G stefanucci s kurth a rubio eku gross phys rev b 77

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G. Stefanucci, S. Kurth, A. Rubio, E.K.U. Gross, Phys. Rev. B 77, 075339 (2008)
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Bound state oscillations and memory effects Analytical : G. Stefanucci, Phys. Rev. B, 195115 (2007)) Numerical : E. Khosravi, S. Kurth, G. Stefanucci, E.K.U.G., Appl. Phys. A 93 , 355 (2008), and Phys. Chem. Chem. Phys. 11 , 4535 (2009) If Hamiltonian of a (non-interacting) biased system in the long-time limit supports two or more bound states then current has steady, I (S), and dynamical, I (D) , parts: ) t ( I I ) t ( I ) D ( ) S ( (D) bb' b b' b,b' I (t) sin[( )t]    Note : - bb’ depends on history of TD Hamiltonian (memory!) Questions : -- How large is I (D) vs I (S) ? -- How pronounced is history dependence? Sum over bound states of biased Hamiltonian
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1-D model: start with flat potential, switch on constant bias, wait until transients die out, switch on gate potential with different switching times to create two bound states note: amplitude of bound-state oscillations may not be small compared to steady-state current History dependence of undamped oscillations
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Model system U Time-dependent picture of Coulomb blockade
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QD T bias L,R ˆ ˆ ˆ ˆ ˆ H t H H H H t  T link 1 , 0 , i 1 ˆ ˆ ˆ H V c c h.c.       i 1 , i , i 1 ˆ ˆ ˆ H t Vc c h.c.        bias i , , i 1 ˆ ˆ H t U t n       QD ext 0 0 0 ˆ ˆ ˆ ˆ H v n Un n
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KS QD,KS T bias L,R ˆ ˆ ˆ ˆ ˆ H t H t H H H t  QD,KS KS 0 0 ˆ ˆ H t v n t n 0 0 n t n t KS 0 ext 0 xc 0 1 v n t v Un t v n t 2 Solve TDKS equations (instead of fully interacting problem): LDA functional for v xc is available from exact Bethe-ansatz solution of the 1D Hubbard model. N.A. Lima, M.F. Silva, L.N. Oliveira, K. Capelle, PRL 90, 146402 (2003)
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S. Kurth, G. Stefanucci, E. Khosravi, C. Verdozzi, E.K.U.G., Phys. Rev. Lett. 104, 236801 (2010)
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Is this Coulomb blockade?
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Steady-state density as function of applied bias for KS potential with smoothened discontinuity U L /V Fingerprint of Coulomb blockade S. Kurth, G. Stefanucci, E. Khosravi, C. Verdozzi, E.K.U.G., Phys. Rev. Lett. 104, 236801 (2010)
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Most commonly used approximation for t r ρ v xc Adiabatic Approximation adiab approx xc xc,stat n (r t) v r t : v n  hom stat , xc v = xc potential of static homogeneous e-gas How restrictive is the adiabatic approximation, i.e. the neglect of memory in the functional v xc [ρ(r’,t’)](r,t) ? Can we assess the quality of the exact adiabatic approximation? e.g. ALDA hom xc xc,stat v r t : v r t
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M. Thiele, E.K.U.G., S. Kuemmel, Phys. Rev. Lett. 100, 153004 (2008) 4-cycle pulse with λ = 780 nm, I 1 = 4x10 14 W/cm 2 , I 2 =7x10 14 W/cm 2 Solid line: exact Dashed line: exact adiabatic
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  • Quantum Chemistry, density functional theory, Alda, Stefan Kurth, Gianluca Stefanucci

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