Gerben
  • Member for 11 years
  • Last seen more than 9 years ago
Why is it hard to solve the Ising-model in 3D?
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15 votes

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....

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Need some help interpreting a formula inspired from Coulomb's law
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7 votes

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 ...

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How useful is programming in physics?
5 votes

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 ...

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Olympic games and the local g
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4 votes

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....

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Is it possible to restart formal higher education in physics at a later age?
4 votes

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 ...

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When is the "minus sign problem" in quantum simulations an obstacle?
3 votes

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 ...

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How far will water squirt out from a hole in a can?
3 votes

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 ...

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Is kinetic energy a scalar?
3 votes

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, ...

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Studying electrodynamics problems
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3 votes

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 ...

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Estimating Partition functions
3 votes

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}(...

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Why can't we set the lattice spacing 'a' in lattice QCD?
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} \...

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fermions and quantum gates
2 votes

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 ...

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How general is the Lagrangian quantization approach to field theory?
2 votes

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 ...

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Vortex in liquid collects particles in center
2 votes

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 ...

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Can we make a change of variables (for example to polar coordinates) into a divergent integral?
1 votes

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 ...

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proof of gauge invariance for quantum 1D ring
1 votes

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'...

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A question on smooth 1-manifolds
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1 votes

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 ...

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Are there measurable effects to scaling the action by a constant?
0 votes

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,...

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Green functions in Quantum Mechanics
0 votes

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) = \...

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