# Tag Info

5

This is clearly completely hopeless. Many particle systems in QFT or even in non-relativistic QM are computationally intractable. Just to store the many-body Schroedinger wave function of more than a few particles is out of the question (it is a function of $3^N$ variables, where $N$ for your problem would be $O(10^{23}))$. In practice, lattice QCD is ...

4

Well, let's do some thinking here. You didn't specify what the cubic meter is composed of, but let's for sake of argument say that it is a gas of single, non-interacting particles (like, say, neutrons or something) at standard temperature and pressure. So we know we have 1 mole of gas in that cubic meter. Let's further assume that we only needed a single, ...

2

Independent of the physical process, this question is mathematically ill-posed. If you want to convert the integral from the 1D form that you gave to the 2D form that you gave, you are not making an "ordinary" change of variables where you can use a Jacobian matrix to adjust the measure. (As you noted yourself, the Jacobian in this case won't be square, so ...

1

I assume you are not asking about how parallel tempering works as an algorithm for sampling from probability distributions, but that you are in fact interested in finding the global minimum of a target function $E(x)$. If that's not the case, please clarify what exactly you didn't understand from the Wikipedia page you linked and I'll be happy to edit my ...

1

A couple of comments on your implementation: You initialize your distribution functions in an unconventional way; usually, we want to convert known macroscopic 'lattice' quantities like $\rho$ and $\vec{u}$ into $f_i$. An easy way to do this is using the equilibrium distribution you define above: ...

1

Once you have an understanding of fluid mechanics, the two best books for CFD specifically that I have used are: Computational Fluid Dynamics by John Anderson. I don't know if you have ever used any of Anderson's fluid dynamics books, but I highly recommend all of them. His books are all very readable and spend most of the text describing what to do rather ...

1

This is because we want to avoid extensive mathematical calculations of pairwise interactions with all particle inside or outside the box. MIC is a way of providing a cutoff distance over which we are not calculating pairwise potential. The cutoff is usually half the box length. This means if distance between particle i and particle j is more than L/2, you ...

1

When physicists simulate a quantum system, what is the output of such computation? Is it the probability wave function of the system? This depends on the simulation, but in general it will either be the full $n$-body system's wavefunction, or an approximation to it, using e.g. few-body states. If your simulation does not have access to the ...

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