Ly : localized modes in linear chain and localization effects

[jaykay]

urgently need help: localized modes in linear chain and localization effects

Hello everyone, it is great place you have here, hope I can learn a lot from you

I am doing some readings and there are couple of concepts that I havent
been familiar with and if you spend a little time to help me with I would
be really grateful:

Can you please give some explanation aobut the concepts of "localised
modes", "localisation effects" and "localisation length" for a linear (atonmic) chain.

The definition I am given is "For the normalised eigenvectors q(wr) ‘localised’ modes may be thought of as those for which only a contiguous subset of the
components of q(wr) are significantly different from zero" which I find
hard to understand.

Can you please explain abit more about localisation effect and how we would get an estimate of the "localisation length".


If it is too much trouble for you please point me to a source of information

Any help greatly appreciated


Thanks

 

[jaykay]

Please please help


is the localisation effect is when there's disorder or impurity in the chain and it will be detectable in the the spectrum of normal mode somehow?

and what is the localisation length :(

pplease help, just take you a minute

 

[jaykay]

can you please tell me what does this equation imply?

 

[jaykay]

why no body is helping :((
pleasezzzzz

 

[vincentchan]

becasue no one understand what is your question...can you post the whole paragraph instead of one sentence, or at least explain a little bit what is q, w and r means...I took a classical dynamics course last year and it did cover using matrix to solve this kind of problem... but i don't think you gave me enough information to help you...

 

[jaykay]

that's all i am given. I don't know it myself, this is a computing problem that i need to understand to implement computational to calculate the localisation length.

basically we have a linear monoatomic chain. and we have a disorder like that, one atom with a different mass. the it is said

For the normalised eigenvectors q(wr) ‘localised’ modes may be thought of as those for which only a contiguous subset of the components of q(wr) are significantly different from zero

wr is just the eigen frequency, q is the coressponding eigen vector

in the equation qj(wr) is the j component of the eigen vector (i believe) then gamma is the localisation length. jd i don't know

we can see an exponential decay around the eigen vector, which indicate the localisation length is the decay constant. but what exactly this equation means i don't understand.

I heard that this is "anderson localisation" but i haven't found this equation anywhere else to find out more

please help

 

[vincentchan]

what textbook are you using... maybe i can rush to the library and take a look... hopefully can give u an answer by tomorrow