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


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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

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slide1

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).

slide2
Coupled defect mode with propagating over waveguide lightManolatou, et al, IEEE J. Quant. Electronics, (1999)
slide4

Инверсия по времени

Одно-модовый резонатор

CMT
  • Х. Хаус, Волны и поля в оптоэлектронике
slide5
CMT
  • Много-модовый резонатор

IEEE J. Quantum Electronics, 40, 1511 (2004)

slide6
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

slide7

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

slide8

W is matrix NxM where N is the number of eigen states of closed quantum

system, M is the number of continuums (channels)

slide10

Проекционные операторы:

Уравнение Липпмана-Швингера

s matrix
S-matrix

Basis of closed billiard

The biorthogonal basis

slide13
c

H.-W.Lee, Generic Transmission Zeros and In-Phase Resonances

in Time-Reversal Symmetric Single Channel Transport,

Phys. Rev. Lett. 82, 2358 (1999)

2d case
2d case

Limit to continual case

matlab calculation

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
slide18

Волновая функция полубесконечного m-го провода

N=1

numerical results n 1

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

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