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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1 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

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).


1 1957 2 u fano phys rev 124 1866 1961

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


Coupled mode theory

Одно модовый резонатор

Coupled mode theory


1 1957 2 u fano phys rev 124 1866 1961

Инверсия по времени

Одно-модовый резонатор

CMT

  • Х. Хаус, Волны и поля в оптоэлектронике


1 1957 2 u fano phys rev 124 1866 1961

CMT

  • Много-модовый резонатор

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


1 1957 2 u fano phys rev 124 1866 1961

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


1 1957 2 u fano phys rev 124 1866 1961

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


1 1957 2 u fano phys rev 124 1866 1961

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

system, M is the number of continuums (channels)


1 1957 2 u fano phys rev 124 1866 1961

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


1 1957 2 u fano phys rev 124 1866 1961

Проекционные операторы:

Уравнение Липпмана-Швингера


S matrix

S-matrix

Basis of closed billiard

The biorthogonal basis


1 1957 2 u fano phys rev 124 1866 1961

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


Datta s site representation

Datta’s site representation


Effective hamiltonian for time periodic case

For stationary case

l

Effective Hamiltonian for time-periodic case


1 1957 2 u fano phys rev 124 1866 1961

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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