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Ideal gas law for a quantum particle
Building: Cero Infinito
Room: Posters hall
Date: 2024-12-10 04:30 PM – 06:30 PM
Last modified: 2024-11-19
Abstract
The extension of thermodynamic laws to the quantum regime is a topic of significant contemporary interest. In this study, we explore the applicability of the ideal gas law (IGL), which classically correlates the pressure of a gas with its temperature and volume in the thermodynamic limit, to a single quantum particle confined within a two-dimensional cavity. By treating the quantum wave function as a probability density analogous to an ideal gas, we investigate how the energy equipartition principle can be employed to define the temperature of the quantum state. In classical thermodynamics, the concept of ergodicity—where time and spatial averages converge—is essential for equilibrium. Here, we approach ergodicity from the perspective of dynamical systems, analyzing how isotropy and chaotic dynamics contribute to the validity of the IGL for quantum systems. Our findings demonstrate that, on average, the eigenfunctions of the quantum system conform to the IGL. However, for coherent states, deviations from the law are observed, particularly in the form of excess pressure along the cavity boundary. These results offer new insights into the behavior of quantum gases and suggest potential implications for the development of quantum devices, highlighting the need for careful consideration in future explorations of quantum thermodynamics.