Path Integrals and Effective Potentials in the Study of Monatomic Fluids at Equilibrium

Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres

“…The PI formalism is perfectly suited for performing path integral Monte Carlo (PIMC) and molecular dynamics (PIMD) computer simulations of quantum N -particle systems at nonzero temperatures [ 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 ]. With due attention to the special characteristics of quantum averages [ 33 , 38 , 44 , 45 , 46 , 47 ], the latter PI simulations can follow classical-like procedures [ 56 , 57 , 58 , 59 , 60 ]. To illustrate this situation, it is sufficient to recall the most basic PI description in the canonical ensemble of an actual quantum monatomic system in which exchange interactions can be neglected.…”

“…(The actual quantum system is retrieved in the Trotter’s limit [ 61 ], while the classical limit is . Special techniques are available to improve the P description and reduce computations (e.g., pair actions and higher-order propagators [ 33 , 34 , 35 , 37 , 38 ] combined with algorithms for moving the beads) [ 33 , 41 , 47 , 62 , 63 ]. In this connection, depending on the technique selected, there may or may not exist equivalence between all the beads in the model sample, which is a fact that turns out to be crucial for the study of structures [ 33 , 35 , 38 , 47 ].…”

“…Special techniques are available to improve the P description and reduce computations (e.g., pair actions and higher-order propagators [ 33 , 34 , 35 , 37 , 38 ] combined with algorithms for moving the beads) [ 33 , 41 , 47 , 62 , 63 ]. In this connection, depending on the technique selected, there may or may not exist equivalence between all the beads in the model sample, which is a fact that turns out to be crucial for the study of structures [ 33 , 35 , 38 , 47 ]. Thus, one speaks in this context of the structurally significant (equivalent among themselves) beads; their number, say X , takes the convenient values P or .…”

“…By focusing attention on quantum monatomic systems at equilibrium, with diffraction effects dominating their behavior, it is worthwhile to specify the three general categories of physically significant structures [ 31 , 33 , 38 , 39 , 47 ] that are revealed by PI: (a) instantaneous; (b) total thermalized-continuous linear response; and (c) centroids (centroid = proper center-of-mass of a PI necklace) [ 38 , 47 ]. For each of these categories, three points must be highlighted [ 47 ].…”

“…By focusing attention on quantum monatomic systems at equilibrium, with diffraction effects dominating their behavior, it is worthwhile to specify the three general categories of physically significant structures [ 31 , 33 , 38 , 39 , 47 ] that are revealed by PI: (a) instantaneous; (b) total thermalized-continuous linear response; and (c) centroids (centroid = proper center-of-mass of a PI necklace) [ 38 , 47 ]. For each of these categories, three points must be highlighted [ 47 ]. First, a given category is associated with the linear response from the system to a distinct weak external field: the instantaneous case is associated with a localizing field (e.g., as in elastic neutron scattering), this usually being the category linked to “the structure” of a quantum system; the total thermalized-continuous linear response with, for example, a continuous field; and the centroids with specifically a constant-strength field.…”