arXiv subjects

Joaquín Figueroa

Publications and source records attributed to Joaquín Figueroa.

2 recordsLinked to original sources

arXiv2025

A Novel Transfer Matrix Framework for Multiple Dirac Delta Potentials

We present an analytical framework for studying quantum tunneling through multiple Dirac delta potential barriers in one dimension. Using the transfer matrix method, we derive a closed-form expression for the total transfer matrix of a system composed of $N$ equally spaced delta barriers. In a systematic manner, a compact expression is obtained for the first element of the transfer matrix, based on triangular numbers. This, in turn, allows us to compute the transmission coefficient exactly as a function of the number of barriers. The proposed method successfully reproduces well-known results for one and two barriers and efficiently captures complex interference effects for larger values of $N$, such as $N=4$.

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arXiv2018

Nucleation of superfluid-light domains in a quenched dynamics

Strong correlation effects emerge from light-matter interactions in coupled resonator arrays, such as the Mott-insulator to superfluid phase transition of atom-photon excitations. We demonstrate that the quenched dynamics of a finite-sized complex array of coupled resonators induces a first-order like phase transition. The latter is accompanied by domain nucleation that can be used to manipulate the photonic transport properties of the emerging superfluid phase; this in turn leads to an empirical scaling law. This universal behavior emerges from the light-matter interaction and the topology of the array. The validity of our results over a wide range of complex architectures might lead to to a promising device for use in scaled quantum simulations.

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