and one of my courses this term is statistical mechanics which I am finding to be overwhelmingly difficult to understand. Apparently the course is considered "graduate level," although they still require us to...

Homework Statement A system of N particles has three possible energy levels namely; 0, E and 4E. How many particles does one expect in the second state at temperature T? Homework Equations It's a sample problem for our finals. Our Text book is Statistical Mechanics by Roger Bowley and...

Homework Statement A system of N distinguishable particles is arranged such that each particle can exist in one of the two states: one has energy \epsilon_{1}, the other has energy \epsilon_{2}. The populations of these states are n_{1} and n_{2} respectively, (N = n_{1}+n_{2}). The system is...

We don't have rigorous approach to statistical mechanics but have an intuitive one.We follow Concepts of Modern Physics by Sir Arthur Beiser. It is given that n(ε)=g(ε)f(ε) Here ε is the energy state. where according to my understanding n(ε)=number of particles which are present in an...

I am planing to study thermal physics on my own as I got an incompetent faculty who doesn't know anything about this subject. I want to have a detailed understanding about the topic. So can somebody suggest me which book I should follow from the following list. 1. Schroeder, Thermal...

I'm taking stat mech right now (Kittel book) and...I might hate it. I love e&m, quantum, classical, relativity, but I like almost none of what we're doing in this class. It's not the type of physics I'm interested in and it's abstract in a way I don't like (I normally like abstraction). I know...

Prove that the following two statements of the second law are equivalent (each one can be derived from the other): (a) “It is impossible for heat to flow spontaneously from a colder to a warmer body without causing other changes” (b) “It is impossible to convert all the heat taken from a...

I'm taking Stat Mech at the graduate level and I find the course incredibly frustrating in that it just feels like a whole lot of mathematical formalism without any examples. I've looked in Paritha, Huang, and Salinas and all these books seem the same in that they just looks like a bunch of...

An Introduction To Thermodynamics And Statistical Mechanics by Stowe is the course textbook for my Statistical Physics course I am having trouble with the book as it does NOT provide good examples and explanations nor does it have solutions just answers. I was wondering if there is Schaums or...

In a aislate system, the probability on a microcanonical state \Gamma is p(\Gamma ) = 1/K , if E<H<E + ΔE, and 0 on otherwise with K = \int_{\Gamma : E<H<E+ΔE} d \Gamma a) Show that ΔE →0, then p(\Gamma) = \frac{\delta (E-H)}{\int_{\Gamma : H=E} \delta(E-H)} b) Show that if...

Homework Statement Consider a system consists of two subsystem A and A' in which A contains 3 spins and A' contains 2 spins. Suppose that, when the systems A and A' are initially separated from each other, measurements show the total magnetic moment of A to be - 3{\mu _0} and the total...

I'm looking for a book on statistical physics. One's I've used already are Huangs Intro one and Sachs/Sens/Sexton. They're both great and the problems are great but neither provide answers nor are there any solutions to be found online so I have no idea if I understand the material. Could...

Homework Statement \frac{dq}{dT}=\sum_{i} g_i \frac{dq}{dT} e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2}\sum_{i} g_i ε_i e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2} \bar{ε} q Homework Equations q=\sum_{i} e^{-\frac{ε_i}{kT}} or for degenerate states, q=\sum_{I} g_i e^{-\frac{ε_I}{kT}} The Attempt at a...

Homework Statement In a large system of distinguishable harmonic oscillators, how high does the temperature have to be for the probable number of particles occupying the ground state to be less than 1? Homework Equations N(E_{n})=NAe^{\frac{-En}{K_{B}T}} E_{0}=0 (the textbook...

For the people who are in either of these fields, which math did you encounter most frequently in the field? Abstract Algebra, Analysis, Probability, Statistics, Calculus, or other? I have taken introductory courses for both topics at university and both seem to involve a wide range of math...

Hello, i need solve de following integral \int ^{\infty}_0 \frac{x^3}{e^x+1} dx i tried with the fermi function but the factor e^x is different to e^{x-\eta}, and with the gamma function but the factor e^x+1 is different to e^x-1. Help please

I am specifically referring to textbook "Statistical Mechanics" by Kerson Huang. It is not a general physics question, I am just trying to understand what is written in this specific book. So you can only really help if are familiar with it and have it at hand. I'm having trouble following...

Homework Statement I am supposed use stat mech to find the particle density in Earth's atmosphere given only the particle mass, and temperature, and the planet's mass I guess. And I don't really know where to begin. Obviously I need to use the grand canonical ensemble but I don't know where to...

Homework Statement What is the density of states g(E) for a quantum system having the energy levels: En=hv(n+1/2)1/2 ,where n is a positive integer? Homework Equations g(E) = \frac{d\zeta}{dE} \zeta= area under curve of constant energy\area per state The Attempt at a Solution...

Hello, I'm a first year graduate student, and one of the required texts for my class is the book alluded to in the title. However, it seems to me that this book is written in the language of a mathematician, and is a bit inaccessible to me. Particularly, I'm having trouble following the...

This topic is about history of physics so I decided to post it in general physics section but it would be nice to have a history of physics(or maybe science)section. Anyway,during my statistical mechanics course,I realized QM is being used from the beginning,in contrast to other parts of...

[hi] can you help me to solve these problems from statistical mechanics by pathria?? these problems are 7,8,11,13 and 14 in page 27 thank you

Author: Mark Tuckerman Title: Statistical Mechanics: Theory and Molecular Simulation Amazon Link: https://www.amazon.com/dp/0198525265/?tag=pfamazon01-20

Author: Donald McQuarrie Title: Statistical Mechanics Amazon Link: https://www.amazon.com/dp/1891389157/?tag=pfamazon01-20

Homework Statement Imagine a system with N distinguishable particles. Each particle may be in two states of energy: -ε and +ε. Find the the partition function of the system Homework Equations The Attempt at a Solution I know that I have to find the partition function for a...

I have gone through two volumes of Cohen (Quantum Mechanics). Now I need a book on Quantum Statistical Mechanics. The book should use axiomatic formulation using density matrix. Please give me a suggestion. ( I'm also introduced with 2nd quantization slightly) Thanks for any help in advance.

Homework Statement An isolated system has N=3 distinguishable particles A, B, C with single particle states equally spaced at intervalsof E and a total energy U=3E. ie the macrostate is defined by N=3, U=3E. The system has single particle levels 0, E, 2E, 3E. Homework Equations...

can someone please explain "Postulates of Classical Statistical Mechanics" , "priori probability" , "equilibrium" ..i m a post graduatation student .and in physics these chapters are seem very difficult i need some step by step explanation ..

Homework Statement A quasi-3 level solid-state laser gain medium consists of a ground state manifold containing two energy levels within which a single electron can be promoted, with the second energy 10meV above that of the lowest level. A. Where the gain medium is not optically pumped...

I was wondering if it's common in undergraduate studies for statistical mechanics to be covered in the last 3-4 weeks of a thermodynamics course? I feel like the same is done for infinite series in a 2nd semester of calculus. Needless to say, both topics deserve much more time to fully do them...

Homework Statement Part a: A monoatomic ideal gas is confined to move in two dimensions. What is Cv for this gas? Part b: Consider a system composed of N independent harmonic oscillators in two dimensions. What is Cv for the system?Homework Equations Cv = ∂U/∂T U = (number of degrees of...

I'm looking for a first-year graduate level stat mech textbook. What are the best ones out there?

My advanced statistical mechanics prof told me that it wouldn't make any physical sense to allow N (the number of particles in a system) to be negative. But, somehow, I think that this possibility should be theoretically left open; perhaps there are some systems whose statistical behavior would...

Hi. I'm reading my third year of a Swedish engineering degree and we are about to read Statistical Mechanics. The scope of this course is Thermodynamics (although we have already had a small course in it), Statistical Mechanics and some Quantum statistics. The course book is "Concepts in...

Hello,I'm studing the fundamental principles of statistical mechanics and I don't understand the "principle of equal a priory probabities" for this reason: the principle states that all states in the representative emsemble have the same probability which means that the density \rho(p,q) should...

Homework Statement There are two problems: The first problem is to calculate the slope of a phase-equilibrium line of a substance given its properties (Helium, Water, etc.) as the temperature approaches a certain value (in this case, T approaches zero). The second problem is the effusion of...