Límites en la velocidad de evolución en sistemas cuánticos de dos fermiones

Abstract

En el trabajo que se presenta a continuación se investigan los límites fundamentales en la evolución temporal de sistemas cuánticos conformados por dos fermiones idénticos no interactuantes, con cuatro niveles accesibles cada uno. Para poder estudiar dichos sistemas se utilizó el método de la segunda cuantización, el cual permite una formulación más práctica de la dinámica de los sistemas cuánticos, facilitando la construcción de los estados en los que se encuentra el sistema bipartito. Con esta base, se han considerado tres configuraciones distintas en los niveles energéticos del sistema, y para cada una de ellas se ha calculado el llamado límite de rapidez cuántica, que establece el tiempo mínimo que se requiere para que un estado inicial evolucione hacia un estado ortogonal.

In the work presented below, the fundamental limits on the temporal evolution of quantum systems composed of two identical non-interacting fermions, each with four accessible energy levels, are investigated. In order to study these systems, the method of second quantization was used, which allows for a more practical formulation of quantum system dynamics, facilitating the construction of the states in which the bipartite system is found. Based on this approach, three different configurations of the system’s energy levels were considered, and for each of them the so-called quantum speed limit was calculated, which establishes the minimum time required for an initial state to evolve into an orthogonal state.

In addition to the analytical study, Wolfram Mathematica software was used to generate graphs representing, for each configuration, the corresponding quantum speed limit for such temporal evolution. A color scale was employed to facilitate the identification of key points, which allow the calculation of the minimum time in which an initial state of the quantum system evolves to reach an orthogonal state for a specific system.

By obtaining these limits, progress was made in the understanding and establishment of lower bounds on the speed of evolution in two-fermion systems under different configurations.