Dear all, sorry for a naive question, but I am confused by ldos function. Two questions: 1) Why it does not work if system has no leads? 2) Imagine I have an infinite homogeneous stripe which I artificially divide into a scattering region and two leads. Why does ldos give different results depending on the length of the scattering region? Is it a numerical error or something physical behind it? Thanks, Sergey
Dear Sergey, 1) ldos computes the local density of states at a given energy. In a finite system, the density of states is a sum of delta functions (for each of the eigenenergies), but this means that one would have to choose the energy to coincide with an eigenergy by hand to find a nonzero ldos. For a finite system asking for the ldos for a given energy is thus not a very useful question. This is why it is not supported in kwant via ldos. For system with leads this is different, as the broadening through the leads gives a finite ldos for a continuous range of energies. The algorithm in the function ldos then makes use of the fact that there are propagating states in the leads to compute ldos: This is the technical reason for why ldos will fail for a system without leads. For a finite system, you should rather compute in kwant the eigenenergies and eigenstates. 2) What you describe here sounds not correct: Indeed, if you have an infinite, homogeneous system, and you compute the ldos for different length of the scattering region you should get the same result, since the system is globally translationally invariant. Can you post an example where this is not the case? Best, Michael
Am 10 jan. 2016 um 02:06 schrieb Sergey <sereza@gmail.com>:
Dear all, sorry for a naive question, but I am confused by ldos function. Two questions: 1) Why it does not work if system has no leads?
2) Imagine I have an infinite homogeneous stripe which I artificially divide into a scattering region and two leads. Why does ldos give different results depending on the length of the scattering region? Is it a numerical error or something physical behind it?
Thanks, Sergey
Dear Michael, Thank you! Here is an example. This was done to plot Friedel oscillations in ldos from point impurity at (0, posimp). The current code just sets zero impurity potential, so, I expect an ldos that does not depend on x. Best wishes, Sergey On 10/01/16 07:33, Michael Wimmer wrote:
Dear Sergey,
1) ldos computes the local density of states at a given energy. In a finite system, the density of states is a sum of delta functions (for each of the eigenenergies), but this means that one would have to choose the energy to coincide with an eigenergy by hand to find a nonzero ldos. For a finite system asking for the ldos for a given energy is thus not a very useful question. This is why it is not supported in kwant via ldos.
For system with leads this is different, as the broadening through the leads gives a finite ldos for a continuous range of energies. The algorithm in the function ldos then makes use of the fact that there are propagating states in the leads to compute ldos: This is the technical reason for why ldos will fail for a system without leads.
For a finite system, you should rather compute in kwant the eigenenergies and eigenstates.
2) What you describe here sounds not correct: Indeed, if you have an infinite, homogeneous system, and you compute the ldos for different length of the scattering region you should get the same result, since the system is globally translationally invariant.
Can you post an example where this is not the case?
Best,
Michael
Am 10 jan. 2016 um 02:06 schrieb Sergey <sereza@gmail.com>:
Dear all, sorry for a naive question, but I am confused by ldos function. Two questions: 1) Why it does not work if system has no leads?
2) Imagine I have an infinite homogeneous stripe which I artificially divide into a scattering region and two leads. Why does ldos give different results depending on the length of the scattering region? Is it a numerical error or something physical behind it?
Thanks, Sergey
Dear Michael, Thank you! Here is an example. This was done to plot Friedel oscillations in ldos from point impurity at (0, posimp). The current code just sets zero impurity potential, so, I expect an ldos that does not depend on x. Best wishes, Sergey On 10/01/16 07:33, Michael Wimmer wrote:
Dear Sergey,
1) ldos computes the local density of states at a given energy. In a finite system, the density of states is a sum of delta functions (for each of the eigenenergies), but this means that one would have to choose the energy to coincide with an eigenergy by hand to find a nonzero ldos. For a finite system asking for the ldos for a given energy is thus not a very useful question. This is why it is not supported in kwant via ldos.
For system with leads this is different, as the broadening through the leads gives a finite ldos for a continuous range of energies. The algorithm in the function ldos then makes use of the fact that there are propagating states in the leads to compute ldos: This is the technical reason for why ldos will fail for a system without leads.
For a finite system, you should rather compute in kwant the eigenenergies and eigenstates.
2) What you describe here sounds not correct: Indeed, if you have an infinite, homogeneous system, and you compute the ldos for different length of the scattering region you should get the same result, since the system is globally translationally invariant.
Can you post an example where this is not the case?
Best,
Michael
Am 10 jan. 2016 um 02:06 schrieb Sergey <sereza@gmail.com>:
Dear all, sorry for a naive question, but I am confused by ldos function. Two questions: 1) Why it does not work if system has no leads?
2) Imagine I have an infinite homogeneous stripe which I artificially divide into a scattering region and two leads. Why does ldos give different results depending on the length of the scattering region? Is it a numerical error or something physical behind it?
Thanks, Sergey
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Michael Wimmer

Sergey