1 / 19

1 . М. С. Лифшиц, ЖЭТФ ( 1957 ). 2 . U.Fano, Phys. Rev. 124, 1866 (1961).

Подход эффективного гамильтониана. 1 . М. С. Лифшиц, ЖЭТФ ( 1957 ). 2 . U.Fano, Phys. Rev. 124, 1866 (1961). 3 . H. Feshbach,, Ann. Phys. (New York) 5 (1958) 357 ; 19 (1962) 287. 4 . C. Mahaux, H.A. Weidenmuller, ( Shell-Model Approach to Nuclear

demont
Download Presentation

1 . М. С. Лифшиц, ЖЭТФ ( 1957 ). 2 . U.Fano, Phys. Rev. 124, 1866 (1961).

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Подход эффективного гамильтониана 1. М. С. Лифшиц, ЖЭТФ (1957). 2. U.Fano, Phys. Rev. 124, 1866 (1961). 3. H. Feshbach,, Ann. Phys. (New York) 5 (1958) 357; 19 (1962) 287. 4. C. Mahaux, H.A. Weidenmuller, (Shell-Model Approach to Nuclear Reactions), North-Holland, Amsterdam, 1969. 5. I.Rotter, Rep. Prog. Phys., 54, 635 (1991). 6. S.Datta, (Electronic transport in mesoscopic systems) (1995). 7. S. Albeverio, et al J.Math. Phys. 37, 4888 (1996). 8. Y.V. Fyodorov and H.-J. Sommers, J. Math. Phys. 38, 1918 (1997) 9. F. Dittes, Phys. Rep. (2002). 10. Sadreev and I. Rotter, J.Phys.A (2003). 11. J. Okolowicz, M. Ploszajczak, and I. Rotter, Phys. Rep. 374, 271(2003). 12. D.V. Savin, V.V. Sokolov V.V., and H.-J. Sommers, PRE (2003). 13. Sadreev, J.Phys.A (2012). • Coupled mode theory (оптика) H.A.Haus, (Waves and Fields in Optoelectronics) (1984). C. Manolatou, et al, IEEE J. Quantum Electron. (1999). S. Fan, et al, J. Opt. Soc. Am.A20, 569 (2003). S. Fan, et al, Phys. Rev. B59, 15882 (1999). W. Suh, et al, IEEE J. of Quantum Electronics, 40, 1511 (2004). Bulgakov and Sadreev, Phys. Rev. B78, 075105(2008).

  2. Coupled defect mode with propagating over waveguide lightManolatou, et al, IEEE J. Quant. Electronics, (1999)

  3. Одно модовый резонатор Coupled mode theory

  4. Инверсия по времени Одно-модовый резонатор CMT • Х. Хаус, Волны и поля в оптоэлектронике

  5. CMT • Много-модовый резонатор IEEE J. Quantum Electronics, 40, 1511 (2004)

  6. Два порта, две моды %CMT for transmission through resonator with two modes clear all E=-2:0.01:2; D=[sqrt(0.1) sqrt(0.25) sqrt(0.1) sqrt(0.25)]; G=0.5*D'*D; H0=diag([-0.25 0.25]); H=H0-1i*G; for j=1:length(E) Q=E(j)*diag([1 1])-H; in=[1; 0]; IN=1i*D'*in; A=Q\IN;; A1(j)=A(1); A2(j)=A(2); t(:,j)=-in+D*A; end

  7. T волновод с двумя резонаторами, Булгаков, Садреев, Phys. Rev. B84, 155304 (2011)

  8. W is matrix NxM where N is the number of eigen states of closed quantum system, M is the number of continuums (channels)

  9. S.Datta, (Electronic transport in mesoscopic systems) (1995).

  10. Проекционные операторы: Уравнение Липпмана-Швингера

  11. S-matrix Basis of closed billiard The biorthogonal basis

  12. c H.-W.Lee, Generic Transmission Zeros and In-Phase Resonances in Time-Reversal Symmetric Single Channel Transport, Phys. Rev. Lett. 82, 2358 (1999)

  13. 2d case Limit to continual case

  14. Na=input('input length along transport Na=') Nb=input('input length cross to transport Nb=') Nin=input('input numerical position of the input lead Nin=') Nout=input('input numerical position of the output lead Nout=') NL=length(Nin); NR=length(Nout); vL=1;vR=vL;tb=1; %Leads E=-2.9:0.011:1; HL=zeros(NL,NL); HL=HL-diag(ones(1,NL-1),1); HL=HL+HL'; HL=HL-diag(sum(HL),0); for np=1:NL kpp=acos(-E/2+EL(np,np)/2); kp(np,1:length(E))=kpp; end HR=HL; %Dot N=Na*Nb; HB=zeros(N,N); HB=HB-diag(ones(1,N-1),1)-diag(ones(1,N-Na),Na); HB(Na:Na:N-Na,Na+1:Na:N-Na+1)=0; HB=tb*(HB+HB'); %Coupling matrix psiBin=psiB(Nin,:); psiBout=psiB(Nout,:); WL=vL*psiBin'*psiL'; WR=vR*psiBout'*psiL'; DB=diag(ones(Na*Nb,1)); for j=1:length(E) g=diag(exp(i*kp(:,j))); gg=diag(sin(real(kp(:,j))).^0.5); WW=WL*g*WL'+WR*g*WR'; Heff=diag(EB)-WW; QQ=DB*E(j)-Heff; PP=QQ^(-1); SS=2*i*(WL*gg)'*PP*WR*gg; t(n,j)=SS(1,1); psS=psiB*PP*WL; Matlab calculation

  15. Datta’s site representation

  16. For stationary case l Effective Hamiltonian for time-periodic case

  17. Волновая функция полубесконечного m-го провода N=1

  18. m=-1, 0, 1 21 quasi energies Numerical results N=1 l=0.75, vC=0.25 H. Fukuyama, R. A. Bari, and H.C. Fogedby, PRB (1973). BS, J. Phys. C (1999): Критерий применимости теории возмущений

More Related