Theory and applications of the stress density

Filippetti, Alessio; Fiorentini, Vincenzo

doi:10.1103/physrevb.61.8433

Cited by 143 publications

(97 citation statements)

References 42 publications

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“…The contribution of the exchange-correlation energy to the stress field is only in the diagonal (pressure-like) terms, which is the proper behavior for local density functionals 14 and is identical to the exchange-correlation stress derived in Ref. 21.…”

Section: The Dft Stress Fieldsupporting

confidence: 66%

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Geometric formulation of quantum stress fields

2002

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We present a derivation of the stress field for an interacting quantum system within the framework of local density functional theory. The formulation is geometric in nature and exploits the relationship between the strain tensor field and Riemannian metric tensor field. Within this formulation, we demonstrate that the stress field is unique up to a single ambiguous parameter. The ambiguity is due to the non-unique dependence of the kinetic energy on the metric tensor. To illustrate this formalism, we compute the pressure field for two phases of solid molecular hydrogen. Furthermore, we demonstrate that qualitative results obtained by interpreting the hydrogen pressure field are not influenced by the presence of the kinetic ambiguity. 03.65.-w, 62.20.-x, 02.40.-k, 71.10.-w Typeset using REVT E X 1

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Section: The Dft Stress Fieldsupporting

confidence: 66%

“…Coulombic term can be obtained by Filippetti and Fiorentini's formalism if one chooses the so-called Maxwell gauge 21 . We emphasize that it has been mathematically proven in the gravitational literature that the usual energy-momentum tensor for electromagnetism is unique [39][40][41] .…”

Section: The Dft Stress Fieldmentioning

confidence: 99%

Geometric formulation of quantum stress fields

2002

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“…Spatial variations in the planar stress can provide an insight into the forces operating in systems that are not in equilibrium (Nielsen & Martin 1985). Filippetti & Fiorentini (1999, 2000 envision using the microscopic stress as what they refer to as a stress microscope to examine the stress's role in explaining the physics of certain surface and interface phenomena. Ramer et al (1998) applied the microscopic stress field to study piezoelectric effects in perovskites.…”

Section: Stress As a Microscopic Fieldmentioning

confidence: 99%

Revisiting quantum notions of stress

Maranganti

Sharma

2010

Proc. R. Soc. A.

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An important aspect of multi-scale modelling of materials is to link continuum concepts, such as fields, to the underlying discrete microscopic behaviour in a seamless manner. With the growing importance of atomistic calculations to understand material behaviour, reconciling continuum and discrete concepts is necessary to interpret molecular and quantum-mechanical simulations. In this work, we provide a quantum-mechanical framework to a distinctly continuum quantity: mechanical stress. While the concept of the global macroscopic stress tensor in quantum mechanics has been well established, there still exist open issues when it comes to a spatially varying local quantum stress tensor. We attempt to shed some light on this topic by establishing a general quantummechanical operator-based approach to continuity equations and from those, introduce a local quantum-mechanical stress tensor. Further, we elucidate the analogies that exist between the (classical) molecular-dynamics-based stress definition and the quantum stress. Our derivations appear to suggest that the local quantum-mechanical stress may not be an observable in quantum mechanics and therefore traces the non-uniqueness of the atomistic stress tensor to the gauge arbitrariness of the quantum-mechanical state function. Lastly, the virial stress theorem (of empirical molecular dynamics) is re-derived in a transparent manner that elucidates the analogy between quantum-mechanical global stresses.

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“…This perspective has been revived many times. The publications [6][7][8][9][10] are representative of the questions that have been addressed periodically, but there have been many other significant contributions, such as those of Clausius, Maxwell, Born & Huang, Irving & Kirkwood, Noll, Tsai, Hardy, and Murdoch. There is a need to unify the atomistic basis of stress if the concept, itself, is to survive as a rational fundamental element of importance in small-scale modeling.…”

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confidence: 98%