Exact and asymptotic local virial theorems for finite fermionic systems

Brack, Matthias; Koch, Andreas; Murthy, M. V. N.; Roccia, Jérôme

doi:10.1088/1751-8113/43/25/255204

Cited by 6 publications

(20 citation statements)

References 52 publications

(245 reference statements)

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“…Note that in the derivation of (16) we have used that Av belongs to the domain of H. This is not a restriction if H is defined in the whole Hilbert space, but in many occasions the self-adjoint Hamiltonian has a domain that is only dense in H and if A does not preserve this domain, extra boundary terms should be added to the standard Ehrenfest theorem, see refs. [49]- [51] where the occurrence of this kind of anomaly in quantum mechanics has been studied.…”

Section: The Virial Theorem In Quantum Mechanicsmentioning

confidence: 99%

A geometric approach to a generalized virial theorem

Cariñena¹,

Falceto²,

Rañada³

2012

J. Phys. A: Math. Theor.

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The virial theorem, introduced by Clausius in statistical mechanics, and later applied in both classical mechanics and quantum mechanics, is studied by making use of symplectic formalism as an approach in the case of both the Hamiltonian and Lagrangian systems. The possibility of establishing virial's like theorems from oneparameter groups of non-strictly canonical transformations is analysed; and the case of systems with a position dependent mass is also discussed. Using the modern symplectic approach to quantum mechanics we arrive at the quantum virial theorem in full analogy with the classical case.The virial theorem was originally introduced in classical statistical mechanics (that was the original matter studied by Clausius) but later became important in many other different branches of physics. The quantum mechanical version of the theorem is due to Born, Heisenberg, and Jordan [3] and presently it is a tool frequently used in many body quantum mechanics (e.g. systems of fermions) and in molecular physics; in addition, this matter has also been related to certain fundamental questions arising in nonrelativistic quantum mechanics as the Hellmann-Feynman theorem (see [4]-[18] and references therein). We also mention the importance of the virial theorem in solar and stellar astrophysics [19]. The important point therefore is the wide range of applicability of the virial theorem with applications ranging from dynamical (even relativistic) and thermodynamical systems, to the dust and gas of interstellar space, as well as cosmological considerations of the universe as a whole and in other discussions concerning the stability of clusters, galaxies and clusters of

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Section: The Virial Theorem In Quantum Mechanicsmentioning

confidence: 99%

A geometric approach to a generalized virial theorem

Cariñena¹,

Falceto²,

Rañada³

2012

J. Phys. A: Math. Theor.

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“…This theorem has been generalised for the specific case of isotropic harmonic oscillator potential in d dimensions. 24 Moreover, this theorem has been extended for the case of a linear potential in d dimensions. 24,26 Let us return to Eq.…”

Section: Local Virial Theoremmentioning

confidence: 99%

“…24 Moreover, this theorem has been extended for the case of a linear potential in d dimensions. 24,26 Let us return to Eq. ( 54) and take the partial derivative of both sides with respect to z, leading to…”

Section: Local Virial Theoremmentioning

confidence: 99%

Airy gas model: From three to reduced dimensions

Bencheikh,

Putaja,

Rasanen

2020

Preprint

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We derive explicit expressions for the edge particle density and the corresponding kinetic energy density (KED) of the Airy gas model in d dimensions (d=1,2,3). The densities are shown to obey the local virial theorem. We obtain a functional relationship between the positive KED and the particle density and its gradients in d dimensions. We analyze the results inside the bulk as a limit of the local-density approximation. We show that in this limit the KED functional reduces to that of the Thomas-Fermi model in d dimensions.

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“…Also, a local version of the virial theorem for systems of fermions has recently been formulated (see Refs. [12,13]). Another kind of generalization is the hypervirial theorem [14] that works, in principle, for any operator G and can be written ψ n |[H,G]ψ n = 0.…”

Section: Introductionmentioning

confidence: 99%

“…Also recently it has been formulated a local version of the virial theorem for systems of fermions, see refs. [12] and [13].…”

Section: Introductionmentioning

confidence: 99%