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78149246085
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A short account of this work was reported previously (Ref.).
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A short account of this work was reported previously (Ref.).
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Springer, New York
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Time-Dependent Density Functional Theory
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Verdozzi, C.1
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78149236599
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This condition also applies to the first argument.
-
This condition also applies to the first argument.
-
-
-
-
33
-
-
78149252784
-
-
In extended Coulomb systems, w and the Hartree potential ΣH are infinite but with a finite sum and must be treated together. In this work, we consider model systems with short-range interactions and such a procedure is not mandatory.
-
In extended Coulomb systems, w and the Hartree potential Σ H are infinite but with a finite sum and must be treated together. In this work, we consider model systems with short-range interactions and such a procedure is not mandatory.
-
-
-
-
34
-
-
78149275904
-
-
In Ref., the concept of "partial summations" is used to describe approximations beyond HFA, i.e., with a self-energy involving correlation effects.
-
In Ref., the concept of "partial summations" is used to describe approximations beyond HFA, i.e., with a self-energy involving correlation effects.
-
-
-
-
35
-
-
78149263318
-
-
In the spin-independent treatment P= Σσ Pσ.
-
In the spin-independent treatment P = Σ σ P σ.
-
-
-
-
36
-
-
78149277705
-
-
There exist also contributions coming from ladder diagrams with interactions only/also in the electron-hole channel, usually of principal relevance in exciton-type problems; however, such contributions are not the dominant ones in the low-density limit for our Hubbard clusters with one orbital/site; and in the rest of the paper, we do not consider them altogether, limiting ourselves to particle-particle or hole-hole ladder contributions.
-
There exist also contributions coming from ladder diagrams with interactions only/also in the electron-hole channel, usually of principal relevance in exciton-type problems; however, such contributions are not the dominant ones in the low-density limit for our Hubbard clusters with one orbital/site; and in the rest of the paper, we do not consider them altogether, limiting ourselves to particle-particle or hole-hole ladder contributions.
-
-
-
-
40
-
-
78149271983
-
-
The Dyson equations for T or W are solved in a similar way.
-
The Dyson equations for T or W are solved in a similar way.
-
-
-
-
41
-
-
78149259406
-
-
†. This will henceforth be implicit in all similar symmetry relations
-
†. This will henceforth be implicit in all similar symmetry relations.
-
-
-
-
42
-
-
78149278477
-
-
< (t,t )
-
< (t, t).
-
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44
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0037120381
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10.1103/PhysRevLett.89.126401;
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Ku, W.1
Eguiluz, A.G.2
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45
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78149259886
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Ph.D. thesis, The University of Tennessee
-
or W. Ku, Ph.D. thesis, The University of Tennessee, 2000.
-
(2000)
-
-
Ku, W.1
-
46
-
-
78149251001
-
-
In general, it would correspond to the occupation numbers of the single-particle basis.
-
In general, it would correspond to the occupation numbers of the single-particle basis.
-
-
-
-
48
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0043141369
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10.1103/PhysRevLett.20.1445
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Lieb, E.H.1
Wu, F.Y.2
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49
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78149237393
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C.-O Almbladh, in Ref., p. 127
-
C.-O Almbladh, in Ref., p. 127.
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50
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0000935939
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10.1103/PhysRevB.57.2108
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B. Holm and U. von Barth, Phys. Rev. B 57, 2108 (1998). 10.1103/PhysRevB.57.2108
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Holm, B.1
Von Barth, U.2
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51
-
-
78149255626
-
-
Continuous broadened ground-state spectral functions have been found for few electron quantum dots (Ref.), in contrast, for the systems considered here our results show only discrete spectral features
-
Continuous broadened ground-state spectral functions have been found for few electron quantum dots (Ref.), in contrast, for the systems considered here our results show only discrete spectral features.
-
-
-
-
52
-
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56349119793
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10.1103/PhysRevB.78.195109
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Li, W.1
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29744460464
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Von Barth, U.1
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0009475350
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10.1103/PhysRevLett.76.3610
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R. van Leeuwen, Phys. Rev. Lett. 76, 3610 (1996). 10.1103/PhysRevLett.76. 3610
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Van Leeuwen, R.1
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57
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-
78149267158
-
-
′ ). We alert the reader that this definition encompasses isolated and (unbiased/biased) contacted systems alike
-
′). We alert the reader that this definition encompasses isolated and (unbiased/biased) contacted systems alike.
-
-
-
-
58
-
-
78149256915
-
-
Initializing with G0 corresponds to a sudden switch on of the interaction as well as of the external field
-
Initializing with G 0 corresponds to a sudden switch on of the interaction as well as of the external field.
-
-
-
-
59
-
-
78149231977
-
-
The different BAs are done using a spin-dependent treatment, which is equivalent to the spin-independent one only when done fully self-consistently
-
The different BAs are done using a spin-dependent treatment, which is equivalent to the spin-independent one only when done fully self-consistently.
-
-
-
-
60
-
-
78149257913
-
-
U. von Barth (unpublished)
-
U. von Barth (unpublished).
-
-
-
-
61
-
-
78149241930
-
-
This conclusion applies to all MBAs here, although partially self-consistent but particle-conserving schemes can be easily devised for GWA but not for TMA
-
This conclusion applies to all MBAs here, although partially self-consistent but particle-conserving schemes can be easily devised for GWA but not for TMA.
-
-
-
-
63
-
-
78149248614
-
-
The theoretical formulation to treat macroscopic leads within the Keldysh formalism will be presented in detail in a future paper.
-
The theoretical formulation to treat macroscopic leads within the Keldysh formalism will be presented in detail in a future paper.
-
-
-
-
64
-
-
78149244075
-
-
The hopping parameter in the central region is, similarly to the isolated case, set to unity throughout the paper
-
The hopping parameter in the central region is, similarly to the isolated case, set to unity throughout the paper.
-
-
-
-
65
-
-
78149264330
-
-
In Figs. , we have, in addition to a nonzero external field shifted the on-site energy by -U/2 in order to have the same filling in the central region as in the isolated clusters
-
In Figs., we have, in addition to a nonzero external field shifted the on-site energy by - U / 2 in order to have the same filling in the central region as in the isolated clusters.
-
-
-
-
66
-
-
78149246332
-
-
The existence of long-lived quasisteady states remains valid in the case that we apply a bias to the leads. In that case the quasisteady state will depend both on how the external field and the bias is switched on
-
The existence of long-lived quasisteady states remains valid in the case that we apply a bias to the leads. In that case the quasisteady state will depend both on how the external field and the bias is switched on.
-
-
-
-
67
-
-
78149258886
-
-
When no bias is applied then the true steady state corresponds to the final ground state. In general, when a bias is applied it is plausible that there will be only one true steady state
-
When no bias is applied then the true steady state corresponds to the final ground state. In general, when a bias is applied it is plausible that there will be only one true steady state.
-
-
-
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68
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For a review, see, 10.1007/s00339-008-4864-9
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10.1103/PhysRevLett.97.046603In this paper, of a self-consistent oscillatory solution was observed in a short wire with Holstein-type phonons, and connected to 1D noninteracting leads.
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78149246084
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note
-
Should these features of the KBE turn out to be artificial, one could try to find ways to suppress the nonphysical behavior while keeping the connection to MBPT. One possibility could be to use the variational properties of the underlying Φ functional and use the Sham-Schlüter equation to determine on the fly the corresponding TDDFT potentials. At full self-consistency, the TDDFT dynamics would just reproduce the damped KBE dynamics. If one instead use optimized one-particle G when constructing the exchange correlation potential, v x c. (Refs.), we expect that the nonphysical damping will be reduced or removed without seriously deteriorating the short-time dynamics. In the BA, this approach consists in using a (time-) optimized independent-particle G when constructing the self-energy and v x c and in Sec. we saw that the damping is indeed reduced. The use of MBPT based TDDFT potentials could also be of great importance, due to the possibility of treating larger and more complex systems.
-
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73
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19744381827
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See, for example, 10.1103/PhysRevB.70.121302
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See, for example, P. Schmitteckert, Phys. Rev. B 70, 121302 (R) (2004). 10.1103/PhysRevB.70.121302
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Schmitteckert, P.1
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78149275427
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R R′ . The space in which the expressions are represented are given by the context.
-
R R′. The space in which the expressions are represented are given by the context.
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78149246853
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Explicit reference to the two-time dependencies is omitted as t1 = t2
-
Explicit reference to the two-time dependencies is omitted as t 1 = t 2.
-
-
-
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