Three-Particle Effects in the Pair Distribution Function for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>Gas

Jordan, Harry F.; Fosdick, Lloyd D.

doi:10.1103/physrev.171.128

Cited by 81 publications

(44 citation statements)

References 19 publications

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“…The above is known as the primitive approximation. Within this scheme, the partition function becomes [30][31][32][33][34] Equation 3 is the discrete path integral expression for the quantum canonical partition function in the primitive approximation. It is written for N distinguishable particles in three dimensions which is relevant in this paper, but can easily be extended to N indistinguishable particles in arbitrary dimensions.…”

Section: Path Integral Monte Carlomentioning

confidence: 99%

Global Optimization: Quantum Thermal Annealing with Path Integral Monte Carlo

Lee

Berne

1999

J. Phys. Chem. A

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We investigate a new method (QTA-PIMC) for global optimization on complex potential energy surfaces which combines the path integral Monte Carlo method with quantum and thermal annealing. This method is applied to the BLN protein model (Honeycutt, J. D.; Thirumalai, D. Biopolymers 1992, 32, 695). We show that this new approach outperforms simulated (thermal) annealing (SA) and that in fact SA is a subset of our method. This means that we could invoke the effects of both quantum and/or thermal annealing in the global optimization process, hence the name quantum thermal annealing (QTA-PIMC). The simulation results also suggest that QTA-PIMC scales better than SA in terms of system size in the search for the global minimum.

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Section: Path Integral Monte Carlomentioning

confidence: 99%

Global Optimization: Quantum Thermal Annealing with Path Integral Monte Carlo

Lee

Berne

1999

J. Phys. Chem. A

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“…We mention in passing that several alternative routes such as various semiclassical approaches [5][6][7][8] or quantum mode-coupling theory 9 have been successfully used to study quantum dynamics of large systems. Numerical PI simulation techniques [10][11][12] are based on the isomorphism 13 between the quantum partition function, represented as an imaginary time PI ͑Refs. 3, 4, 14, and 15͒ and the classical configurational integral of a system of interacting "ring polymers" subject to specific harmonic nearest neighbor interactions.…”

Section: Introductionmentioning

confidence: 99%

On the applicability of centroid and ring polymer path integral molecular dynamics for vibrational spectroscopy

Witt¹,

Ivanov²,

Shiga³

et al. 2009

The Journal of Chemical Physics

222

260

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Centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) are two conceptually distinct extensions of path integral molecular dynamics that are able to generate approximate quantum dynamics of complex molecular systems. Both methods can be used to compute quasiclassical time correlation functions which have direct application in molecular spectroscopy; in particular, to infrared spectroscopy via dipole autocorrelation functions. The performance of both methods for computing vibrational spectra of several simple but representative molecular model systems is investigated systematically as a function of temperature and isotopic substitution. In this context both CMD and RPMD feature intrinsic problems which are quantified and investigated in detail. Based on the obtained results guidelines for using CMD and RPMD to compute infrared spectra of molecular systems are provided.

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“…Our method extends the well known techniques for quantum models with distinguishable particles [1][2][3][4][5][6] to quantum models with identical particles, in such a way that the so-called "sign problem" [7][8][9][10] for fermions is solved, and that for bosons and fermions sample paths over configurations [11][12][13][14][15]8] generated by the permutation symmetry are avoided. This opens the perspective that with the proper algorithms the new process would improve the standard approach [16][17][18][19][20][21][22] used in path integral Monte Carlo for fermions as well as for bosons.…”

Section: Introductionmentioning

confidence: 99%

Many-body diffusion and path integrals for identical particles

1996

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For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical particles, we exploit the fact that this method separates the problem of the potential, dealt with by the Feynman-Kac functional, from the process which gives sample paths of a non-interacting system. For motion in 1 dimension, we emphasize that the permutation symmetry of the identical particles completely determines the domain of Brownian motion and the appropriate boundary conditions: absorption for fermions, reflection for bosons. Further analysis of the sample paths for motion in 3 dimensions allows us to decompose these paths into a superposition of 1-dimensional sample paths. This reduction expresses the propagator (and consequently the energy and other thermodynamical quantities) in terms of well-behaved 1-dimensional fermion and boson diffusion processes and the Feynman-Kac functional.

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Three-Particle Effects in the Pair Distribution Function forHe4Gas

Cited by 81 publications

References 19 publications

Global Optimization: Quantum Thermal Annealing with Path Integral Monte Carlo

Global Optimization: Quantum Thermal Annealing with Path Integral Monte Carlo

On the applicability of centroid and ring polymer path integral molecular dynamics for vibrational spectroscopy

Many-body diffusion and path integrals for identical particles

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