The Experts below are selected from a list of 258 Experts worldwide ranked by ideXlab platform
Francisco M Fernandez - One of the best experts on this subject based on the ideXlab platform.
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on the hellmann Feynman Theorem for degenerate states
arXiv: Quantum Physics, 2019Co-Authors: Francisco M FernandezAbstract:In this paper we discuss the validity of the Hellmann-Feynman Theorem (HFT) for degenerate states. We derive it in a general way and apply it to simple illustrative examples. We also analyze a recent paper that shows results that apparently suggest that the HFT does not apply to degenerate states.
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The Hellmann–Feynman Theorem for statistical averages
Journal of Mathematical Chemistry, 2014Co-Authors: Francisco M FernandezAbstract:We discuss the Hellmann–Feynman Theorem for degenerate states and its application to the calculation of the derivatives of statistical averages with respect to external parameters.
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the hellmann Feynman Theorem for statistical averages
Journal of Mathematical Chemistry, 2014Co-Authors: Francisco M FernandezAbstract:We discuss the Hellmann–Feynman Theorem for degenerate states and its application to the calculation of the derivatives of statistical averages with respect to external parameters.
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comment on breakdown of the hellmann Feynman Theorem degeneracy is the key
Physical Review B, 2004Co-Authors: Francisco M FernandezAbstract:We show that the Hellmann-Feynman Theorem is valid for degenerate states provided that they are chosen to satisfy a simple criterion that removes a recently discussed ambiguity.
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the extended hellmann Feynman Theorem revisited
Chemical Physics Letters, 1995Co-Authors: Francisco M FernandezAbstract:Abstract We give a simpler, shorter and more general proof of the extended Hellmann-Feynman Theorem commonly applied to the calculation of forces between classical and quantal particles.
A R Plastino - One of the best experts on this subject based on the ideXlab platform.
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fisher information the hellmann Feynman Theorem and the jaynes reciprocity relations
Annals of Physics, 2011Co-Authors: Silvana Flego, A Plastino, A R PlastinoAbstract:Abstract We explore intriguing links connecting Hellmann–Feynman’s Theorem to a thermodynamics information-optimizing principle based on Fisher’s information measure.
N H March - One of the best experts on this subject based on the ideXlab platform.
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comment on breakdown of the hellmann Feynman Theorem degeneracy is the key
Physical Review B, 2004Co-Authors: Robert Balawender, A Holas, N H MarchAbstract:In a recent paper, Zhang and George [Phys. Rev. B 66, 033110 (2002)] have made an application of the Hellmann-Feynman Theorem (HFT) to calculate forces acting on an atom of the buckyball ${\mathrm{C}}_{60}$ when subjected to small displacement. They noticed inconsistent results (as compared with that by other method) for forces connected with states belonging to a degenerate-energy level. However a sum of all such HFT forces for a given level was found consistent. Therefore they proposed the average force to be the representative of all forces connected with a degenerate level. Our analysis of these difficulties, based on degenerate perturbation theory, leads to modification of the HFT in application to degenerate-level states. By solving a matrix eigenequation of the extended HFT, as many forces are obtained as degeneracy of the level amounts. The diagonalized matrix involves unperturbed states only. Our considerations are illustrated by a simple system---a particle moving in a harmonic confinement, where forces are connected with anisotropic deformation of an isotropic confinement.
Hong-yi Fan - One of the best experts on this subject based on the ideXlab platform.
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generalized hellmann Feynman Theorem for ensemble average expressed in the formalism of pure state expectation
International Journal of Theoretical Physics, 2012Co-Authors: Changchun Wang, Xiancai Wang, Hong-yi FanAbstract:We show that the generalized Hellmann-Feynman Theorem (GHFT) for ensemble average can be expressed in the formalism of pure state expectation. We employ the thermo field dynamics proposed by Umezawa and Takahash to realize this goal, the pure state |0(β)〉 is defined in doubled eigenvector space of the Hamiltonian. Relation between the GHFT and entropy-variation in the context of |0(β)〉 is also derived.
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statistical properties of the hamiltonian generating phase state derived by using the generalized hellmann Feynman Theorem
Physica A-statistical Mechanics and Its Applications, 2010Co-Authors: Hong-yi FanAbstract:Abstract We study statistical properties of the Hamiltonian ( H = ω a † a + κ a † N + 1 + κ N + 1 a ) generating phase state. Using the generalized Hellmann–Feynman Theorem for ensemble average, we derive its mean energy and find the ratio of the mean energies contributed from the term a † a to that from a † N + 1 + κ N + 1 a . The relation on the entropy-variation with respect to the dynamic parameters ω and κ is also examined.
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calculation of entropy for some coupled oscillators by using the generalized hellmann Feynman Theorem
Modern Physics Letters B, 2010Co-Authors: Hong-yi FanAbstract:The entropies of several typical coupled bosonic oscillators are calculated by virtue of the generalized Hellmann–Feynman Theorem (GHFT). The relation between GHFT and entropy-variation is construct by using von Neumann entropy, which provides us with a new approach for deriving entropy of some complicated systems.
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mean energy of some interacting bosonic systems derived by virtue of the generalized hellmann Feynman Theorem
Journal of Mathematical Physics, 2009Co-Authors: Hong-yi FanAbstract:By virtue of the generalized Hellmann–Feynman Theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications of the Hellmann–Feynman Theorem and may enrich the theory of quantum statistics.
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entropy variation with respect to the resistance in quantized rlc circuit derived by generalized hellmann Feynman Theorem
arXiv: Quantum Physics, 2009Co-Authors: Hong-yi FanAbstract:By virtue of the generalized Hellmann-Feynman Theorem for ensemble average, we obtain internal energy and average energy consumed by the resistance R in a quantized RLC electric circuit. We also calculate entropy-variation with respect to R. The relation between entropy and R is also derived. By depicting figures we indeed see that the entropy increases with the increment of R.
Thomas F George - One of the best experts on this subject based on the ideXlab platform.
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extended hellmann Feynman Theorem for degenerate eigenstates
Physical Review B, 2004Co-Authors: G P Zhang, Thomas F GeorgeAbstract:In a previous paper, we reported a failure of the traditional Hellmann-Feynman Theorem (HFT) for degenerate eigenstates. This has generated enormous interest among different groups. In four independent papers by Fernandez, by Balawender, Hola, and March, by Vatsya, and by Alon and Cederbaum, an elegant method to solve the problem was devised. The main idea is that one has to construct and diagonalize the force matrix for the degenerate case, and only the eigenforces are well defined. We believe this is an important extension to HFT. Using our previous example for an energy level of fivefold degeneracy, we find that those eigenforces correctly reflect the symmetry of the molecule.
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breakdown of the hellmann Feynman Theorem degeneracy is the key
Physical Review B, 2002Co-Authors: G P Zhang, Thomas F GeorgeAbstract:The Hellmann-Feynman Theorem is a powerful and popular method to efficiently calculate forces in a variety of dynamical processes, but its validity has rarely been addressed. Here a surprising failure of this Theorem is reported. The forces calculated by the Theorem can be more than fifty times smaller than the forces calculated by the finite differential method. Numerical evidence shows that the energy-level degeneracy is the main reason. An analytical proof reveals that although eigenvalues do not depend on a linear combination of degenerate wave functions, forces do sensitively depend on it, which leads to ill-defined forces. A scheme is proposed to overcome this difficulty.