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

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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

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).


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


Одно модовый резонатор

Coupled mode theory


Инверсия по времени

Одно-модовый резонатор

CMT

  • Х. Хаус, Волны и поля в оптоэлектронике


CMT

  • Много-модовый резонатор

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


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


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


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

system, M is the number of continuums (channels)


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


Проекционные операторы:

Уравнение Липпмана-Швингера


S-matrix

Basis of closed billiard

The biorthogonal basis


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

Limit to continual case


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


Datta’s site representation


For stationary case

l

Effective Hamiltonian for time-periodic case


Волновая функция полубесконечного m-го провода

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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