arXiv subjects

Leandro Medina

Publications and source records attributed to Leandro Medina.

4 recordsLinked to original sources

arXiv2021

Universality of Pattern Formation

We study a $\mathcal PT$-symmetric scalar Euclidean field theory with a complex action, using both theoretical analysis and lattice simulations. This model has a rich phase structure that exhibits pattern formation in the critical region. Analytical results and simulations associate pattern formation with tachyonic instabilities in the homogeneous phase. Monte Carlo simulation shows that pattern morphologies vary smoothly, without distinct microphases. We suggest that pattern formation in this model may be regarded as a form of arrested spinodal decomposition. We extend our theoretical analysis to multicomponent $\mathcal PT$-symmetric Euclidean scalar field theories and show that they give rise to new universality classes of local field theories that exhibit patterned behavior in the critical region. QCD at finite temperature and density is a member of the $Z(2)$ universality class when the Polyakov loop is used to distinguish confined and deconfined phases. This suggests the possibility of the formation of patterns of confined and deconfined matter in QCD in the critical region in the $μ-T$ plane.

hep-lat↗

arXiv2018

Simulation of Scalar Field Theories with Complex Actions

Many scalar field theory models with complex actions are invariant under the antilinear ($PT$) symmetry operation $L^{\ast}(-χ)=L(χ)$. Models in this class include the $iϕ^{3}$ model, the Bose gas at finite density and Polyakov loop spin models at finite density. This symmetry may be used to obtain a dual representation where weights in the functional integral are real but not necessarily positive. For a subclass of models satisfying a dual positive weight condition, the partition function is manifestly positive. The sign problem is eliminated; such models are easily simulated by a simple local algorithm in any number of dimensions. Simulations of models in this subclass show a rich set of behaviors. Propagators may exhibit damped oscillations, indicating a clear violation of spectral positivity. Pattern formation may also occur, with both stripe and bubble morphologies possible. The existence of a positive representation is constrained by Lee-Yang zeros: a positive representation cannot exist everywhere in the neighborhood of such a zero. Simulation results raise the possibility that pattern-forming behavior may occur in finite density QCD in the vicinity of the critical line.

hep-lat↗

arXiv2017

Simulation of Scalar Field Theories with Complex Actions

We develop a method for the simulation of scalar field theories with complex actions which is local, simple to implement and can be used in any number of space-time dimensions. For model systems satisfying the $\mathcal{PT}$ symmetry condition $L^{*}(ϕ)=L(-ϕ)$, the complex weight problem is reduced to a sign problem. The sign problem is eliminated completely for a large subclass of these models; this class includes models within the $iϕ^{3}$ universality class, and also models with nonzero chemical potential. Simulations of models from this subclass show a rich set of behaviors. Propagators may exhibit damped oscillations, indicating a clear violation of spectral positivity. Modulated phases occur in some models, exhibiting striping and other pattern-forming behaviors. These field theory models are connected to complex systems where pattern formation occurs because of competition between interactions at two different length scales.

hep-lat↗

arXiv2016

Schwinger Pair Production at Finite Temperature

Thermal corrections to Schwinger pair production are potentially important in particle physics, nuclear physics and cosmology. However, the lowest-order contribution, arising at one loop, has proved difficult to calculate unambiguously. We show that this thermal correction may be calculated for charged scalars using the worldline formalism, where each term in the decay rate is associated with a worldline instanton. We calculate all finite-temperature worldline instantons, their actions and fluctuations prefactors, thus determining the complete one-loop decay rate at finite temperature. The thermal contribution to the decay rate becomes nonzero at a threshold temperature $T=eE/2m$, above which it dominates the zero temperature result. This is the lowest of an infinite set of thresholds at $T=neE/2m$. The decay rate is singular at each threshold as a consequence of the failure of the quadratic approximation to the worldline path integral. We argue that that higher-order effects will make the decay rates finite everywhere, and model those effects by the inclusion of hard thermal loop damping rates. We also demonstrate that the formalism developed here generalizes to the case of finite-temperature pair production in inhomogeneous fields.

hep-th↗