Recent content by YaroslavVB

What's a good textbook for that?

I was trying to see if limiting distribution of a a symmetric random walk on R can be modeled as voltage, but now it doesn't seem there's a direct connection

OK, another update.

Yes, I probably mean resistivity, and know voltage instead of current, updated post with fixes

Suppose I have finite wire of known resistivity. I know voltage is 0 volts at x=-1 and x=1, and 1 volt at x=0. How do I find voltage at intermediate points?

d-by-d matrix where d is a power of 2 d,1,1,1,... 1,d,1,1,... 1,1,d,1,.. ... In particular, I'm looking for nice expression for an orthogonal basis of eigenvectors of it

Thanks! Derivation in the attachment, where is it from?

Suppose f(n,p)=integral(n!/(x! (n - x)!dx, for x from -1/2 to p) where n>1, p<n+1/2 Are approximate formulas known for this kind of integral? Empirically, f(n,n+1/2) seems to be close to 2^n More generally, I'm looking for approximate formulas for integrals of n!/(x1!x2!...xn!) over nice...

Thanks, the solid foam explanation makes sense, since boiling corn substance exploding would also be a foam in a sense. BTW, here's the picture of "solid-state beer" <img src="http://yaroslavvb.com/pictures/lj/08-03-ln2/-10.jpg">

1. If you take beer out of the fridge, dip it for 30 seconds in liquid nitrogen, then open it, it will foam up. Skipping the LNO2 cooling stage, it doesn't foam up, why? 2. Pouring a bottle of beer into Dewar of liquid nitrogen, then letting LNO2 evaporate leaves pieces that are shaped like...

Thanks for the reply, it now all makes sense. My original confusion was because half the places I was looking at talked about "quantum Ising model" and the other half "classical Ising model". In the latter case, "Hamiltonian" referred to the energy of a particular configuration, not a quantum...

Suppose we have a two variable Ising system, x1,x2. The system has 4 states -- (-1,-1),(-1,1),(1,-1),(1,1). The states have the following density -- p(x1,x2)=Exp(-x1 x2)/Z How would I find the Hamiltonian and it's spectrum for this system?

Thanks for the explanation, I understand what it means to diagonalize an operator, what was confusing is that when pointed to Hamiltonian of a 1d Ising model, I saw a quadratic form instead of an operator I found a paper titled "Exact eigenvalues of the Ising Hamiltonian ... "...

Thanks for the hints. I'm still confused because I see places use "Ising model Hamiltonian" to denote a a function that gives the energy of a configuration, and what does it mean to find eigenstates of the energy function? For instance first equation in page below seems to be a function that...

Sorry, I didn't specify the context -- I see this notation come when talking about Ising models. So Z is the partition functions, H(x) is the Hamiltonian (for it could be the number of adjacent pairs with aligned spins in a configuration x). Exp[-b H(x)] is the Boltzmann potential for a...