Quantum thermodynamics of solids by means of an effective potential

Cuccoli, Alessandro; Macchi, Alessandro; Neumann, Martin; Tognetti, V.; Vaia, Ruggero

doi:10.1103/physrevb.45.2088

Cited by 53 publications

(21 citation statements)

References 27 publications

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“…For example, the isotopic-mass dependence of the molar volume can be described well from this kind of simulations 21,77 . Moreover, in this context, several authors developed effective (temperature-dependent) classical potentials that reproduce accurately various properties of quantum solids [103][104][105] . Thus, Acocella et al 106 applied an improved effective-potential Monte Carlo theory 107 to study thermal and elastic properties of noble-gas solids.…”

Section: B Heavier Elementsmentioning

confidence: 99%

Path-integral simulation of solids

Herrero

Ramı́rez

2014

J. Phys.: Condens. Matter

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The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practical techniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron-phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity.

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Section: B Heavier Elementsmentioning

confidence: 99%

Path-integral simulation of solids

Herrero

Ramı́rez

2014

J. Phys.: Condens. Matter

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“…The description of the PIECP method can be found in the literatures [14,15] and is summarized here briefly. According to the Feynman ′ s path-integral theory [11,12], the density matrix ρ(R) (R is the 3N -dimensional Cartesian coordinate and N is the number of atoms) is given by the path integral form using the quantum-mechanical real-space representation as…”

Section: A Piecp Methodsmentioning

confidence: 99%

“…For the one-dimensional system, no further approximation is required, while in the multidimensional system like solids (N ∼10 23 ) the quantum fluctuation integrals should be separated out. Here we should come closer to the harmonic approximation, which is the so-called low coupling approximation [14,15]. This approximation consequently assumes that the variational parameters of w and ω k,µ are independent ofR.…”

Section: A[r(u)] Is the Euclidean Action Such Thatmentioning

confidence: 99%

“…The PIECP method is based on the variational path integral theory and assumes a trial Euclidean action A 0 [R(u)] with some variational parameters [14,15]. Since the present purpose is a description of anharmonic vibrational properties of solids, the harmonic approximation such that…”

Section: A[r(u)] Is the Euclidean Action Such Thatmentioning

confidence: 99%

“…It is, however, by far more complicated than the perturbation method and might not be a good candidate for practical applications to EXAFS of complicated systems with many degrees of freedom. The pathintegral effective-classical-potential (PIECP) method has thus been developed to solve the path integral approximately by means of the variational concept [14,15]. Fujikawa et al [16] have applied the PIECP theory to EX-AFS for the first time.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Path Integral Effective Classical Potential Method Applied to Anharmonicity and Quantum Effects in Thermal Expansion of Invar Alloy

Yokoyama

2012

e-J. Surf. Sci. Nanotechnol.

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Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy is a powerful experimental technique to investigate anharmonic vibrational properties of solids especially when one combines experimental EXAFS with quantum mechanical theoretical evaluations. In this article, the path-integral effective-classical-potential (PIECP) theory is applied to temperature dependence of EXAFS in a real system. The anharmonicity and quantum effects in the Invar alloy Fe64.6Ni35.4 that shows anomalously small thermal expansion are investigated. Experimental Fe and Ni K-edge EXAFS measurements and the computational PIECP simulations have been performed. It is experimentally revealed that the first nearest-neighbor (NN) shells around Fe show almost no thermal expansion, while those around Ni exhibit meaningful but smaller expansion than that of fcc Ni. At low temperature (<100 K), the vibrational quantum effect is found to play an essentially important role, which is confirmed by comparing the quantum mechanical simulations to the classical ones, the latter of which exhibit large (normal) thermal expansion at low temperature. It is also clarified that thermal expansion for the Ni-Ni and Ni-Fe pairs is noticeably suppressed, even though the Ni electronic state may not vary depending on the temperature. On the other hand, the anharmonicity (asymmetric distribution) clearly exist for all the first-NN shells as in the case of the normal thermal expansion system, where thermal expansion originates almost exclusively from the anharmonic interatomic potential.

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Path‐Integral Centroid Methods in Quantum Statistical Mechanics and Dynamics

Voth

1996

Advances in Chemical Physics

169

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Quantum thermodynamics of solids by means of an effective potential

Cited by 53 publications

References 27 publications

Path-integral simulation of solids

Path-integral simulation of solids

Path Integral Effective Classical Potential Method Applied to Anharmonicity and Quantum Effects in Thermal Expansion of Invar Alloy

Path‐Integral Centroid Methods in Quantum Statistical Mechanics and Dynamics

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