Quantum Notions of Stress

Maranganti, R.; Sharma, Pradeep; Wheeler, Lewis

doi:10.1061/(asce)0893-1321(2007)20:1(22)

Cited by 21 publications

(20 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The reader is referred to Maranganti et al (2007) and references therein for further discussion. It remains to be seen whether the non-uniqueness of the quantum-mechanical stress is of any physical consequence.…”

Section: Discussionmentioning

confidence: 99%

“…The derivation follows the same methodology as that given for the virial theorem by Fock (1930; see also Nielsen & Martin (1985) and our review article Maranganti et al (2007)). First, we consider a many-body Hamiltonian of the form where V := V int + V ext denotes the potential energy of the whole system; it is a function of the positions of all the particles.…”

Section: ) (C) Macroscopic Stress In Quantum Mechanicsmentioning

confidence: 99%

See 1 more Smart Citation

Revisiting quantum notions of stress

Maranganti

Sharma

2010

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: ) (C) Macroscopic Stress In Quantum Mechanicsmentioning

confidence: 99%

Revisiting quantum notions of stress

Maranganti

Sharma

2010

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Finally, it should be stressed that GBP kinetic energy density up to a factor coincides with a trace of the so-called Schr€ odinger-Pauli kinetic stress tensor, [125][126][127][128]…”

Section: Appendix A: Electron Localization Local Electronic Momentummentioning

confidence: 99%

Spatially resolved characterization of electron localization and delocalization in molecules: Extending the Kohn‐Resta approach

Astakhov

Tsirelson

2018

Int J of Quantum Chemistry

View full text Add to dashboard Cite

In this work, the electron organization of many‐electron systems is considered in a context of the linear response theory extending the Kohn‐Resta view on electron localization phenomenon. The variances of the local electronic position and momentum operators are linked via the fluctuation‐dissipation theorem to the optical conductivity tensor, that is, to observable spectroscopic properties. It is demonstrated that the electron position variance density quantifies a degree of electron delocalization in each point of position space and distinguishes between metallic and insulating character of electronic states. The momentum variance density estimates a degree of electron localization and is immediately related to electronic kinetic energy density in the Ghosh‐Berkowitz‐Parr form giving a physical interpretation to the later. We show that electron localization and delocalization phenomena in atoms and molecules can be probed by external electric field. This approach provides new electronic descriptors distinguishing and quantifying chemical bonds of different types.

show abstract

“…There are many different definitions of the 'quantum' local stress tensor that are compatible with the correspondence principle [24][25][26][27][28], but Eq. (1) is the most common choice in the literature, and is one of several choices that leads to a particularly simple form of the differential virial theorem [1,2],…”

Section: Introductionmentioning

confidence: 98%