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Adaptive Quantum Monte Carlo Approach States for High-Dimensional Systems
Published in Xavier Oriols, Jordi Mompart, Applied Bohmian Mechanics, 2019
Eric R. Bittner, Donald J. Kouri, Sean Derrickson, Jeremy B. Maddox
Here we focus on three clusters, Ne13, Ne17, and Ne37 over a temperature range spanning the solid to liquid transition for bulk Ne. In the figures which display the thermodynamic data the temperature is given in terms of reduced unit which is the temperature in Kelvin multiplied by Boltzmann’s constant and divided by the well depth of the LJ potential, T′ = TkB/ϵ. Figure 5.11 shows the total free energy (scaled to a common T = 0K origin) versus temperature for the three clusters. Figure 5.12 shows the various contributions to the total free energy for the 13-atom cluster with similar behavior for the other clusters. First, the contribution from the quantum potential increases, as it should as T increases. The averaged quantum potential is simply the average quantum kinetic energy and as such is approximately inversely proportional to the de Broglie wavelength squared, 〈Q〉 ∝ λ−2. Hence, 〈Q〉 increases as the system becomes more localized, corresponding to an increasingly shorter thermal de Broglie wavelength as T increases.
Dynamics and Statics
Published in Eli Ruckenstein, Gersh Berim, Wetting Theory, 2018
where Λi=hp/(2πmikBT)1/2 is the thermal de Broglie wavelength of the molecules of component i, kB and hP are the Boltzmann and Planck constants, respectively, T is the absolute temperature, and mi is the molecular mass of component i. The excess free energy contains a contribution from a system of hard spheres Φ[ρA(r),ρB(r)] and a contribution Fat tr[ρA(r),ρB(r)] due to the attractive interactions between molecules. The former contribution has, in Rosenfeld’s approximation,13 the form Φ[ρA(r),ρB(r)]/kBT=−n0 log(1−n3) () +n1n2−n1vn2v1−n3+n23−3n2ξ02+2ξ0324π(1−n3)2
Weakly nonlinear interactions of collective oscillations in a correlated degenerate fluid
Published in Waves in Random and Complex Media, 2022
In the case of high particle density , as we lower the temperature , the thermal de Broglie wavelength (, ℏ is Planck's constant and m is the mass) starts to be comparable to the inter-particle spacing . This is when the phase-space density and wave packets of different particles start to overlap with each other, leading to the quantum degeneracy. Under this circumstance, the wave-like nature (collective phenomena) becomes important and quantum effects must be taken into account. To investigate the collective processes, quantum hydrodynamic (QHD) model is developed from the well-known Wigner–Poisson equations (by taking the velocity moments of the Wigner phase-space distribution) [11–16]. The QHD have the same form as the classical NS hydrodynamic equations, which properly describe the collective dynamics of weakly interacting repulsive Bose gas in Bose–Einstein Condensate (BEC) [17], dense plasma [18–22] and also well explain the nonlinear collective dynamics of gravitating BEC [23]. All these QHD models are for weakly coupled degenerate fluid.
Structure of a nanodrop of a binary mixture on a solid surface
Published in Molecular Physics, 2021
Gersh O. Berim, Eli Ruckenstein
The total Helmholtz free energy is represented as the sum of an ideal gas free energy, , an excess free energy and a free energy due to the interactions between fluid and walls. The ideal gas free energy has a standard form where is the thermal de Broglie wavelength of the molecules of component i, and are the Boltzmann and Planck constants, respectively, T is the absolute temperature and is the molecular mass of component i. The excess free energy consists of a contribution of a reference system of hard spheres and a contribution due to the attractive interactions between the fluid molecules. The former contribution, expressed in Rosenfeld's approximation has the form [22] where free energy density of hard spheres, , is provided by the expression where () and () are averaged densities given by The scalar, , and vector, , weight functions are provided in Ref. [22].