# black body simulation

black body radiation is typically understood from Planck's argument of light resonance in a box, from which the density of states is computed. Now, suppose I want to simulate a black body computationally, as a photon gas in a box; how is this supposed to be done? shouldn't I simulate the interaction between the photons and the box?

edit: the result I would like to recover is the blackbody spectrum, so the question is, what is the simplest simulation involving individual photons such that blackbody radiation is recovered?

• It's hard to figure out how to answer this question until we have a better understanding of what you want to do with your simulation - how far down do you want to go (in terms of first principles) and what do you hope your simulation will achieve? Whether interactions between photons and box need to be simulated really depends on what you want to do with the simulation. – Floris Dec 26 '14 at 18:06
• You need more than photons in a box. Those don't interact and never achieve thermal equilibrium. You also need quantum systems that the light can interact with and that are in thermal contact with a temperature bath. A bunch of harmonic oscillators would do. The next problem is that your choice of harmonic oscillators determines "the color" of your box. If you have just one oscillator in there which has just one frequency the box won't be black. The usual derivation takes care of all of that with suitable assumptions, you would have to satisfy those with specific choices of your system. – CuriousOne Dec 26 '14 at 18:38
• @Floris see edit of question. – chuse Dec 26 '14 at 19:22
• I guess you would have to do a density matrix kind of calculation for your harmonic oscillators. You could, of course, try an ad-hoc time varying random potential approach, but given the size of the phase space for the problem for anything more than a couple of oscillators that sounds like a naive and losing strategy. There is a reason why few people try to do simulations of quantum systems directly... it's expensive! Turn that argument around and you can see why there is such interest in quantum computing. – CuriousOne Dec 26 '14 at 19:33
• There are actually some very interesting questions here, if you can describe exactly what you want to do with your simulation. The number of photons and harmonic oscillators (see @CuriousOne's comments) you would need to reproduce the BB spectrum is truly huge. If you are interested in the simulation of small thermodynamic systems, that show considerable fluctuations in entropy, then yes your approach may be workable. Otherwise, the theory here is much easier than simulation. You can even get theoretical fluctuation limits for different sized systems, so you could simulate them with random ... – WetSavannaAnimal Dec 26 '14 at 22:37