### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Statistical Mechanics PHY 831

MSU

GPA 3.67

### View Full Document

## 63

## 0

## Popular in Course

## Popular in Physics 2

This 3 page Class Notes was uploaded by Quinn Larkin on Saturday September 19, 2015. The Class Notes belongs to PHY 831 at Michigan State University taught by Scott Pratt in Fall. Since its upload, it has received 63 views. For similar materials see /class/207609/phy-831-michigan-state-university in Physics 2 at Michigan State University.

## Reviews for Statistical Mechanics

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/19/15

PRACTICE When you are not practicing remember someone somewhere is practicing and when you meet him he will win 7 E Macauley THINGS TO MEMORIZE S Zpi 1HPi i TdSdEPdVEodN TSEPVEMN ddpddr ddhddr dNee Eo sass 1 1 fr 1 bdy tt lt2Whgtd f QWW new fpbosonsfermions W d5 d5 0 E T7 C E T7 V dT MM P dT PN 3H 3H 7 T 7 T i E i ltq aqgt 7 P 6pgt 7 ltqpgt ltpqgt Don7t memorize factors but know dependencies of more complicated expressions For instance you wouldnt be expected to memorize all the 212 factors in PpT co n71 r 32 p 27 1 3 7 T WT 1 An 7 E B d 6 i 39 i l W 1 was 6 p mag2 dN 7 1 d6 7 32 2i1d6 6 E 261E A2 2 gdeTEe 6 i Eaph a scattering length but you would be expected to know what happens to the second virial coef cient if a repulsive or attractive interaction is added or in what way the pressure would change if a resonance was included 1 Consider two neutrons spin 12 particles They occupy a two level system where the single particle energies are 6 and 6 which is thermalized at a temperature T a What is the average energy of the system as a function of T b What is the chance that the ground state is occupied as a function of T c What is the entropy S of the system as a function of T D 00 4 CT CT Using the last Maxwell relation from Beginning with the expression TdS dE PdV 7 udN derive the Maxwell relations i dT Q T2 d u E dE MT39 and 7 2 dogN g p dp T dT p the previous problem show that if P and SN are 2 LP T T p pZOV39 functions of T and p that E dp LP 5 SN T Consider a system with an order parameter denoted by z along with a particle number N energy E and volume V The system will maximize entropy if E dz EVN Show that if the system has a xed volume and is connected to a bath at temperature TB and chemical potential MB that can can exchange both particles and energy that the total entropy of both the system and the bath will be maximized if the pressure is maximized ie dP 7 0 dz TTB gtMMB V You may use the identity PV TS 7 E MN Consider a particle moving in one dimension according to the Hamiltionian H xp2m2 Bz4 Using the equipartion generalized equi partition or virial theorems nd lt964gt Consider a thermalized two dimensional gas of charged non interacting massless spin zero bosons whose energies are given by e p0 Find the density number per area required for Bose condensation Give answer in terms of c T and h H 00 H O H H Consider the one dimensional case for the massless particles from the previous problem Can you solve for the critical density number per length in this case For massless particles what is the minimum number of dimensions for Bose condensation and how does this compare with the massive case Consider a two dimensional gas of non interacting non relativistic electrons of mass m a What is the density of single particle states DE at the Fermi surface in terms of 6f and m b What is the energy per area for T 0 in terms of m and 6f c In terms of Def and derivatives of Def nd the lowest order expanding in T non zero correction to the energy density at low temperature NT N 2 17qu0 a V 39 Solve for the critical point To and pc in terms of 110 and a Consider the equation of state PN7T7V Consider a two dimensional lattice of three dimensional oscillators where the speed of sound for both longitudinal and transverse modes is 05 a What is the Debye frequency Give wD in terms of cs and NA the number of lattice sites per area b What is the energy of a system of N sites as a function of T if T gtgt hwp Consider the mean eld approximation to the lsing model where the Hamiltonian is H Z ipBai 7 qJltUgtUi where 0 takes on values of 1 or 1 a Beginning with the de nition of ltUgt Ear Uiei HW ltUgt derive a transcendental expression for ltUgt as a function of MB and 1 b What is the critical temperature To c Find the susceptibility X dltUgtdB for T gtgt To Give answer to lowest non zero order in 1T

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.