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seen Feb 23 '13 at 14:16

Feb
19
comment Is that true that real quantum chaos doesn't exist?
Quantum chaos is the study of the quantum behavior of classically chaotic systems. It addresses the question of what are the signatures of classical chaos in the spectra and wave functions of quantum systems
Feb
8
comment Cascade in relativistic turbulence
This is completely wrong. Relativistic fluid dynamics is well understood, and applied extensively to a wide range of phenomena. This includes astrophysics (supernova explosions, jets, disks, etc) and relativistic heavy ion collisions. We now know that the formalism developed in Landau and Weinberg can also be derived from the AdS/CFT correspondence. To the best of my knowledge, there is no fundamental difference between rel and non-rel turbulence, in particular the energy cascade is the same.
Jan
3
comment If the ground states of interacting QFTs are so complicated, how did Nature find them?
The main algorithm we have for find the ground state of an interacting QFT is Euclidean lattice field theory. Simulations indicate that ground state of QCD is complex, but not hard to find (in the sense that simple Metropolis algorithms converge quickly, even if initialized with very poor guesses of the ground state).
Jan
3
comment If the ground states of interacting QFTs are so complicated, how did Nature find them?
One minor comment: For realistic values of the quark masses the phase transition is a smooth crossover.
Dec
27
comment Path integral with zero energy modes
You would first have to include chiral fermions and a coupling to gauge fields.
Dec
26
comment Path integral with zero energy modes
The $\omega$ are discrete Matsubara frequencies. In the case of fermions these can never be zero. For bosons, zero modes can indeed appear. This is related to Bose condensation. You can have anomalies in non-relativistic systems with a Fermi surface, but that's a more complicated story, see for example arxive:1203.2697.
Sep
24
comment Why water is not superfluid?
A rough criterion is the condition for Bose condensation in an ideal gas, $n\lambda^3\sim 1$, where $n$ is the density and $\lambda$ is the thermal wave length. Note that your question is in some sense backwards: Helium is the exception, water is the rule. Most ordinary fluids solidify instead of becoming superfluid at low $T$.
Aug
22
comment Very basic question about QFT at finite density
Walecka and Gorkov are a little more old-fashioned (canonical quantization). You can also check out Kapusta's or LeBellac's book on thermal field theory (they contain some stuff about finite density as well).
Aug
22
comment Very basic question about QFT at finite density
One more remark: The transformation you consider is a gauge transformation. $\mu$ enters as like the zero'th component of a gauge field, and this is why it appears that $\mu$ can be gauged away. In a theory with a U(1) gauge field this is indeed correct, there is no dependence on $\mu$.
Aug
22
comment Very basic question about QFT at finite density
In order to derive a path integral representation you have to start from the finite temperature partition function (we need the trace of an exponential so that we can write it as an imaginary time evolution operator), and take the T->0 limit in the end. There are many details that are explained in standard text books, for example chapter 2,3 of Negele and Orland.
Jun
2
comment What is spontaneous symmetry breaking in QUANTUM systems?
This has nothing to with quantum mechanics. A classical system of N (finite) spins does not have a phase transition either.
May
24
comment Analog Hawking radiation
The important point is this: 1) The dominant contribution to the energy are the kinetic and internal energy, as well as gradient corrections (dissipative terms), 2) Fluctuations are a higher order effect, and in general UV (cutoff) sensitive. This is expected for an effective field theory. 3) The UV completion is not a quantum theory of sound waves, but a kinetic theory (classical or quantum, depending on the fluid) of the microscopic degrees of freedom (typically atoms).
May
24
comment Analog Hawking radiation
We are moving away from the initial question ... Regarding black body radiation Jeremy is of course correct in stating that this is a quantum effect (the classical calculation of the energy density of thermal EM radiation is UV divergent, and this divergence is regularized in QM). There is an interesting question whether there is an analogous divergence in fluid dynamics. I'm not completely sure, since high momentum sound waves are strongly damped.
May
15
comment Area law for Entropy in Loop Quantum Gravity
Thanks. I haven't looked at all of these, obviously. But consider the first paper. From the abstract: ``For macroscopic black holes, the logarithm of the number of these horizon microstates is proportional to the area, irrespective of the values of (non-gravitational) charges''. Doesn't that also say that if the entropy comes from the horizon states, then it is proportional to the area?