Statistical mechanics Definition and 355 Threads

Can anyone refer to some good book on Non-Equilibrium Statistical Mechanics? The book should contain the basics, and can go up to any advanced level. Any level of math is acceptable.

Homework Statement A state of a system of many noninteracting particles can be specified by listing which particle is in which of the accessible single particle states. In each microscopic state we can identify the number of particles in a given single particle state ##k##. This number is...

This is from *Statistical Physics An Introductory Course* by *Daniel J.Amit* The text is calculating the energy of internal motions of a diatomic molecule. The internal energies of a diatomic molecule, i.e. the vibrational energy and the rotational energy is given by...

The third law of quantum mechanics states that a system at absolute zero temperature has zero entropy. Entropy can be conceived as an expression of the number of possible microstates that can produce an identical macrostate. At zero entropy, there should be exactly *one* microstate configuration...

Homework Statement Find the magnetic moment of a crystal when placed (i) in a weak field at high temperature (ii) in a strong field at low temperature Homework Equations This is the last part of a question which I feel I have solved correctly up until this point. The mean magnetic moment I...

I'm following a derivation in my lecture notes of total average particle number in an ideal classical gas (statistical physics approach). I follow it to the line (though the specific terms don't matter): \left<N\right> = e^{\mu/\tau} \frac{\pi}{2} \int_0^\infty \left(n \,dn \,e^{- \frac{\hbar^2...

Homework Statement System of two energy levels, E_0 and E_1 is populated by N particles, at temperature T. The particles populate the levels according to the classical (Maxwell-Boltzmann) distribution law. (i) Write an expression for the average energy per particle. Homework EquationsThe...

Hello, first of sorry for asking what maybe a stupid question. I am teaching myself physics by watching lessons about QM, Classical Mechanics, EMT etc. I was watching Susskind's lectures about statistical mechanics lately and he derived equation of energy E= 3/2 x k x T. 3 in 3/2 came from...

Does anyone have any good books, or other references, that they would recommend for studying for the thermodynamics & statistical mechanics portion of graduate qualifying exams? I didn't have any undergrad Stat Mech and my grad prof/class was really not good, to the point that I didn't really...

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...

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...

Hey all, I'm currently studying for my thermo final and it's really kicking my butt. My average has been a C and if I do EXTREMELY well on my final I'll be REALLY pushing for a B. I'm not sure how thermo is taught in other universities, but I'm learning it through statistical mechanics with...

The colloquial statistical mechanics explanation of entropy as if it is caused by probability is dissatisfying to me, in part because it allows highly organized (i.e. with a real potential for work) arrangements to appear as 'random fluctuations', though with very low probability. But as far as...

I am looking for something to read about the history of solution theories. Is there a good article or book that you may recommend?

I wasn't sure where to post this, I hope this was the right section. I've been struggling quite a bit with implementing an autocorrelation code into my current project. The autocorrelation as it is now, is increasing exponentially from 1 at the start of my MC run, and hitting 2 halfway through...

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 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...

Homework Statement I'm given that the energy of a particle in a rectangular box is the following: E =\frac{\hbar \pi^2}{2m}(\frac{n_x^2}{L_x^2}+\frac{n_y^2}{L_y^2}+\frac{n_z^2}{L_z^2}) I'm to show that if the length of the box is increased adiabatically and quasistatically from L_x to 8L_x...

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...

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...

Hi. I've been reading "Statistical Mechanics Algorithms and Computations". And I came to a problem while processing Algorithm 1.26 (I attach a link at the end). I don't get why the weights are the way they are, specially I can't understand the sequence {1/2l,1/l,...,1/l,1/2l}. Does anyone...

In a degenerate n type semiconductor, when the doping concentration has a gradient(say -ve gradient), then how fermi energy level and intrinsic Fermi energy levels will depend upon the concentration gradient? ~If anyone knows anything about it, kindly help.

Homework Statement A system has three non-degenerate energy levels with energies 0, ε, and 2ε. a) Calculate the entropy of the system if the three levels are populated by two distinguishable particles such that the total energy is U=2ε. b) Calculate the entropy of the system if the three...

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...

From statistical mechanics in zeemansky's book . He states that it's easy to see that for a closed system the no. Of degenerate states ##g_i## for energy level ##E_i## is greater than the number of particles ##N_i##occupying that energy state. I can't find a mathematical proof for it. Can I...

I've just started with statistical mechanics and arrived at the part where they relate entropy to the number of microstates for a given system. The derivation starts of by adding an amount of heat ##\delta Q## to a system and observing the resulting change in internal energy : $$\delta U =...

In my rough understanding Molecular Dynamics using Classical Newtonian mechanics is a 6N dimensional non linear system. 6N dimension because you have 3 position vectors and 3 momentum vectors for each N particles. Nonlinearity because of the terms in force fields. In principle this system can...

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...

Hello, I'm trying to understand how to calculate de probability of finding a system in a specific eigenstate using the density operator. In the book of Balian, Haar, Gregg I've found a good definition of it being the expectation value of the projector Pr in the orientation of the eingenstate...

Im trying to learn transport processes and the Boltzmann transport equation. What books do you guys recommend for beginners? Thanks!

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?

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...

I'm nearly at the end of this derivation but totally stuck so I'd appreciate a nudge in the right direction Consider a set of N identical but distinguishable particles in a system of energy E. These particles are to be placed in energy levels ##E_i## for ##i = 1, 2 .. r##. Assume that we have...

Say I have ##n_{a}## bosons in some state ##a##, then the transition rate from some state ##b## to state ##a##, ##W^{boson}_{b\rightarrow a}##, is enhanced by a factor of ##n_{a}+1## compared to the corresponding transition probability for distinguishable particles, ##W_{b\rightarrow a}##, i.e...

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...

Hello! There are so many Thermodynamics and Statistical Mechanics books that people suggest, that I don't know which one to use in my upcoming undergraduate course. So, which one is your favorite? Thanks in advance!

In statistical physics the calculation to obtain the density of states function seems to involve an integral over an eighth of a sphere in k-space. But why do we bother moving from n-space to k-space, if there's a linear relation between n and k i.e. n = (L/π)k ? Why don't we just integrate over...

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...

Hi all, It seems I haven't completely grasped the use of Partial Derivatives in general; I have seen many discussions here dealing broadly with the same topic, but can't find the answer to my doubt. So, any help would be most welcome: In Pathria's book (3rd ed.), equation (1.3.11) says: P =...

Trying to accomplish a monte carlo simulation on the condensed state of 4He, yet I am in my sophomore year and know only a bit of quantum statistical physics. Is there any documentations recommended for beginners to the algorithm applied to 4He? I've found some but they are not friendly to...

Homework Statement Experimental data for the heat capacity of N2 as a function of temperature are provided. Estimate the frequency of vibration of the N2 molecule. Homework Equations Energy of harmonic oscillator = (n+1/2)ħω C=7/2kB Average molecular energy = C*T But this is an expression...

I'm currently reading through a set of notes on statistical mechanics, and when it comes to deriving the Fermi-Dirac and Bose-Einstein distributions it uses the terminology single-particle state. By this, is it meant that if the particles can be assumed independent, then each particle can be...

A one-dimensional polymer molecule (rubber) is chain of N links of the same length a, the links can go either forward or backward but always stay parallel to the x axis. If one denotes the coordinates of the joints are ${x_0, x_1, . . . , x_N}$ , then $|x_n − x_{n+1}| = a$. The energy of the...

Homework Statement The Hamiltonian for a single diatomic molecule of identical atoms is given as $$H=\dfrac{\vec{p_1}\cdot\vec{p_1}}{2m}+\dfrac{\vec{p_2}\cdot\vec{p_2}}{2m}+\dfrac{K}{2}(\vec{r_1}-\vec{r_2})\cdot(\vec{r_1}-\vec{r_2})$$. Find the grand canonical partition function for a gas of...

Homework Statement We are given a paramagnetic system of N distinguishable particles with 1/2 spin where we use N variables s_k each binary with possible values of ±1 where the total energy of the system is known as: \epsilon(s) = -\mu H \sum_{k=1}^{N} s_k where \mu is the magnetic moment...

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...

I'm practicing for the Physics GRE, and came across a question that has me stumped. "In elementary nuclear physics, we learn about the Fermi gas model of the nucleus. The Fermi energy for normal nuclear density (ρ0) is 38.4 MeV. Suppose that the nucleus is compressed, for example in a heavy ion...

Hi, If I consider for instance N non interacting particles in a box, I can compute the energy spectrum quantum mechanically, and thus the number of (quantum) microstates corresponding to a total energy between $E_0$ and $E_0 + \delta E$. In the limit of large quantum numbers, the result is well...