Physics 75: Thermodynamics
Announcements
11/4/00 New homework added.
10/27/00 New homework added.
10/15/00 Added a few more papers to the list.
10/10/00 Added a few more papers to the list.
10/6/00 We've decided that the exam next Friday will be in-class, closed book.
I'll provide a formulas sheet.
10/5/00 Some more papers added to the list.
10/4/00 To reiterate what we discussed at the beginning of class:
I'd like you to decide what paper you'll discuss in your Wednesday talk by
Monday in time for me to copy the paper and distribute it to the class on Monday
(and earlier is even better!).
Ideally, the presenter will work the details of the paper,
delve into the references if necessary, and
make explicit the ties to stat mech if they're not obvious. The rest of the
class
will read the paper with the aims of getting a basic understanding in order to
be able to add discussion and ask questions. Hopefully our collective
insights will add to our collective understanding.
There will be difficult points
in all of these papers, and I don't expect that you'll be able to figure them
out any of them entirely by yourself (although you should try as best you can).
So, you should EXPECT to come to me to help elucidate the difficult points, which
means you have to have looked at and thought about the paper
in advance (and given me time to study it also). The 1-2 page outline is meant
to force you to think in some detail in advance, and I want it by 5 on Tuesday to
make sure that I've had a chance to read it and that you've had a chance to
reflect on the material before you present it. Practically, , though,
this deadline is too late to allow you to spend much time discussing
difficult points, so I encourage you to get this out of the way much EARLIER.
You have (at least) two weeks between your talks; I suggest that you choose
your next paper immediately after your talk read it (at least skim it)
right away, and let me know what the paper is. In the next several days after that,
write up your 1-2 page outline and collect together your questions on difficult
points to discuss with me. We can resolve those, and once the physics is clear to you
you can, at your leisure, think about which ideas to present to the class
and how best to present them in the time available. As an assignment to do
on Tuesday, reading and digesting a paper, writing two pages on it, and planning
a presentation, is alot of work (even for me), and it probably won't be
especially beneficial. However, it's not meant to be a one-day assignment;
spread over two weeks, it's not bad, and in addition you have the opportunity
to get help.
It might be helpful for me to explicitly state the goals of the exercise:
To allow the class to explore a wider variety of topics related
to stat mech and thermodynamics that is convenient in the usual course format.
Stat mech is more than just the mathematics, and as a discipline it's not very linear.
Working statistical mechanicians often have a broad view of the applicability of
their field to a range of problems, within and beyond traditional physics.
This emphasis on the interdisciplinary aspect differentiates stat mech
from many of the traditional subfields (within physics, much of dynamical
systems theory also falls within the pale of stat mech). Workers spend
considerable time looking looking at simple models, but also finding
physical motivations/applications for their models.
To permit the reader to explore in greater depth some subject of interest
related to stat mech and thermodynamics (including subjects relevant to your thesis).
If you find a subject that interests you, you can do a series of related talks
on the same subject. In the course of detailed study of even two or three papers
(or book chapters, if you prefer) you can often penetrate pretty deeply into even a
difficult subject. I'm happy to help you choose your readings to optimize your
study or to help you on physics/technical material that goes beyond what we've
covered in class.
To give the reader practice in making scientific presentations to colleagues,
and to allow the rest of the class an explicit opportunity
to reflect on what works and doesn't work in such presentations.
In the beginning I suggested a 10 minute time limit, but I've let you run
as long as you chose. This was in part to let you see how it feels (and reduce
the pressure of giving a talk a bit), and in part because a I realized 10 minutes
was a miscalculation on my part: a typical conference talk is 10(-15) minutes, with
several minutes at the end for questions. The audience usually saves its questions
for the end. In our talks, the audience has asked more questions during
the talk and fewer at the end. Since our setting is more informal than a
conference talk and our goals more pedagogical, I'm happy to encourage the
interactive discussion. Still, some structure is necessary, if only to ensure
equitable distribution of time. So, let's say we cap the talks at a total of
20 minutes. You should plan on 10-15 minutes of
talking (which by now you see isn't all that much), with 5 minutes factored in for
questions throughout the talk. I'll time the talk and cut off at 20 minutes.
If you're not used to giving a timed talk, practice in advance. I'll reserve a total
of 10 minutes for myself, to make administrative remarks or closing comments for
each talk. If you have the time, I encourage you to experiment a bit, with style
or format (e.g. if you haven't given a talk with overheads, give it a try).
This experiment might work well or poorly, depending on a variety of
factors, and I'm still not certain that this is the best expenditure of time
in an undergraduate class. A necessary condition for it to be useful at all is
for us all to make a serious effort to understand the papers. Hopefully these
changes in format will make the task easier, and as always I'll be grateful for your
comments. I have yet to incorporate a formal, mandatory mechanism for explicit
feedback on these talks, relying instead on the emails I've been asking you to send
me evaluating your own and the other talks (which I receive only sporadically).
A few of you have asked me what the rest of the class thinks of your talk, though,
so I may try harder to squeeze more detailed explicit critiques from you. Your
peers are certainly interested in what you think of their effort.
10/2/00 Homework list updated. Exam #1 date changed to Friday, 10/13/00.
Lecture list updated. Presentation schedule updated. Some new papers
added.
Instructor
Professor Will Loinaz
Office: 223 Merrill Science Center
Phone: (413) 542-7968
email: waloinaz@amherst.edu
Office Hours: Thurs 1-3, or any time you can find me (you're always
welcome, but Thurs 1-3 I promise I'll be in and ready to discuss stat mech).
I also have office hours Thurs 10-12 for Physics 16. You're welcome to
come by then, but if there's a student from Physics 16 that needs help
I'll give them priority during that time.
Course Information
Course Description
This course covers introductory thermodynamics and statistical mechanics,
including:
- First, second and third laws of thermodynamics with applications to
various physical systems
- Phase transitions
- Applications to low temperature physics, including superconductors
and liquid helium
- Introductory kinetic theory and statistical mechanics
- Applications of Fermi-Dirac and Bose-Einstein statistics
Schedule
MWF 10-11, Th 11:30-12:30 in Rm. 209 Merrill Science Center
Prerequisites
Physics 35 or the equivalent, or my permission.
Course requirements
- Attendance:
There are only four of you. If you don't show up,
I'll notice. If you know in advance that you must miss class, please do
me the courtesy of informing me, if possible.
- Homework:
I'll assign and grade homework weekly. Kittel has some
nice problems and I'll assign some from there, but I'll draw from
other sources as well. I'll distribute the homeworks and solutions in
class. I'll try to post the assignments and solutions
on the web, as well as any corrections, hints, or elaborations that
might be necessary. However, I don't
guarantee that everything I say in class will make it onto the website in
a timely manner. You are encouraged to discuss homework problems; however,
the final writeup should be your own. In class we've agree to having
homework due on Friday at 5 pm. If you decide you want one, I can schedule
a separate problem session to discuss current and/or old homework
problems.
Hmwk 1: KK, Chap 2, #2,3,4,5 Due 9/15/00
Hmwk 2: KK, Chap 3, #1,3,6,7,9,10,11 Due 9/22/00
Hmwk 3: KK, Chap 4, #1,3,6,7,8,11,14,15,19 Due 9/29/00 (extended to 10/2/00)
Hmwk 4: KK, Chap 5, #3,4,6,7,10,12 Due 10/6/00
Hour Exam #1: In class, Friday, 10/13/00
Hmwk 5: KK, Chap 6, #1,3,4,9,10,11,15
Extra Problem: Write down the (partition function, average energy,
Helmholtz free energy, entropy, and chemical potential) of a gas of
non-interacting particles confined to the surface of a d-dimensional
torus with radius R in each dimension.
Due 10/20/00
Hmwk 6: KK, Chap 7, #1,2,3,5,6,8,12
Due 10/27/00 (extended to 10/30/00)
Hmwk 7: KK, Chap 8, Due 11/3/00 (Extended to 11/6/00)
KK, Chap 8, # 2,5,7 (more than a simple yes-or-no answer, please),9, and the
following extra problem:
Extra -- engine cycles:
The Carnot cycle is the engine cycle best known to physicists, but there
are others commonly considered by engineers. Here are a few that I
worked in my intro engineering thermodynamics class. For each,
please calculate the efficiency of the engine and the work done on the
gas at each stage of the cycle (if any). I'll describe the cycle, but
you should sketch it (qualitatively, just for your own convenience)
in the P-V plane as Kittel does for the Carnot cycle in Fig. 8.6 (c).
In each case, treat the gas in the engine as an ideal gas of with
specific heats C_P and C_V fixed constants. It may be convenient to
express results in terms of gamma = C_P / C_V.
(a) Otto Cycle: This is an idealization of an internal combustion engine.
Start at some point 1 (P_1, V_1) in the PV plane.
(1 -> 2) Adiabatic compression to point 2 (P_2, V_2)
(2 -> 3) Increase the pressure at constant volume to point 3 (P_3, V_3 = V_2)
(3 -> 4) Adiabatic expansion back to the original volume to point 4 (P_4, V_4 = V_1)
(4 -> 1) Decrease pressure at constant volume back to point 1 (P_1, V_1)
For the Otto cycle, express results in terms of the compression ratio, r = V_2 / V_1
(b) Diesel Cycle:
Start at some point 1 (P_1, V_1) in the PV plane.
(1 -> 2) Adiabatic compression to point 2 (P_2, V_2)
(2 -> 3) Isobaric (constant pressure) expansion to point 3 (P_3 = P_2, V_3)
(3 -> 4) Adiabatic expansion back to the original volume to point 4 (P_4, V_4 = V_1)
(4 -> 1) Decrease pressure at constant volume back to point 1 (P_1, V_1)
(c) Joule Cycle:
Start at some point 1 (P_1, V_1) in the PV plane.
(1 -> 2) Adiabatic compression to point 2 (P_2, V_2)
(2 -> 3) Isobaric expansion to point 3 (P_3 = P_2, V_3)
(3 -> 4) Adiabatic expansion back to the original pressure to point 4 (P_4 = P_1, V_4)
(4 -> 1) Isobaric compression back to point 1 (P_1, V_1)
Hmwk 8: KK, Chap 9, #1,2,4,5 Due 11/10/00
Hmwk 9: KK, Chap 10, # 1,4,5,6,8 Due 12/1/00 (extended to 12/4/00)
Hmwk 10: KK, Chap 14, # 1,3,4,5,6 Due 12/11/00
- Exams:
Two hour-exams (tentatively 10/13 and 11/17)
and a two hour final. They'll be closed book, but I'll give you some
sort of formula sheet so it won't be a memory test.
- Journal presentations:
OK, this part is experimental, controversial, and
subject to revision. But, in its current form: Each
week two of you will be scheduled to give a presentation to the
class. We'll agree on some journal article for you to read and dissect.
They'll be articles that are accessible but not trivial (say, from
Physics Today, American Journal of Physics, or Scientific American),
and of some relevance to statistical mechanics/thermodynamics.
On Tuesdays you'll give a ten minute presentation to the class on your
paper, discussing the paper's purpose, key results, any interesting
or controversial intermediate steps, and if necessary, tying it in
to stat mech/thermo. On the day before (Monday), you'll give me a 1-2 page
synopsis of what you'll be talking about (so that I have a preview of
your take on the material and will be prepared to offer some
constructive commentary). It doesn't have to be impeccable prose, just
enough for me to understand what it is you'll be taking about and see
the steps in your logic. I'll be happy to suggest papers on a variety
of subjects, and I'll post interesting candidates on this web page.
But, if you come across particular papers of interest to you (say,
some background reading relevant to your thesis, or pertinent to
work you're doing in another course), that's fine too---just run it past me
first. Alternately, rather than dissect a paper, I have a set of
computer simulations that you could program in, experiment with, and report
on. Some of these are in Mathematica, some in C.
Honestly, I'm not sure how well this will work. It's an
experiment. The purpose is
(1) to help you become comfortable with giving oral presentations,
(2) giving you experience extracting information from journal articles,
and (3) expose the class to the breadth of stat mech/thermodynamics.
While it's bound to take a non-negligible amount of time, I don't want
it to become onerous, especially since the core of the course is
really the problem sets. I want you to get used to extracting information
from papers efficiently, but even when you're good at it it takes some time.
We can adjust the frequency of talks,
the difficulty of the papers assigned, and the amount of direct
assistance from me, as appropriate. I'll rely on you to keep me apprised
of how it's all going and what adjustments need to be made (or if
the whole idea should be scrapped).
Grading
Tentatively,
- Homework: 30%
- Hour exams: 15% each
- Final: 25%
- Presentations: 15%
Textbook
Required:
- Thermal Physics (2nd ed), Kittel & Kroemer
Additional useful references (if the library doesn't have them, I'll try to get them):
- Thermal Physics, Baierlein
- Fundamentals of Statistical and Thermal Physics, Reif
- Introduction to Thermal Physics, Schroeder
- Equilibrium Thermodynamics, Adkins
- Thermodynamics and an Introduction to Thermostatistics, 2nd Edition, Callen
- Statistical Physics, Mandl
- Statistical Mechanics, a Set of Lectures, Feynman
- Feynman Lectures on Physics (vol. 1), Feynman
- A Modern Course on Statistical Physics, L. E. Reichl
- Selected articles from American Journal of Physics
Lecture Schedule
I'll try to post at least an outline of the lecture on the web, if I have
time. This is more to motivate me to write them up that it is likely to
be a useful resource for you... I'll also try to arrange some guest
lectures from people that work in statistical mechanics or related field.
A tentative lecture schedule will soon be available on the courseinfo
website. However, since this is my first time teaching this course
it will be very tentative, subject to change based on our interests and
your background preparation.
Lecture 1: Tues. 9/5/00 Administrative issues; What are Stat Mech
and thermodynamics?
Lecture 2: Wed. 9/6/00 Counting states (associated reading: KK, Ch. 1)
Lecture 3: Fri. 9/8/00 Density of states in the binary phase model;
Sharpness of the DoS, Gaussian distributions; Physical impact of sharp DoS
(associated reading: KK, Chap. 1)
Lecture 4: Sat. 9/9/00 Deriving the gaussian distribution from
the exact multiplicity function; derive Stirling's approximation;
(KK, Chap. 1)
Lecture 5: Mon. 9/11/00 Finish up binary state model (calculate
s^2); Preliminaries of entropy and temperature: fundamental assumption
of thermal physics; ensembles and probability in thermal physics
(KK, end of Chap. 1, start of Chap. 2)
Lecture 6: Wed. 9/13/00 Prelude to thermal equilibrium: how is
energy distributed between subsystems in thermal contact in the special case
of the binary state system? What does this question mean in statistical
mechanics? extend to more general system: extremum of total entropy defines
most probable state; temperature and thermal equilibrium defined;
(KK, Chap. 2)
Lecture 7: Thurs. 9/14/00 Law of increase of entropy, stated and
proven in statistical mechanics sense; start on deriving Boltzmann factor:
systems and reservoirs; (KK, end of Chap. 2, start of Chap. 3)
Lecture 8: Fri. 9/15/00 Derive Boltzmann factor by extremizing
total entropy; partition function defined; U from partition function;
Example: two-state system; definition of reversible process;
(KK, Chap. 3)
Lecture 9: Mon. 9/18/00 Definition of pressure as isentropic energy
change; derive thermodynamic identity; define Helmholtz free energy, show
it's an extremum at equilibrium; (KK, Chap. 3)
Lecture 10: Wed. 9/20/00 Journal talks: Keith (Entropy and Time),
Matt (An Introduction to Global Warming);
Lecture 11: Thurs. 9/21/00 Show that Helmholtz free energy is
a minimum at equilibrium; What does F mean? Obtain F from Z, deriving
some thermodynamic relations along the way; Example: binary state system
in a magnetic field; (KK, Chap. 3)
Lecture 12: Fri. 9/22/00 Ideal Gas (KK, Chap. 3)
Lecture 13: Mon. 9/25/00 Introduction to Photon Gas (KK, Chap. 4)
Lecture 14: Wed. 9/27/00 Journal talks:
Ben (Laser-enhanced NMR spectroscopy),
Chris (In Introduction to Random Walks, drawing on Reif, Chap. 1);
Lecture 15: Thurs. 9/28/00 Photon Gas (KK, Chap. 4)
Lecture 16: Fri. 9/29/00 Phonon gas; preview of Chemical potential;
(end of KK, Chap. 4, beginning of KK, Chap. 5)
Lecture 17: Mon. 10/2/00 Chemical Potential: Formulation and
definition; Example: ideal gas; interpretation as a potential energy;
internal vs. external; Example: barometric pressure; (KK, Chap. 5)
Lecture 18: Wed. 10/4/00 Journal Talks:
Matt (Black Hole Thermodynamics),
Keith (Entropy and Time);
Lecture 19: Thurs. 10/5/00 more chemical potential;
start to derive Gibbs factor; derive a preliminary thermodynamic
identity; (KK, Chap. 5)
Lecture 20: Fri. 10/6/00 a bit more on thermodynamic
identities; derive Gibbs factor;
Gibbs sum and its uses;
Gibbs sum: simple example; (KK, end of Chap. 5)
No Lecture: Mon. 10/9/00 Mid-Term Break
Lecture 21: Wed. 10/11/00 Journal talks:
Ben (An economic analogy to thermodynamics, Am. J. Phys. 67(12) December
1999 pp. 1239-1247),
Chris (Introduction to the Ising Model, based on Chap. 8, sec. 2 of
Thermal Physics, by D. Schroeder)
Lecture 22: Thurs. 10/12/00
lightning review of quantum statistics; Fermi-Dirac distribution,
Bose-Einstein distribution, classical limit; Classical limit of ideal gas;
(KK, beginning of Chap. 6)
Fri. 10/13/00 Hour Exam #1
Lecture 23: Mon. 10/16/00
Classical limit of ideal gas:
collect and rederive the thermodynamic quantities; ideal gases
with internal degrees of freedom: gibbs sum, start deriving thermodynamic
quantities (KK, Chap. 6)
Lecture 24: Wed. 10/18/00 Journal talks: Matt
(Thermodynamic properties of a fermionic anharmonic oscillator),
Keith (What if entropy were dimensionless?)
Lecture 25: Thurs. 10/19/00 finish deriving
thermodynamics functions of ideal gas with internal degrees of freedom;
fun with ideal gases: isothermal and isentropic expansions (KK, Chap 6)
Lecture 26: Fri. 10/20/00 finish ideal gases (isentropic and
sudden expansions); start Fermi gases: calculate Fermi energy
(KK. Chap 7)
Lecture 27: Mon. 10/23/00 more on Fermi gases: ground state
energy, density of states (KK, Chap 7)
Lecture 28: Wed. 10/25/00 Journal talks:
Ben
(Capture of the lamb: Diffusing predators seeking a diffusing prey),
Chris (Introduction to Monte Carlo methods)
Lecture 29: Thurs. 10/26/00 more on Fermi gases:
density of states, chemical potential, specific heat (KK, Chap. 7)
Lecture 30: Fri. 10/27/00 finish Fermi gases (real-world examples);
start Bose gases (KK, Chap. 7)
Lecture 31: Mon. 10/30/00 more on Bose gases (KK, Chap. 7)
Lecture 32: Wed. 11/1/00 Journal talks: Matt (Feynman's
treatment of the 2D Ising model), Keith (Teaching the renormalization group)
Lecture 33: Thurs. 11/2/00 Classical Thermodynamics: heat, work,
carnot efficiency (KK, Chap. 8)
Lecture 34: Fri. 11/3/00 Classical Thermodynamics: heat engines,
refrigerators, Carnot cycle (KK, Chap. 8)
Lecture 35: Mon. 11/6/00 almost to the end of thermodynamics:
assorted comments on reversibility and entropy; sources of irreversibility;
reversible and irreversible work and heat; work at constant temperature
(Helmholtz free energy), effective work at constant pressure, enthalpy
(KK, Chap. 8);
Lecture 36: Wed. 11/8/00 Journal talks: Ben (experimental view of BEC),
Chris (Monte Carlo methods)
Lecture 37: Thurs. 11/9/00
finish classical thermodynamics: enthalpy, Gibbs free energy, chemical work
(KK, Chap. 8), Chemical reactions (KK, Chap. 9)
Lecture 38: Fri. 11/10/00 Finish Chemical reactions (KK, Chap. 9);
some extra comments on Bose gases;
Lecture 39: Mon. 11/13/00 finish extra comments on Bose gases;
start thermodynamics of first-order phase transitions: phenomenology,
typical phase diagrams, start derivation of Clausius-Clapeyron equation;
(KK, Chap 9/10)
Lecture 40: Wed. 11/15/00 Journal talks: Keith (1-D ice) and Matt
(Gibbs Free energy and fuel cells)
Lecture 41: Thurs. 11/16/00 First order phase transitions:
derivation of Clausius-Clapeyron equation; start quick reprise of 1-D ice
(KK, Chap 10)
Lecture 42: Fri. 11/17/00 Hour Exam #2
Lecture 43: Mon. 11/27/00 Models of first-order
phase transitions: finish 1-D ice; start van der Waals models
(KK, Chap 10)
Lecture 44: Wed. 11/29/00 First-order phase transitions:
finish the van der Waals model (KK, Chap 10)
Lecture 45: Thurs. 11/30/00 Phase transitions: bubble
nucleation; Ising model; start mean field theory solution of
Ising model (KK, Chap 10)
Lecture 46: Fri. 12/1/00 Phase transitions: finish
mean field theory solution of Ising model; start Landau theory
of phase transitions (KK, Chap 10)
Lecture 47: Mon. 12/4/00 Phase transitions: Landau
theory for second-order phase transitions; start Landau theory
of first-order phase transitions (KK, Chap 10)
Lecture 48: Wed. 12/6/00 Journal talks: Ben (saturated
absorption spectrospopy), Chris (negative temperatures)
Lecture 49: Thurs. 12/7/00 Course evaluations; finish
Landau theory of first order phase transitions
Lecture 50: Fri. 12/8/00 Kinetic Theory: derivation of
ideal gas law, Maxwell velocity distribution, some discussion of
equipartition theorem
Lecture 51: Mon. 12/11/00 mean free path; some comments
on diffusion; Liouville's theorem
No lecture: Wed. 12/13/00 Reading period
No lecture: Thurs. 12/14/00 Reading period
No lecture: Friday. 12/15/00 Reading period
Final Exam: Sat. 12/16/00, 9:00 am Merrill 209
Website
I'll keep scheduling information on this site primarily. I'm not yet
used to
Courseinfo, but as I get used to it I may post more stuff on there.
Useful Links
I'll post interesting or useful links pertinent to the course
here as they I come across them. If you come across any others, please
let me know. Most of the articles from American Journal of Physics
are appropriate for class presentations. The ones from the Los Alamos archive
are typically professional preprints and are sometimes quite long and/or
heavy going.
Presentation Schedule:
I'll post the schedule below. If you can't talk on your designated day,
please give a a little advanced warning so that we can reschedule.
When you tell me what you'd like to speak on, I'll post it below
(and a link to the paper, if possible).
I'd suggest that the two that aren't speaking at least have a glance at the
papers that the speakers will be presenting; it will make it easier for you
to digest the talk and to take an interest in the presentation.
Those that are presenting, I encourage you to discuss your paper with me,
your classmates, other faculty, anyone else that might be interest.
Again, you can choose your own paper (run it past me first) or I can
suggest one for you. If it turns out that a paper you're interested in
requires material beyond what we've covered in the course so far, I can
give you a preview.
Wednesday, Sept. 20
Matt: Introduction to Global Warming
Keith: Entropy and Time
Wednesday, Sept. 27
Ben: Laser-enhanced NMR
Chris: Introduction to Random Walks
Wednesday, Oct. 4
Matt: Black Hole Thermodynamics
Keith: Entropy and Time
Wednesday, Oct. 11
Ben: An economic analogy to thermodynamics
Chris: An Introduction to the Ising Model
Wednesday, Oct. 18
Keith: What if entropy were dimensionless?
Matt: Thermodynamics properties of a fermionic anharmonic oscillator
Wednesday, Oct. 25
Ben: Capture of the lamb: Diffusing predators seeking a diffusing prey
Chris: Introduction to Monte-Carlo methods
Wednesday, Nov. 1
Matt: Feynman's treatment of the 2D Ising model
Keith: Teaching the renormalization group
Wednesday, Nov. 8
Ben: Experimental view of BEC
Chris: Monte carlo methods (cont'd)
Wednesday, Nov. 15
Matt: Fuel cells
Keith: 1-D ice
Wednesday, Dec. 6
Ben: Saturated-absorption spectroscopy
Chris: Negative temperatures
Other Interesting talks in the Five-College area:
Robert Nozick (Harvard U),
9/7/00, "The Ultimate Theory of the World", CANCELLED
Steven J. Gould, 9/12/00, 4 pm, Johnson Chapel, AC (ticket required)
Jonathan Lear, 9/21/00, 4:30 pm, Stirn Auditorium, AC
"Freud's Death Drive as a Limit of Explanation"
Colin McGinn, 10/12/00, 4:30 pm, Cole Assembly Rm, Converse Hall, AC,
"Can We Explain Consciousness"
Steven Weinberg (UT Austin),
10/20/00, 4:30 pm, Cole Assembly Rm, Converse Hall, AC,
"Can Science Explain Everything"
Interesting and useful papers
Entropy:
Entropy and Time
(American Journal of Physics, Vol. 67, No. 12, pp. 1068-1073)
[covered by Keith]
Thermodynamics
A fresh look at the second law of thermodynamics,
(Physics Today, Vol. 53, No. 4, April 2000, pp. 32-37)
Applications of Thermodynamics
Thermodynamics properties of an anharmonic fermionic oscillator
(American Journal of Physics, Vol. 60, No. 12, pp. 1122-1126)
[covered by Matt]
The magic of helium-3 in two, or nearly two, dimensions,
(Physics Today, Vol. 51, No. 6, June 1998, pp. 30-36)
Negative pressures and cavitation in Liquid Helium,
(Physics Today, Vol. 53, No. 2, February 2000, pp. 29-34)
Quantum calorimetry
(Physics Today, Vol. 52, No. 8, August 1999, pp. 32-37)
"Temperatures Scales below 1 Kelvin", R.J Soulen, Jr. and W.E. Fogle,
1997, vol. 50, no. 8, p. 36.
Probability and Random Walks
Random walks and diffusion
(American Journal of Physics, Vol. 48, No. 1, pp. 49-56)
A theorem for physicists in the theory of random variables, D. Gillespie
(American Journal of Physics, Vol. 51, No. 6, pp. 520-532)
Asymmetry and convergence of the central limit theorem: An approach for
physicists, P. Pury
(American Journal of Physics, Vol. 58, No. 1, pp. 62-66)
Random multiplicative processes: An elementary tutorial, S. Redner
(American Journal of Physics, Vol. 58, No. 3, pp. 267-273)
Random walks: a pedestrian approach to polymers, critical phenomena, and
field theory
(American Journal of Physics, Vol. 59, No. 7, July 1991, pp. 633-645)
The mathematics of Brownian motion and Johnston noise
(American Journal of Physics, Vol. 64, No. 3, pp. 225-240)
Multi-variate Langevin and Fokker-Planck equations
(American Journal of Physics, Vol. 64, No. 10, pp. 1246-1256)
Statistical estimation of pi using random vectors
(American Journal of Physics, Vol. 67, No. 4, pp. 298-303, April 1999)
Monte Carlo estimations of e
(American Journal of Physics, Vol. 66, No. 2, pp. 138-140, February 1998)
Statistical Mechanics
Fermion-boson transmutation and comparison of statistical ensembles
in one dimension (American Journal of Physics, Vol. 64, No. 9, pp. 1168-
1176, September 1996)
Ideal quantum gases in two dimensions
(American Journal of Physics, Vol. 63, No. 4, pp. 369-375, April 1995)
Connection between nonlinear resonance and statistical behavior
(American Journal of Physics, Vol. 50, No. 4, pp. 363-373)
A method for evaluating two-spin correlations of a one-dimensional
Ising model
(American Journal of Physics, Vol. 56, No. 2, pp. 169-171)
"Chaotic Dynamics and the Origin of Statistical Laws", G.M. Zaslavsky,
1999,vol. 52, no. 8. pt. 1, p. 39.
Bose Einstein Condensation
Experimental studies of Bose-Einstein condensation
(Physics Today, Vol. 52, No. 12, December 1999, pp. 30-36)
The theory of Bose-Einstein condensation in dilute gases
(Physics Today, Vol. 52, No. 12, December 1999, pp. 37-42)
Other Applications of Statistical Mechanics
Genetic algorithms: A general search procedure
(American Journal of Physics, Vol. 62, No. 6, June 1994, pp. 549-552)
Introduction to the Ising Model (you can do a treatment using a chapter
from one of the textbooks that covers it: e.g. Schroeder, Baierlein,
Huang (more difficult), Chandler, etc.) [covered by Chris]
Non-Equilibrium Statistical Mechanics
Nonequilibrium patterns in granular mixing and segregation,
(Physics Today, Vol. 53, No. 3, March 2000, pp. 25-30)
Black holes
Black hole thermodynamics in an undergraduate thermodynamics course
(American Journal of Physics, Vol. 48, No. 12, pp. 1066-1070)
[covered by Matt]
Black hole evaporation and Hawking radiation
[I don't have a single good source for this at an
introductory level. There are a few short sources which could be put together
to give a talk, though: Space, Time and Gravity, Chap. 10, by R. Wald;
Simple model for emission of particles by black holes, Am. J. Phys 46(6), June 1978,
p. 678; Comment on "Simple model for the emission of particles by black holes",
Am. J. Phys. 47(6), June 1979, p. 553; Another simple model for energy emission by
black holes, Am. J. Phys 48(9), Sept. 1980, p.725-727; Black Holes, White
Dwarfs, and Neutrons Stars, by Shapiro, et. al., sec. 12.8. All of these are
short, a few pages at most, and none are complicated. But, they're not very
satisfying, either. I'll keep looking for better references at the introductory
level.
Update: J. Traschen, a professor at UMass, has written a paper on
black hole evaporation:
An Introduction to Black Hole Evaporation
. This requires some quantum field theory, so you're not in a position to
read it end-to-end. But, with my help and some extra reading you could make
considerable headway. Along the way you'll see that even the idea of
`particle' is not such a clear-cut feature of quantum field theory in curved
space.
]
Renormalization group
Teaching the renormalization group (Am. J. Phys. 46(6), June 1978, p. 652-656)
[covered by Keith]
Textbooks and Monographs: There are quite a few books on interesting
stat-mech-related subjects that are at a level that's accessible to you.
You could read a chapter or two and discuss. However, these are rarely
self-contained, and it's difficult to get both a picture of what's interesting
about the subject and some quantitative information by just reading a chapter.
You'd probably want to choose a book of interest and then plan two or three
related talks on subsequent chapters. You should check with me before
pursuing these, though, since the substance, length, and difficulty of chapters
can vary considerably within a text.
Introduction to Percolation Theory, Stauffer and Aharony
Fractal Concepts in Surface Growth, Barabasi and Stanley
Monte Carlo Methods in Statistical Physics, Newman and Barkema
Basic Stochastic Processes, Brzezniak and Zastawniak
Statistical Mechanics, Feynman
The Mathematics of Financial Derivatives, Mott, et. al.
The Mathematical Theory of Communication, Shannon
Stochastic Processes in Chemistry and Physics, van Kampen
Exactly Solved Models in Statistical Mechanics, Baxter
Some longer research papers from the Los Alamos Archive (you can download a PDF
version of the paper by clicking on Other Formats). These are too long
to do as talks, although you could do a piece of one of them if one catches your eye.
Not all of them will be accessible to you, but you can see what people do for
research in these subfields.