Ballistic Thermal Transport by Phonons at Low Temperatures in Low-Dimensional Quantum Structures - Nanoscale Energy Transport and Harvesting - page 166

easilyobtain the following expression:
N I

( A I Pn − B I Pn ) k I Pn η

n ( y ) + ( A I SVn + B SVn ) n W I n ( y )

η

n = 0

( A I Pn −

B I SVn ) n

n ( y ) ,

N II

W II

B I Pn ) k I Pn η

II
n ( y )

( A I SVn +

II

= + η

n = 0

(4.72)

( A I Pn + B I Pn )

n ( y )

N I

n W I

n ( y ) + ( A I SVn − B SVn ) k SVn χ

I I

− χ

n = 0

( A I Pn +

B I Pn )

n ( y ) ,

N II

W II

n

II
n ( y )

( A I SVn − B I SVn ) k I SVn χ

II

= − χ +

n = 0

(4.73)

N I

)

( A I Pn + B I Pn )( k I Pn ) 2

I
n ( y )

λ + μ − η

( 2

n = 0

n ( y )

+ ( B SVn − A I SVn ) k SVn n W I η

I

B I Pn ) n

2

N I

W I

( A I Pn +

I
n ( y )

+

0 λ

− η

n =

n ( y )

+ ( A I SVn − B SVn ) k SVn n W I η

I

N II

) − ( A I Pn + B I Pn )( k I Pn ) 2

II

=

(

λ +

2

μ η

n ( y )

=

n 0

I n ( y )

+ ( B I SVn − A I SVn ) k I SVn n W II η

− ( A I Pn + B I Pn ) n W II

2

N II

II

+

0 λ

η

n ( y )

=

n

I n ( y ) ,

+ ( A I SVn − B I SVn ) k I SVn n W II η

(4.74)