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I'm a postdoc in condensed matter theory, working mainly on cold atoms and quantum phase transitions.


Jul
26
revised Angular momentum for 3D harmonic oscillator in two different bases
added 8 characters in body
Jul
26
comment What does “optical conductivity” mean?
Isn't there also a difference between direction of the E field? In one case it is transverse and in the other longitudinal?
Jul
22
comment Coleman-Weinberg potential: resum at 2 loops?
@bechira: Look at the effective potential at one loop. The classical propagator includes the $\lambda\phi_b^2$ term. If you expand the propagator in the log, that will give rise to the $\phi_b^2$ terms that need to be resummed if you use the free propagator.
Jul
22
answered Coleman-Weinberg potential: resum at 2 loops?
Jul
14
comment Mean field theory = large-N approximation?
Thanks for the comment. One question: in your case, are you talking about quantum Ising spins or classical spins ?
Jul
11
comment O(N) sigma model at large N
@user43283: Yes. There's whole chapter on the large N limit, though he uses a sharp cut-off. But the problem you have is generic to the $\phi^4$ model for any N, in $d=4$, so any chapter on that would do I guess. The only difference is that in the large N limit the one loop result is essentially exact (if you resume it properly). My advice would be: read the chapter in ZJ but redo the calculation with dimensional regularization, that should solve your problem. Then post the answer ;-)
Jul
10
comment O(N) sigma model at large N
I think that what you effectively do when you send $\epsilon\to0$ at fixed $\mu$, you effectively take the continuum limit (corresponding to $\Lambda\to\infty$ with a sharp cut-off). The O(N) model is known to exist in $d=4$ in the continuum limit only if the theory is free, which is indeed what you get. Did you have a look at Zinn-Justin book ?
Jul
8
comment How to prove that the ground state of the Hubbard model is not a Slater determinant?
In that case, I let you figure out a better approach yourself.
Jul
8
comment How to prove that the ground state of the Hubbard model is not a Slater determinant?
In that case, can't you prove that by induction? Show that it does not work for 2 particles, then show that if it does not work for n, it can't work for n+1.
Jul
7
comment How to prove that the ground state of the Hubbard model is not a Slater determinant?
Then I might not get what you mean by Slater determinant: isn't it just build from the localized one-body wave-function? Or do you just mean that in general, one cannot write the ground-state of an interacting system cannot be written in terms of the (antisymmetrized) product of a possibly complicated one-body wavefunction ?
Jul
7
comment In what limit do we *really* get Maxwell-Boltzmann statistics from Bose-Einstein and Fermi-Dirac?
The dilute gas limit, where the MB distribution is recovered corresponds to $T\ll |\mu|$, with $\mu<0$. Note that the temperature can still be high compare to the typical energy ($\epsilon$). Starting from a quantum gas, one can show in a virial expansion that the classical results (using MB) are recovered in this limit.
Jul
3
comment How to prove that the ground state of the Hubbard model is not a Slater determinant?
Write the state, apply the Hamiltonian, and you'll find that it is not an eigenstate. The easiest way would be to use second quantification.
Jul
3
comment Hubbard Model Hamitonian
Are you talking about fermions or bosons ? That looks like bosons (since there are only one species), but double occupancy is used in discussions about fermions (you can put as many bosons as you want on one site).
Jul
2
comment Particle/Pole correspondence in QFT Green's functions
I'm not sure it's a well defined question. Particles are defined by the poles: this matches both the free theory, the perturbative calculations as well as the exacts results from integrable models, and give a practical tools for non-perturbative problem.
Jul
2
answered Particle/Pole correspondence in QFT Green's functions
Jun
27
comment I am trying to calculate how $<r>$ in the hydrogen atom evolves with time
@user120404: apply what the gradient is on $r$, and you'll find that $\partial_t r=p/m$ as expected.
Jun
27
comment I am trying to calculate how $<r>$ in the hydrogen atom evolves with time
@JohnRennie: Nobody said the state is an eigenstate of $H$.
Jun
26
comment Would a high energy bottom quark 'decay' to a top quark?
@jk88: $b^2$ is invariant and gives $m_b^2$ in all frame. The only non-trivial quantity is $W.t$, which is the most easily seen to be positive in the rest frame of the $W$ (or the $t$).
Jun
26
comment Would a high energy bottom quark 'decay' to a top quark?
@innisfree: ok. Though that was confusing because the v2 was referring to the rest frame of the $b$.
Jun
26
comment Would a high energy bottom quark 'decay' to a top quark?
@innisfree: Shouldn't you have $W.t=E_t E_W- p_t p_W$, as well as $p_t=-p_W$ (and conservation of energy) ?