Física Estadística

*What is the coefficient of the differential of work in the case of onedimensional gas atoms in a harmonic trap?    Solution: We remember that the Hamiltonian for this problem is      Then, we obtain the partition function, and the logarithm of it  To get the coefficient required (which is a thermodynamic variable and an observable) we use the expression mentioned on page 43 from course's notes. This is   *Use the formula (87) to calculate the fluctuations of this coefficient. Does the result make sense? Solution: The formula (87) is Using the equipartion theorem we have that* Replacing the results we have Finally  Note: I use this page to get the equations on images, using latex language: https://www.codecogs.com/latex/eqneditor.php?lang=es-es

Lecture notes

Good morning everybody. If you have still questions or doubts how to solve Tarea 06. Please post them, here. I will give feed back.

Oh, and I would like to remind you to the homework "Tarea 06" which is due for this Friday. If you have any questions, doubts, etc. please post to this blog.

Dear all, from the questions related to the fluctuations of the coefficients of the work differential, we still don't have any good solution for the last question. In the case of the atoms in a onedimensional harmonic trap, everything can be calculated without problems.

the instruction for  T05.3(b)is: Write a computational program, which allows us to generate an arbitraty number of spins configurations for a certain pre-defined temperature. first thing i did was defining the variables needed fot the ising model: then, according to the previous results, calculate the probability of a +1 and -1 spin: For the values that i choose for temperature, i got the following results for the probabilities: this indicates that in the random generation of spins we should get a little bit more +1 spins than -1 spins. To generate spins according to their probability, i generated a chain of random numbers between 0 and 1, and we sum this to the probability of getting a spin +1. If we have a high probability of a +1 spin (for example 0.9) almost all the sums will be greater than 1, and also the other way around, of we have a low probability almost none of the sums will be greater than 1. So If the result of the sum between probability and random d...

I did this in the case of the ideal gas and the real gas.   Note: I couldn't upload images in the post comments, that's why I did it in this post.

I couldn't comment, but this is what I found for the fluctuation questions, I don't know if it's correct. For the real gas case I couldn't find the fluctuation.

This is the program of Mitzi. In principle it does exactly what was asked in the assignment. However, the sample used was very small, Q=10. To obtain statistically significant results, one should take Q as large as possible, may by 10^5 or 10^6. For a computer this should be doable within a few minutes. The values for J (J=10) and mu  (mu=0.5) are chosen just in the wrong order. the interaction J should be much smaller than the external magnetic field mu.