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Jun
24
comment An integral involving the Bose-Einstein distribution
I thought of it, but I didn't use the approximation because when $k=0$ also $E_k = 0$ and the assumption doesn't hold. However using it I'm able to obtain the result, so apparently that's the way to go, and there should be some argument according to which the low $k$ modes do not count. Thank you very much!
Jun
20
comment An integral involving the Bose-Einstein distribution
I don't think I need to list every single way I know of solving an integral that didn't work in this case... Do I? As per site rules I would have shared relevant work which may be useful. Of course I do not share work which turned out to be useless, or which showed that the method does not work here. However, as you ask, substitution does not work because, as the expression is not analytical in T there is no way of obtaining a T-expansion. By definition the saddle point method is not applicable, as the integrand grows indefinitely and there is no point to saddle.
Jun
20
asked An integral involving the Bose-Einstein distribution
Apr
21
awarded  Popular Question
Mar
12
awarded  Notable Question
Jan
7
awarded  Yearling
Sep
2
revised Alignment of a system in equilibrium and its potential energy
Fixed grammar
Sep
2
suggested approved edit on Alignment of a system in equilibrium and its potential energy
Aug
30
comment What measurement of time is so small that it qualifies as quantum?
en.wikipedia.org/wiki/Planck_time
Aug
24
comment Is passing on knowledge/information from one body to another and the resultant state is ever studied as any branch of physics?
You may be interested, speaking of Physics, in the concept of entropy, Shannon information theory, quantum information, Kolmogorov complexity. Look them up on Wikipedia, you may like them. However, as already noted, seems like your question (and, most of all, your example) could be better answered in a Biology forum.
Aug
6
awarded  Nice Answer
Aug
6
accepted Mapping a continuum XY model to a discrete one
Aug
5
answered What is $c + (-c)$?
Jul
17
revised Mapping a continuum XY model to a discrete one
added 115 characters in body
Jul
17
revised Mapping a continuum XY model to a discrete one
added 133 characters in body
Jul
17
asked Mapping a continuum XY model to a discrete one
Jul
2
awarded  Curious
May
13
comment Why doesn't the LHC accelerate electrons?
You are right, but still the disadvantages of a lepton collider are counterbalanced by the much cleaner events you get. So it seems to me that the two approaches have been competing, and I wouldn't be so decisive in declaring circular electron/positron collider not viable. There have been some serious proposals: arxiv.org/abs/1305.6498
May
6
awarded  Critic
May
6
comment Radiation pressure question
You guess is right, the pressure must be very slight. And you have to compare it with the gravitational force, which basically keeps the planets on their orbit. This force is so much stronger than the radiation pressure, that makes is essentially irrelevant.