Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “PATH INTEGRALS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Path integral Liouville dynamics: Applications to infrared spectra of OH, water, ammonia, and methane

Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals

Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

High-order sampling schemes for path integrals and Gaussian chain simulations of polymers

In this work, we demonstrate that path-integral schemes, derived in the context of many-body quantum systems, benefit the simulation of Gaussian chains representing polymers. Specifically, we show how to decrease discretization corrections with little extra computation from the usual O(1/P{sup 2}) to O(1/P{sup 4}), where P is the number of beads representing the chains. As a consequence, high-order integrators necessitate much smaller P than those commonly used. Particular emphasis is placed on the questions of how to maintain this rate of convergence for open polymers and for polymers confined by a hard wall as well as how to ensure efficient sampling. The advantages of the high-order sampling schemes are illustrated by studying the surface tension of a polymer melt and the interface tension in a binary homopolymers blend.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Maximally-localized position, Euclidean path-integral, and thermodynamics in GUP quantum mechanics

In dealing with quantum mechanics at very high energies, it is essential to adapt to a quasiposition representation using the maximally-localized states because of the generalized uncertainty principle. In this paper, we look at maximally-localized states as eigenstates of the operator ξ=X+iβP that we refer to as the maximally-localized position. We calculate the overlap between maximally-localized states and show that the identity operator can be expressed in terms of the maximally-localized states. Furthermore, we show that the maximally-localized position is diagonal in momentum-space and that the maximally-localized position and its adjoint satisfy commutation and anti-commutation relations reminiscent of the harmonic oscillator commutation and anti-commutation relations. As application, we use the maximally-localized position in developing the Euclidean path-integral and introduce the compact form of the propagator for maximal localization. The free particle momentum-space propagator and the propagator for maximal localization are analytically evaluated up to quadratic-order in β. Finally, we obtain a path-integral expression for the partition function of a thermodynamic system using the maximally-localized states. The partition function of a gas of noninteracting particles is evaluated. At temperatures exceeding the Planck energy, we obtain the gas’ maximum internal energy N∕2β and recover the zero heat capacity of an ideal gas.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A path integral ground state Monte Carlo algorithm for entanglement of lattice bosons

A ground state path integral quantum Monte Carlo algorithm is introduced that allows for the study of entanglement in lattice bosons at zero temperature. The Rényi entanglement entropy between spatial subregions is explored across the phase diagram of the one dimensional Bose-Hubbard model for systems consisting of up to L=256 L = 256 sites at unit-filling without any restrictions on site occupancy, far beyond the reach of exact diagonalization. The favorable scaling of the algorithm is demonstrated through a further measurement of the Rényi entanglement entropy at the two dimensional superfluid-insulator critical point for large system sizes, confirming the existence of the expected entanglement boundary law in the ground state. The Rényi estimator is extended to measure the symmetry resolved entanglement that is operationally accessible as a resource for experimentally relevant lattice gases with fixed total particle number.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Pairwise connected tensor network representation of path integrals

It has been recently shown how the tensorial nature of real-time path integrals (PIs) involving the Feynman-Vernon influence functional can be utilized with matrix product states, taking advantage of the finite length of the bath-induced memory. Tensor networks (TNs) promise to provide a unified language to express the structure of a PI. A generalized TN specifically incorporating the pairwise interaction structure of the influence functional and its invariance with respect to the average forward-backward position or the sojourn value in the form of the blip representation is derived and implemented. This pairwise connected TNPI (PC-TNPI) is illustrated through applications to typical spin-boson problems and explorations of the differences caused by the exact form of the spectral density. The storage and performance scalings are reported, showing the compactness of the representation and the efficiency of the contraction process. Finally, taking advantage of the compressed representation, the viability of using PC-TNPI for simulating multistate problems is demonstrated. The PC-TNPI structure can be shown to yield other TN algorithms currently in use. Consequently, it should be possible to use it as a starting point for deriving other optimized procedures.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Path integral Monte Carlo calculation of the momentum distribution of the homogeneous electron gas at finite temperature

Path integral Monte Carlo (PIMC) simulations are employed to calculate the momentum distribution of the homogeneous electron gas at finite temperature. Open paths are introduced to sample off-diagonal elements of the real-space density matrix. Here it is demonstrated how the restricted PIMC method can be extended to incorporate open paths in order to allow for the simulations in fermionic systems where a sign problem is present. The computed momentum distribution shows significant deviations from behavior of free fermions when strong correlations are present but agrees with predictions from variational methods.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Hollow-grams: generalized entanglement wedges from the gravitational path integral

Recently, Bousso and Penington (BP) made a proposal for the entanglement wedge associated to a gravitating bulk region. In this paper, we derive this proposal in time-reflection symmetric settings using the gravitational path integral. To do this, we exploit the connection between random tensor networks (RTNs) and fixed-geometry states in gravity. We define the entropy of a bulk region in an RTN by removing tensors in that region and computing the entropy of the open legs thus generated in the “hollowed” RTN. We thus derive the BP proposal for RTNs and hence, also for fixed-geometry states in gravity. By then expressing a general holographic state as a superposition over fixed-geometry states and using a diagonal approximation, we provide a general gravitational path integral derivation of the BP proposal. We demonstrate that the saddles computing the Rényi entropy Sn depend on how the bulk region is gauge-invariantly specified. Nevertheless, we show that the BP proposal is universally reproduced in the n → 1 limit.

2D Gravity↗
DOE OSTI2026

Path-integral predictions for preasymptotic quantum tunneling

When tunneling occurs out of generic initial states, a significant fraction of probability is lost at early times, during which the dynamics is governed by excited resonance states. However, first-principles analyses based on path-integrals have only captured the leading asymptotic behavior, during which the tunneling rate is dominated by the false vacuum contribution. In this work, we discuss the behavior in the preasymptotic regime from a first-principles path-integral perspective. We demonstrate how the relevant expressions can be evaluated systematically through semiclassical methods in the recently developed steadyon picture. This approach allows one to trace the role of the relevant physical scales, making transparent the underlying assumptions and approximations, and offering a clear path to establishing a systematically improvable framework to evaluate tunneling rates nonperturbatively.

Lin, Joshua↗
DOE OSTI2014

Path-integral calculation of the second virial coefficient including intramolecular flexibility effects

We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H{sub 2}) and deuterium (D{sub 2}) in the temperature range 15–2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H{sub 2} between 100 and 200 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Iterative quantum-classical path integral with dynamically consistent state hopping

We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Path integral games with de Sitter α-vacua

The α-vacua are a 1-parameter family of quantum field vacua in de Sitter space which are invariant under the isometry group SO(1, d). In this work give a path integral construction of the de Sitter α-vacua. We explain that these states can be prepared by acting on the Bunch-Davies vacuum with a certain non-local charge operator. While most conserved charges live on a single codimension-1 manifold, we show that this particular charge lives on a pair of two codimension-1 manifolds which are antipodal mirrors of each other. The rules for the manipulation of this charge as an insertion in the path integral are explained. We further explain how this charge can be used to solve for the wavefunctionals of the α-vacua at $\mathcal{I}$ | (in the regime that α is small) by deforming the equator of de Sitter space to $\mathcal{I}$ + /$\mathcal{I}$ – .

Global Symmetries↗
DOE OSTI2026

Thermophysical Properties of Liquid Tritium: A Path Integral Monte Carlo Study

Here, we present worm-algorithm, path integral Monte Carlo simulations of bulk liquid tritium. The simulations are benchmarked against empirically known thermophysical properties of liquid deuterium and liquid tritium. Results for the pair correlation function, chemical potential, isothermal compressibility, isochoric heat capacity, and single-particle momentum distributions are reported. Given the benchmark comparisons, our predictions of liquid tritium properties are expected to be accurate to within a few percent. Our simulations unambiguously demonstrate the significance of nuclear quantum effects to the properties of liquid tritium. In particular, under saturated vapor pressure, the average molecular kinetic energy of the liquid is found to be more than 60% higher than the value expected from the classical equipartition theorem.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Direct path integral estimators for isotope fractionation ratios

Fractionation of isotopes among distinct molecules or phases is a quantum effect which is often exploited to obtain insights on reaction mechanisms, biochemical, geochemical, and atmospheric phenomena. Accurate evaluation of isotope ratios in atomistic simulations is challenging, because one needs to perform a thermodynamic integration with respect to the isotope mass, along with time-consuming path integral calculations. By re-formulating the problem as a particle exchange in the ring polymer partition function, we derive new estimators giving direct access to the differential partitioning of isotopes, which can simplify the calculations by avoiding thermodynamic integration. We demonstrate the efficiency of these estimators by applying them to investigate the isotope fractionation ratios in the gas-phase Zundel cation, and in a few simple hydrocarbons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Simulating signatures of two-dimensional electronic spectra of the Fenna-Matthews-Olson complex: By using a numerical path integral

A framework for simulating electronic spectra from photon-echo experiments is constructed by using a numerical path integral technique. This method is non-Markovian and nonperturbative and, more importantly, is not limited by a fixed form of the spectral density functions of the environment. Next, a two-dimensional (2D) third-order electronic spectrum of a dimer system is simulated. The spectrum is in agreement with the experimental and theoretical results previously reported [for example, M. Khalil, N. Demirdöven, and A. Tokmakoff, Phys. Rev. Lett. 90, 047401 (2003)]. Finally, a 2D third-order electronic spectrum of the Fenna-Matthews-Olson (FMO) complex is simulated by using the Debye, Ohmic, and Adolphs and Renger spectral density functions. It is shown that this method can clearly produce the spectral signatures of the FMO complex by using only the Adolphs and Renger spectral density function. Plots of the evolution of the diagonal and cross-peaks show that they are oscillating with the population time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Quantum partition functions of composite particles in a hydrogen-helium plasma via path integral Monte Carlo

We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H{sup −}, H{sub 2}{sup +}, and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A path-integral approach to the problem of time

Quantum transition amplitudes are formulated for model systems with local internal time, using intuition from path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing canonical treatments. In particular, a successful transition through a turning point is provided in the model systems, together with a new definition of such a transition in general terms. Some of the results rely on a fruitful relation between the problem of time and general Gribov problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

An analysis of quantum effects on the thermodynamic properties of cryogenic hydrogen using the path integral method

In this paper, we describe the analysis of the thermodynamic properties of cryogenic hydrogen using classical molecular dynamics (MD) and path integral MD (PIMD) method to understand the effects of the quantum nature of hydrogen molecules. We performed constant NVE MD simulations across a wide density–temperature region to establish an equation of state (EOS). Moreover, the quantum effect on the difference of molecular mechanism of pressure–volume–temperature relationship was addressed. The EOS was derived based on the classical mechanism idea only using the MD simulation results. Simulation results were compared with each MD method and experimental data. As a result, it was confirmed that although the EOS on the basis of classical MD cannot reproduce the experimental data of saturation property of hydrogen in the high-density region, the EOS on the basis of PIMD well reproduces those thermodynamic properties of hydrogen. Moreover, it was clarified that taking quantum effects into account makes the repulsion force larger and the potential well shallower. Because of this mechanism, the intermolecular interaction of hydrogen molecules diminishes and the virial pressure increases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗