Effects of Lorentz violation in the Bose-Einstein condensation
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| Number of Parts | 43 | |
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| License | CC Attribution 3.0 Germany: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. | |
| Identifiers | 10.5446/50452 (DOI) | |
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| Production Year | 2020 | |
| Production Place | Universidade Federal do Cariri |
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00:00
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Transcript: English(auto-generated)
00:00
Hello, my name is Joep Sarajevo, I'm from Federal University of Calgary and I'm going to talk about the effects of fluorescence violation in Bose-Einstein conversation. Let me first introduce our model. Our model consists of the usual complex scalar sector, modified by this tensor here, K-su mu nu, which is symmetric but traceless, and it defines a preferred direction in the
00:29
space-time violating, then, the Lorentz symmetry. And this whole new term here, that also violates Lorentz symmetry, and it's composed by this
00:44
vector K-A mu, which is CPT odd, while this other one is CPT even. And the discrete symmetry properties of both Lorentz-violating parameters are described in this table here. Note that this tensor K-su mu nu is dimensionless, while the other one has dimension of mass.
01:06
So we are mainly interested in the finite temperature effects, and especially in the Bose-Einstein condensation effects. So the Lagrangian that we have shown you possesses an obvious U1 symmetry, so that
01:22
we can easily calculate the conserved current here by applying this theorem, and the Euler-Lagrange equations will give us the equations of motion for our system. And we can also calculate the charge density here, and we use the conventional approach
01:45
by splitting the fields phi and phi star into two real components, phi 1 and phi 2, as it is present here in equation 6 and 7, so that we can rewrite the Lagrangian in a more convenient form, as it is expressed here in equation 8.
02:02
So we can calculate the canonically conjugated momenta and the Hamiltonian. With all this, we have our ingredients to construct our generating function, our partition function, that will allow us to calculate the finite temperature effects.
02:22
What I would like to highlight here is that we must include first the chemical potential here to perform the calculations. So this is in equation 12 our generating function, so I would like to highlight also that the temporal integral was replaced by a temperature integral with this beta here as 1 over T.
02:48
So that by replacing the Hamiltonian, we can simplify our partition function as it is present here in equation 13. So that the integration of the momenta can be straightforwardly done, and this n prime
03:07
here is just a normalization factor that is not important to the thermodynamic parameters. By Fourier expanding the phi fields, phi 1 and phi 2, we obtain a final form for
03:22
the natural logarithm of the partition function. This first term here is super important, because it controls all the infrared behavior and consequently it controls also the Bose-Einstein behavior.
03:47
The other contributions will give us the thermodynamic parameters such as pressure, energy, specific heat and charge density. But in order to obtain this natural logarithm of the partition function, we have to consider
04:05
a conventional condition, we obtain a modified conventional condition that states that the absolute value of the chemical potential minus half of the temporal component of the tensor kA must be less or equal than m.
04:22
There is a modification of the usual convergence condition first stated in the work of Harvey in 1981. This convergence condition will set a different value for the temperature for the Bose-Einstein condensation, as we will see further.
04:41
From now on, we can calculate the thermodynamic parameters using the equation of state for the system, which allow us to obtain the pressure, the internal energy, specific heat and charge density. From this point on, it is convenient to work separately with the temporal component
05:07
of the tensor kA and the spatial component of it. First of all, let us analyze the temporal component, which is simpler because the sigma here and lambda becomes equal, so in the non-condensate phase, which means that we
05:26
set this zeta to zero, we can find the pressure, the internal energy, specific heat and we plot numerically the specific heat for several values of the chemical potential
05:43
as well as the charge density for several values of the chemical potential, modifying also the value of the Lorentz-Bélekin parameter. As we have talked already, the modified convergence condition sets another temperature for the
06:08
Lorentz-Einstein condensation to a whole and, in fact, this modification in the temperature is of second order in the Lorentz-Bélekin parameter. But since the bounds on the Lorentz-Bélekin parameter are extremely low, we have a
06:27
very small modification in the critical temperature. For the vectorial components of the tensor kA, you can see more details in the archive.
06:42
In summary, we have studied the corrections emergent from the Lorentz-Bélekin CPT-OR extension of the complex color sector to the Bose-Einstein condensation and to the thermodynamic parameters. And we have shown that the presence of a modification of a CPT-OR modification gives
07:03
rise to a different convergence criteria for the generating functional. That gives rise to a modification in the critical temperature that sets the Bose-Einstein condensation and this modification is of second order in the coefficient.
07:21
That will be all. Thank you.