Confined Quantum Hard Spheres

• Main Authors: Sergio Contreras, Alejandro Gil-Villegas
• Format: Article
• Language: English
• Published: MDPI AG 2021-06-01
• Series: Entropy
• Subjects: hard spheres; perturbation theory; quantum fluids; quantum Monte Carlo
• Online Access: https://www.mdpi.com/1099-4300/23/6/775

We present computer simulation and theoretical results for a system of <i>N</i> Quantum Hard Spheres (QHS) particles of diameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula> and mass <i>m</i> at temperature <i>T</i>, confined between parallel hard walls separated by a distance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mi>σ</mi></mrow></semantics></math></inline-formula>, within the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>≤</mo><mi>H</mi><mo>≤</mo><mo>∞</mo></mrow></semantics></math></inline-formula>. Semiclassical Monte Carlo computer simulations were performed adapted to a confined space, considering effects in terms of the density of particles <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>ρ</mi><mo>*</mo></msup><mo>=</mo><mi>N</mi><mo>/</mo><mi>V</mi></mrow></semantics></math></inline-formula>, where <i>V</i> is the accessible volume, the inverse length <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>H</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> and the de Broglie’s thermal wavelength <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>λ</mi><mi>B</mi></msub><mo>=</mo><mi>h</mi><mo>/</mo><msqrt><mrow><mn>2</mn><mi>π</mi><mi>m</mi><mi>k</mi><mi>T</mi></mrow></msqrt></mrow></semantics></math></inline-formula>, where <i>k</i> and <i>h</i> are the Boltzmann’s and Planck’s constants, respectively. For the case of extreme and maximum confinement, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.5</mn><mo><</mo><msup><mi>H</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>H</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, respectively, analytical results can be given based on an extension for quantum systems of the Helmholtz free energies for the corresponding classical systems.