scholarly journals Parent Hamiltonians of Jastrow wavefunctions

2021 ◽  
Vol 4 (4) ◽  
Author(s):  
Mathieu Beau ◽  
Adolfo del Campo
Keyword(s):  
Yukawa Potential ◽  
Three Dimensional ◽  
Higher Dimensions ◽  
Spatial Dimension ◽  
Many Body ◽  
Bright Soliton Solution ◽  
Pairwise Product ◽  
Three Body ◽  
Body Potential ◽  
Pair Function

We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a two-body pairwise potential as well as a three-body potential. We thus generalize the Calogero-Marchioro construction for the three-dimensional case to an arbitrary spatial dimension. The resulting family of models is further extended to include a one-body term representing an external potential, which gives rise to an additional long-range two-body interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of well-known systems such as the Calogero-Sutherland and Calogero-Moser models. We also introduce novel models, generalizing the McGuire many-body quantum bright soliton solution to higher dimensions and considering ground-states which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverse-engineered to construct models with a given potential, such as a pair-wise Yukawa potential, and to identify models governed exclusively by three-body interactions.

Halide Ion Micro-Hydration: Structure, Energetics, and Spectroscopy of Small Halide–Water Clusters

2019 ◽  
Author(s):  
Pushp Bajaj ◽  
Marc Riera ◽  
Jason K. Lin ◽  
Yaira E. Mendoza Montijo ◽  
Jessica Gazca ◽  
...  
Keyword(s):  
Water Clusters ◽  
Quantitative Description ◽  
Three Dimensional ◽  
Many Body ◽  
Ion Hydration ◽  
Potential Energy Functions ◽  
Hydrogen Bond Networks ◽  
Correct Representation ◽  
Dynamics Simulations ◽  
Body Potential

<div> <div> <div> <p>Replica exchange molecular dynamics simulations and vibrational spectroscopy calculations are performed using halide-water many-body potential energy functions to provide a bottom-up analysis of the structures, energetics, and hydrogen-bonding arrangements in X−(H2O)n=3−6 clusters, with X = F, Cl, Br, and I. Independently of the cluster size, it is found that all four halides prefer surface-type structures in which they occupy one of the vertices in the underlying three-dimensional hydrogen-bond networks. For fluoride-water clusters, this is in contrast with previous reports suggesting that fluoride prefers interior-type arrangements, where the ion is fully hydrated. These differences can be ascribed to the variability in how various molecular models are capable to reproduce the subtle interplay between halide-water and water-water interactions. Our results thus emphasize the importance of a correct representation of individual many-body contributions to the molecular interactions for a quantitative description of halide ion hydration. </p> </div> </div> </div>

GOLD DEPOSITION ON GaAs(001) SURFACES: MOLECULAR-DYNAMICS SIMULATIONS

2002 ◽  
Vol 13 (06) ◽  
pp. 759-769 ◽  
Author(s):  
ŞAKIR ERKOÇ ◽  
LYNDA AMIROUCHE ◽  
LEILA ROUAIGUIA
Keyword(s):  
Molecular Dynamics ◽  
Gold Atom ◽  
Potential Energy Function ◽  
Gold Deposition ◽  
Many Body ◽  
Atomic Interactions ◽  
Dynamics Simulations ◽  
Three Body ◽  
Body Potential ◽  
Different Characteristics

We have simulated the gold deposition on arsenic and gallium terminated GaAs(001) surfaces at low and room temperatures. It has been found that gallium terminated surface is relatively less stable in comparison to the arsenic terminated surface. On the other hand, a single gold adatom on the surface has different characteristics than full coverage gold atoms on the surface; a single gold atom diffuses into the surface at room temperature. Simulations have been performed by considering classical molecular-dynamics technique using an empirical many-body potential energy function comprising two- and three-body atomic interactions.

Generalization of Tomonaga–Luttinger Liquids and the Calogero–Sutherland Model: Microscopic Models for the Haldane Liquids

1998 ◽  
Vol 12 (16) ◽  
pp. 607-614 ◽  
Author(s):  
Kazumoto Iguchi
Keyword(s):  
Fermi Surface ◽  
Higher Dimensions ◽  
One Dimension ◽  
Body System ◽  
Many Body ◽  
Luttinger Liquids ◽  
Microscopic Models ◽  
Sutherland Model ◽  
Body Potential

We discuss the quantum many-body system interacting with a separately symmetric two-body potential in higher dimensions as a generalization of the Calogero–Sutherland model in one dimension. This system exhibits the properties of a Haldane liquid such as Haldane–Wu (i.e., fractional exclusion) statistics, broken particle–hole symmetry and the existence of pseudo-Fermi surface as a generalization of the cencept of Tomonaga–Luttinger liquids in one dimension.

A lattice dynamical study of Cu and Ni based on a new empirical many-body potential

1995 ◽  
Vol 73 (3-4) ◽  
pp. 143-146 ◽  
Author(s):  
I. Akgün
Keyword(s):  
Potential Energy Function ◽  
Many Body ◽  
Dynamical Study ◽  
Dynamical Behaviors ◽  
Atomic Interactions ◽  
The Face ◽  
Experimental Values ◽  
Three Body ◽  
Body Potential ◽  
Good Agreement

In the present work, a recently developed empirical many-body potential-energy function (PEF) is first used, as an application, to investigate the dynamical behaviors of the face-centred-cube d-band metals, Cu and Ni. The new PEF contains both two- and three-body atomic interactions. The two-body potential is a kind of hybrid function and the three-body potential is expressed in terms of the two-body interactions. The parameters defining the PEF for the metals are computed following a procedure similar to a method given by Girifalco and Weizer. The input data for evaluating the necessary parameters are independent of the phonon frequencies and elastic constants of the metals. The phonon frequencies along the principal symmetry directions of Cu and Ni are calculated using the computed two- and three-body force constants. The results are found to be in good agreement with the corresponding experimental values.

EMPIRICAL MANY-BODY POTENTIAL ENERGY FUNCTION CALCULATION FOR LITHIUM CLUSTERS IN BCC AND FCC SURFACE SYMMETRIES, AND CHEMISORPTION ENERGY OF ATOMIC OXYGEN ON LITHIUM BCC CLUSTERS

1995 ◽  
Vol 10 (02) ◽  
pp. 125-131 ◽  
Author(s):  
NURI KOLSUZ ◽  
MEHMET ÇIVI ◽  
ŞAKIR ERKOÇ
Keyword(s):  
Potential Energy ◽  
Energy Function ◽  
Potential Energy Function ◽  
Many Body ◽  
Atomic Interactions ◽  
Function Calculation ◽  
Three Body ◽  
Body Potential ◽  
Lithium Clusters ◽  
Chemisorption Energy

We have investigated the structure and energetics of lithium clusters containing 3 to 10 atoms in different bcc and fcc surface symmetries, and the interaction of an oxygen atom with lithium clusters in the bcc(100) and bcc(110) surface symmetries. Calculations have been performed by using an empirical many-body potential energy function, which comprises two- and three-body atomic interactions.

Halide Ion Micro-Hydration: Structure, Energetics, and Spectroscopy of Small Halide–Water Clusters

2019 ◽  
Author(s):  
Pushp Bajaj ◽  
Marc Riera ◽  
Jason K. Lin ◽  
Yaira E. Mendoza Montijo ◽  
Jessica Gazca ◽  
...  
Keyword(s):  
Water Clusters ◽  
Quantitative Description ◽  
Three Dimensional ◽  
Many Body ◽  
Ion Hydration ◽  
Potential Energy Functions ◽  
Hydrogen Bond Networks ◽  
Correct Representation ◽  
Dynamics Simulations ◽  
Body Potential

<div> <div> <div> <p>Replica exchange molecular dynamics simulations and vibrational spectroscopy calculations are performed using halide-water many-body potential energy functions to provide a bottom-up analysis of the structures, energetics, and hydrogen-bonding arrangements in X−(H2O)n=3−6 clusters, with X = F, Cl, Br, and I. Independently of the cluster size, it is found that all four halides prefer surface-type structures in which they occupy one of the vertices in the underlying three-dimensional hydrogen-bond networks. For fluoride-water clusters, this is in contrast with previous reports suggesting that fluoride prefers interior-type arrangements, where the ion is fully hydrated. These differences can be ascribed to the variability in how various molecular models are capable to reproduce the subtle interplay between halide-water and water-water interactions. Our results thus emphasize the importance of a correct representation of individual many-body contributions to the molecular interactions for a quantitative description of halide ion hydration. </p> </div> </div> </div>

Implications of many-body forces for equations of state at high pressure

1992 ◽  
Vol 339 (1654) ◽  
pp. 395-402 ◽  
Keyword(s):  
High Pressure ◽  
Equations Of State ◽  
Closed Shell ◽  
Molecular Orbital Calculations ◽  
Many Body ◽  
Detonation Products ◽  
Body Forces ◽  
Three Body ◽  
Body Potential ◽  
Many Body Interactions

In this paper we review our recent work concerned with assessing the significance of many-body forces for short-range interactions of closed shell atoms and molecules. Ab initio molecular orbital calculations (of the supermolecule type) have been carried out to determine three-body potentials for the following species: He, Ne, H 2 , N 2 , CO and CO 2 . For He, Ne, H 2 and N 2 we have also carried out calculations of the four-body potential for a limited number of orientations. These studies show that, for all these species, there are significant deviations from pair-wise additivity at short separations. The effect of these many-body interactions on the equation of state for dense fluids (such as detonation products) is being investigated by Monte Carlo simulation, and recent results for high-pressure helium are described.

Massively Parallel Molecular Dynamics and Simulations for Many-Body Potentials

1995 ◽  
Vol 408 ◽  
Author(s):  
L. T. Wille ◽  
C. F. Cornwell ◽  
W. C. Morrey
Keyword(s):  
Molecular Dynamics ◽  
Complexity Analysis ◽  
Many Body ◽  
Multiple Data ◽  
Parallel Molecular Dynamics ◽  
Dynamics Simulations ◽  
Three Body ◽  
Body Potential ◽  
Specific Timing ◽  
General Time

AbstractWe discuss the implementation of classical molecular dynamics simulations on Single- Instruction Multiple-Data computers with two-dimensional mesh connectivity. Specific timing results are given for the MasPar MP-1, complemented by a general time complexity analysis. Our main interest is in simulations with a number of particles N that is comparable to the number of processors P. In particular, we discuss results for large Si-clusters with up to 2000 particles, using a Stillinger-Weber potential. Particular attention is paid to the problem of handling in an efficient way the calculation of the three-body potential and force.

REPRESENTATION OF THE PAIRED INTERACTION POTENTIAL IN THE FORM OF MULTIDIMENSIONAL RATIONAL SERIES IN JACOBI VARIABLES FOR MANY-BODY PROBLEMS

2021 ◽  
Vol 0 (4) ◽  
pp. 9-15
Author(s):  
R.F. AKHMETYANOV ◽  
◽  
E.S. SHIKHOVTSEVA ◽  
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Many Body ◽  
Power Functions ◽  
Spatial Variables ◽  
Physical Problems ◽  
Rational Series ◽  
T Matrix ◽  
Three Body ◽  
Three Dimensional Space

Scalar power functions of the form x1 + + xN -v Î are in some cases found in physical problems and applications, especially in many-body problems with paired interactions. There are known decompositions for two vectors in three-dimensional space. In this paper, we consider analogous decompositions with any number of N arbitrary M-dimensional vectors in Euclidean space as a product of a multidimensional rational series with respect to spatial variables and hyperspheric functions on the unit sphere SM-1. Such an advantage of expansion arises in three-body problems when solving the Faddeev equation, where it is known that the main problem is the approximate choice of approximation of interaction potentials, in which the t-matrix scattering elements acquired a separable form.

ENERGETICS OF ARSENIC TERMINATED GaAs(001) SURFACES

2000 ◽  
Vol 11 (06) ◽  
pp. 1225-1237 ◽  
Author(s):  
ŞAKIR ERKOÇ ◽  
HATICE KÖKTEN
Keyword(s):  
Potential Energy ◽  
Energy Function ◽  
Potential Energy Function ◽  
Many Body ◽  
Surface Energies ◽  
Atomic Interactions ◽  
Surface Models ◽  
Three Body ◽  
Body Potential

We have investigated systematically the energetics of arsenic terminated GaAs(001) surfaces. Available surface models proposed in the literature have been considered, and relaxation and surface energies of each model have been calculated using an empirical many-body potential energy function comprising two and three-body atomic interactions.

Sign in / Sign up

Export Citation Format

Share Document