arXiv subjects

Gustavo Alvarez

Publications and source records attributed to Gustavo Alvarez.

4 recordsLinked to original sources

arXiv2026

Inverse Laplace and Mellin integral transforms modified for use in quantum communications

Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum chromodynamics, in which the optic theorem and the renormalization group equation can be solved by a unique contour integral written in two different "dual" ways related between themselves by a complex map in the complex plane of Mellin variable. The inverse integral transformation should be modified to be applied for these contour integral solutions. These modified inverse transformations may be used in security protocols for quantum computers. Here we do a brief review of the basic integral transforms and propose their modification for the extended domains.

quant-ph↗

arXiv2026

Anomalous Thermal Transport Reveals Weak First-Order Melting of Charge Density Waves in 2H-TaSe2

How ordered phases melt in low-dimensional quantum materials remain difficult to resolve because the relevant fluctuations are dynamic and charge neutral. In this work, we show that thermal transport provides a sensitive probe of these hidden fluctuations in the layered transition metal dichalcogenide 2H-TaSe2. We observe a striking V-shaped temperature dependence of the thermal conductivity that cannot be explained by conventional phonon-phonon scattering. Instead, it originates from scattering by persistent local charge-density-wave (CDW) correlations, consistent with our phenomenological model linking thermal transport to spatial CDW fluctuation. Electron diffraction reveals short-range periodic lattice distortions persisting to at least 300 K, while X-ray diffraction shows thermal hysteresis of the CDW wavevector. Together, these results reveal a dislocation- and fluctuation-driven weak first-order melting of the CDW state.

cond-mat.str-el↗

arXiv2023

Analytical solution to DGLAP integro-differential equation in a simple toy-model with a fixed gauge coupling

We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be ${\cal N} =4$ supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of momentum transfer and of Bjorken $x$. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behaviour in the vicinity of the point $x=0$ and a smooth behaviour in the vicinity of the point

hep-ph↗

arXiv2019

Analytical solution to DGLAP integro-differential equation via complex maps in domains of contour integrals

A simple model for QCD dynamics in which the DGLAP integro-differential equation may be solved analytically has been considered in our previous papers arXiv:1611.08787 [hep-ph] and arXiv:1906.07924 [hep-ph]. When such a model contains only one term in the splitting function of the dominant parton distribution, then Bessel function appears to be the solution to this simplified DGLAP equation. To our knowledge, this model with only one term in the splitting function for the first time has been proposed by Blumlein in hep-ph/9506403. In arXiv:1906.07924 [hep-ph] we have shown that a dual integro-differential equation obtained from the DGLAP equation by a complex map in the plane of the Mellin moment in this model may be considered as the BFKL equation. Then, in arXiv:1906.07924 we have applied a complex diffeomorphism to obtain a standard integral from Gradshteyn and Ryzhik tables starting from the contour integral for parton distribution functions that is usually taken by calculus of residues. This standard integral from these tables appears to be the Laplace transformation of Jacobian for this complex diffeomorphism. Here we write up all the formulae behind this trick in detail and find out certain important points for further development of this strategy. We verify that the inverse Laplace transformation of the Laplace image of the Bessel function may be represented in a form of Barnes contour integral.

hep-th↗