There is a result I only heard about recently: it has been proven that computing partition functions for the Ising-model in dimensions > 2 is NP-complete. (The paper can be found at http://www.cs....

It's nothing you can rigorously derive from Coulomb's law, but the idea is probably the following: the rightmost factor $$\frac{p^j - p^i}{|p^j - p^i|}$$ is just the unit vector pointing from particle ...

An addition to the above answers: I believe there are a couple of ways modern physicists use computers. On the most theoretical level, people use computer algebra systems (CAS) to do lengthy ...

You can estimate that someone swimming in water has a Reynolds number of about $10^6 - 10^7$; what counts is that this number is $\gg 1.$ In that case, you're dealing with the drag equation: http://en....

Taking a short hiatus should not prove fatal to your futur career, whatever that may be. I believe the theorist Dijkgraaff went to art school halfway through his studies! You're still very young, and ...

As for the lattice part: here, you're interested in doing Monte Carlo Markov chains, which consists of summing over configurations $s$, each having a certain weight $p(s)$ and for which your ...

If David's right, and this is a homework problem, I'll just give a few hints. Consider a hole at height d. Since there is a flow in the can, there is a streamline; draw it. Now apply Bernoulli's law ...

Just to add some explicitness to the above answers: take an isolated particle at rest; it's KE is zero. Now switch to a reference frame with relative velocity $\beta$ wrt the particle. In this frame, ...

In my humble experience, solving Griffiths problems gets you good at solving Griffiths problems, but not much more. Typically, they've already done/seen the math required, so I'd only work on the ...

Good question! The reponse really depends on what you 'need': if you're sampling a small system and you're lucky enough to actually be able to count (or estimate...) the number of states $\mathcal{N}(... View answer 2 votes I'll try to explain what is meant by "putting$a = 1$". You always simulate a finite volume$V = L^D$, where$L$is usually of the order of a few particle radii. Let's say you choose$L = 10^{-10} \...

First of all, you need to be careful what you mean by a NOT gate. If you have only one qubit, you could use the gate (typically called X) $$\begin{pmatrix}0 & 1\\1& 0\end{pmatrix},$$ which ...

As far as you're wondering about 'quantum' field theories, all bets are off - just take a look at the arXiv or on Google. However, most of those theories seem (to me) less well studied than regular ...

The word viscosity hasn't been used above, and yet it's crucial to understand the problem. Since tea is viscous, it obeys a type of 'non-slip condition': it's completely at rest against the sides and ...

Important point: a change of variables cannot improve convergence! When you regulate an divergent integral $I$ ($=\infty$), you're actually calculating another integral $J$ (that might depend on some ...

I believe you're seeing a problem where there isn't one. Indeed we have $n + k \in \mathbb{Z},$ so if you shift $k$, say $$k \mapsto k + \delta,$$ you need to adjust $$n \mapsto n - \delta.$$ I wouldn'...

The examples you are giving of S and T don't leave a lot of room for debate: S is an open interval (say $]0,1[$) and T is a circle, $S^1$. Already, if you're adding the points A and B to S, you're ...

Your argument is absolute correct; a change of sign/scale factor won't change the solutions to the 'classical' equation $\delta S = 0.$ However, observables do change. If you've seen some field theory,...
In more 'down-to-earth' QM, you use Green's functions to find the density of states. I'm deprived of my books so at a loss for giving a good reference, but the idea is to calculate G(x,x';E) = \...