Sistemas ópticos para la caracterización de sistemas coloidales de nanopartículas y consideraciones teóricas cuánticas : implementación del modelo de Ising en Cirq y análisis de entornos acoplados con operadores básicos de Lindblad.

Abstract

This study presents the simulation of the quantum Ising chain using the Cirq and OpenFermion libraries. Chains with open, periodic, and anti periodic boundary conditions were investigated in both the ferromagne tic and disordered magnetic phases. The transverse field magnetization, energies, and interspin correlation of the ground states were simulated, along with the numerical calculation of the energy gaps between exci ted states and the entanglement entropy. The results were validated th rough theoretical predictions and numerical calculations available in the literature. The simulation demonstrated the quantum phase transition and parity symmetry breaking at the critical point h = J under periodic boundary conditions. Additionally, the hamiltonians and ground states of four-spin chains with periodic boundary conditions were exported to a program in Julia. Utilizing the QSWalk.jl library, the time evolution of the system coupled to environments modeled with Lindblad operators follo wing the GKSL equation was analyzed. Various configurations of ladder operators σ± and transition operators were employed. The results sho wed that the system evolves towards steady states at different rates, with magnetization oscillating when using ladder operators. The use of the σ+ operator on all spins suggests the existence of the superradiance pheno menon.