Solving the Bars-Green equation for moving mesons in two-dimensional QCD

The two-dimensional QCD in the large $N$ limit, generally referred to as the 't Hooft model, is numerically investigated in the axial gauge in a comprehensive manner. The corresponding Bethe-Salpeter equation for a bound $q\bar{q}$ pair, originally derived by Bars and Green in 1978, was first numerically tackled by Li and collaborators in late 1980s, yet only for the {\it stationary} mesons. In this paper, we make further progress by numerically solving the Bars-Green equation for {\it moving} mesons, ranging from the chiral pion to charmonium. By choosing several different quark masses, we computed the corresponding quark condensates, meson spectra and their decay constants for a variety of meson momenta, and found satisfactory agreement with their counterparts obtained using light-cone gauge, thus numerically verified the gauge and Poincar\'{e} invariance of the 't Hooft model. Moreover, we have explicitly confirmed that, as the meson gets more and more boosted, the large component of the Bars-Green wave function indeed approaches the corresponding 't Hooft light-cone wave function, while the small component of the wave function rapidly fades away.Comment: v2, 25 pages, 12 figures, and 1 table; Some figures updated, references added, typo corrrected; to appear in JHE

Heat engine in the three-dimensional spacetime

We define a kind of heat engine via three-dimensional charged BTZ black holes. This case is quite subtle and needs to be more careful. The heat flow along the isochores does not equal to zero since the specific heat $C_V\neq0$ and this point completely differs from the cases discussed before whose isochores and adiabats are identical. So one cannot simply apply the paradigm in the former literatures. However, if one introduces a new thermodynamic parameter associated with the renormalization length scale, the above problem can be solved. We obtain the analytical efficiency expression of the three-dimensional charged BTZ black hole heat engine for two different schemes. Moreover, we double check with the exact formula. Our result presents the first specific example for the sound correctness of the exact efficiency formula. We argue that the three-dimensional charged BTZ black hole can be viewed as a toy model for further investigation of holographic heat engine. Furthermore, we compare our result with that of the Carnot cycle and extend the former result to three-dimensional spacetime. In this sense, the result in this paper would be complementary to those obtained in four-dimensional spacetime or ever higher. Last but not the least, the heat engine efficiency discussed in this paper may serve as a criterion to discriminate the two thermodynamic approaches introduced in Ref.[29] and our result seems to support the approach which introduces a new thermodynamic parameter $R=r_0$.Comment: Revised version. Discussions adde

Energy-Momentum Tensor and Related Experimental Analysis of Electromagnetic Waves in Media

We find that the energy-momentum tensor of electromagnetic waves in media is very similar to that of ordinary fluids, and concepts such as density, pressure, and energy transfer rate can be similarly defined. On this basis, we conducted a detailed theoretical analysis on the mean momentum and equivalent mass of photons in the medium, the relationship between pressure and polarization of beams, the influence of polarization energy and magnetization energy of the medium, the Bernoulli effect of beams and the energy-momentum tensor of beams in moving media. We also obtain a conservation new energy-momentum tensor based on the interaction term between the electromagnetic field and the medium. From this energy-momentum tensor, we can derive both the Minkowski momentum and the Abraham momentum simultaneously. We find that Minkowski momentum is actually a canonical momentum that considers the influence of the interaction between electromagnetic waves and media, while Abraham momentum is actually a mechanical momentum that does not consider the influence of the interaction between electromagnetic waves and media. Based on the theory obtained in this paper, we have provided theoretical explanations for Jones'experiment of light pressure in a medium, Ashkin's free liquid surface deformation experiment, Weilong's optical fiber deformation experiment, and frequency shift measurement experiment. The theory obtained in this paper can self-consistently explain the above experiments simultaneously. Unlike the Minkowski and Abraham tensors, according to the energy-momentum tensor proposed in this paper, a beam in a medium also generates a pressure on its side, and the direction of this pressure is related to the polarization of the beam. The findings of this paper may shed new light on the application of light.Comment: Page 29, Figure