Coarse-grained V representability

Lammert, Paul E.

doi:10.1063/1.2336211

Cited by 17 publications

(27 citation statements)

References 18 publications

(27 reference statements)

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“…The problem of N-representability has been solved, and it can be shown that any non-negative function can be written in terms of some antisymmetric Ψ(r 1 , · · · , r N ) in the form (2.2) [56,60]. The v-representability problem is still an ongoing investigation, although some results regarding it can be found in [37,155,92].…”

Section: Density Functional Theory (Dft) Formalismmentioning

confidence: 99%

Relativistic quasiparticle random phase approximation in deformed nuclei

Arteaga

Ring

2007

Progress in Particle and Nuclear Physics

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Covariant density functional theory is used to analyse the response to the E1 and M1 electromagnetic transition operators in superfluid deformed nuclei in the framework of self-consistent Hartree-Bogoliubov theory and relativistic quasiparticle random phase (RQRPA) approximation. The fully self-consistent RHB+RQRPA equations are posed for the case of axial symmetry and for three different kinds of energy functionals, and solved with the help of a new parallel code. Special care is taken in order to validate the proper decoupling of spurious modes. Results of the first multipole magnetic operator (M1) response in light and heavy deformed nuclei are presented and analysed; in particular, the scissors mode and spin excitations. Qualitative agreement with experiment is obtained for the position of the scissors mode, and its structure as a rotation of the deformed neutron density against the deformed proton density reproduced. In addition to the scissors mode, a soft M1 mode with strong orbital character is found in heavy nuclei at relatively low energies. From the analysis of the proton and neutron transition densities in the intrinsic frame, and from the structure of the RQRPA amplitudes, it is concluded that this mode corresponds to a collective rotation of the deformed neutron skin against the deformed proton-neutron core. The response in light and heavy nuclei to the electric dipole operator (E1) is also given consideration. The position of the Giant Dipole Resonance is well reproduced within the RHB+RQRPA framework in axial symmetry. The effects of superfluidity and deformation on the Pygmy Dipole Resonance are closely examined. Excellent agreement with recent experimental results is found. v vi AcknowledgementsFirst and foremost I would like to thank my supervisor, Prof. Dr. Peter Ring, not only for stimulating discussions and timely advice, but also for his support throughout the various phases of the work presented in this document. His understanding and experience in many areas has made a pleasure working with him. I am particularly grateful for his optimism and overall confidence in the project, always trying to point me on the right direction but giving me enough leeway to learn from my own mistakes.Many thanks go to Roger Hilton, who was always a source of good humour and interesting conversations while at the TUM. He patiently read the first drafts and helped me polish all the rough edges, both in the contents and in the use of the English language.It is a pleasure for me to thank all my colleagues at the TUM Theory Department and at the TUM campus in Garching, who have provided support and company during my time in Munich, with a special mention to

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Section: Density Functional Theory (Dft) Formalismmentioning

confidence: 99%

Relativistic quasiparticle random phase approximation in deformed nuclei

Arteaga

Ring

2007

Progress in Particle and Nuclear Physics

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“…13 Since the lattice can be arbitrarily dense, this effectively solves the V-representability problem in DFT. In a related approach, V-representability was recently proven by Lammert 14 for coarse-grained systems.…”

Section: Dft On Lattice Spacesmentioning

confidence: 99%

Time-dependent V-representability on lattice systems

Ullrich

2008

The Journal of Chemical Physics

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We study the mapping between time-dependent densities and potentials for noninteracting electronic systems on lattices. As discovered recently by Baer ͓J. Chem. Phys. 128, 044103 ͑2008͔͒, there exist well-behaved time-dependent density functions on lattices which cannot be associated with any real time-dependent potential. This breakdown of time-dependent V-representability can be tracked down to problems with the continuity equation which arise from discretization of the kinetic-energy operator. Examples are given for lattices with two points and with N points, and implications for practical numerical applications of time-dependent density-functional theory are discussed. In the continuum limit, time-dependent noninteracting V-representability is restored.

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“…Building on the results of §4, the existence and regularity results for the coarse-grained theory will be presented in §6. In addition to the considerably simpler and more intuitive proofs, those results go beyond the previous version of the theory [20][21][22] by treating spin-densities.…”

Section: Coarse-grainingmentioning

confidence: 99%

“…This section reviews the basic notions of the coarsegrained DFT framework [20][21][22] , augmented to handle SDFT. Much of it looks nearly the same on the surface as the conventional fine-grained theory of §2.…”

Section: Coarse-grainingmentioning

confidence: 99%

“…On a lattice, short distance scales are completely eliminated; this is a fundamentally different quantum mechanics than the orthodox continuum version. Another way to keep short-distance-scale degrees of freedom from causing problems without altering the underlying continuum quantum mechanics was introduced as coarse-grained DFT 20 . The idea is that we only allow ourselves to specify densities with some limited spatial resolution.…”

Section: Introductionmentioning

confidence: 99%

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Coarse-grained spin density-functional theory: Infinite-volume limit via the hyperfinite

Lammert

2013

Journal of Mathematical Physics

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Coarse-grained spin density functional theory (SDFT) is a version of SDFT which works with number/spin densities specified to a limited resolution -averages over cells of a regular spatial partition -and external potentials constant on the cells. This coarse-grained setting facilitates a rigorous investigation of the mathematical foundations which goes well beyond what is currently possible in the conventional formualation. Problems of existence, uniqueness and regularity of representing potentials in the coarse-grained SDFT setting are here studied using techniques of (Robinsonian) nonstandard analysis. Every density which is nowhere spin-saturated is V-representable, and the set of representing potentials is the functional derivative, in an appropriate generalized sense, of the Lieb internal energy functional. Quasi-continuity and closure properties of the set-valued representing potentials map are also established. The extent of possible non-uniqueness is similar to that found in non-rigorous studies of the conventional theory, namely non-uniqueness can occur for states of collinear magnetization which are eigenstates of S z .

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Coarse-grained V representability

Cited by 17 publications

References 18 publications

Relativistic quasiparticle random phase approximation in deformed nuclei

Relativistic quasiparticle random phase approximation in deformed nuclei

Time-dependent V-representability on lattice systems

Coarse-grained spin density-functional theory: Infinite-volume limit via the hyperfinite

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