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Suppression of scattering from slow to fast subsystems and application to resonantly Floquetdriven impurities in strongly interacting systems
by Friedrich Hübner
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Submission summary
Authors (as registered SciPost users):  Friedrich Hübner 
Submission information  

Preprint Link:  https://arxiv.org/abs/2210.08380v5 (pdf) 
Date accepted:  20231204 
Date submitted:  20231129 00:41 
Submitted by:  Hübner, Friedrich 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We study solutions to the LippmannSchwinger equation in systems where a slow subsystem is coupled to a fast subsystem via an impurity. Such situations appear when a highfrequency Floquetdriven impurity is introduced into a lowenergy system, but the driving frequency is at resonance with a highenergy band. In contrast to the case of resonant bulk driving, where the particles in the lowenergy system are excited into the highenergy band, we surprisingly find that these excitations are suppressed for resonantly driven impurities. Still, the transmission through the impurity is strongly affected by the presence of the highenergy band in a universal way that does not depend on the details of the highenergy band. We apply our general result to two examples and show the suppression of excitations from the lowenergy band into the highenergy band: a) bound pairs in a FermiHubbard chain scattering at a driven impurity, which is at resonance with the Hubbard interaction and b) particles in a deep optical lattice described by the tightbinding approximation, which scatter at a driven impurity, whose driving frequency equals the band gap between the two lowest energy bands.
Published as SciPost Phys. 16, 005 (2024)
Author comments upon resubmission
I took care of the minor revisions asked for by the referee. I added more citations about nonequilibrium Green's function methods. I have also clarified the sentence '... which would be useful to describe impurities which are too complicated to study via nonperturbative methods ...'. and replaced `too complicated' by `too computationally expensive'.
About this I would like to add the following comment: Of course one can in principle study any impurity in any model using NEGF or other nonperturbative methods. What I meant with 'too complicated' was that for sufficiently complicated impurities, performing analytical or numerical computations using exact nonperturbative methods might become infeasible given the available resources. I am not an expert in the theory of NEGF, but to my understanding, in practice, if one would like to apply NEGF to impurity scattering it seems very crucial that the selfenergy of the leads is known. For the standard tightbinding lattices without particle interaction these are of course well known.
Please consider the two examples I discuss in appendix G and H. In appendix G I discuss an impurity where the leads are given by semiinfinite Hubbard chains (so particles in the leads are interacting). In appendix H the leads are given by semiinfinite optical lattices (particles are noninteracting, but this model contains infinitely many bands). I do not think the full nonperturbative selfenergies of both models are known.
For more general impurities, especially if they are embedded in interacting systems in higher dimensions, an exact numerical analysis using nonperturbative methods might become infeasible due to the exponentially large Hilbert space. This is of course a general problem in interacting manybody quantum systems and there have been many ideas on how to still make good predictions. One of them is the idea of separation of scales, which is the basis for my analysis (but also behind other wellknown techniques like the highfrequency expansion or hydrodynamic gradient expansions): The two above mentioned examples can be solved analytically in the regime I am considering, which demonstrates the drastic simplification compared to exact nonperturbative methods. Due to the completely general derivation my technique can also be applied to more general models (in particular interacting ones) given that they are in the correct regime. Even if the resulting simplified expressions are not analytically solvable, they can still add physical intuition and systematically pinpoint the most relevant objects to be computed via other methods. In this paper I only discussed the zeroth order approximation, but by extending to higher order one can systematically gain insight into resonant scattering at impurities even if the system is only approximately in that regime.
So to conclude, in my opinion the method I developed in this paper can help to gain understanding of impurities in physical situations which are difficult to treat with exact nonperturbative methods due to finite availability of resources.
Kind regards,
Friedrich Huebner
List of changes
Changed sentence '... which would be useful to describe impurities which are too complicated to study via nonperturbative methods ...' to 'This could complement exact
nonperturbative methods (like the nonequilibrium Green’s function methods [21,39–45]) in
studying scattering at impurities and could perhaps be used to gain insights into impurities
that are too computationally expensive to treat in practice via these methods.'