In previous work, we have predicted novel effects, such as exchange
broadening, anomalous scaling of the localization length and a blue shift of
the absorption spectrum with increasing disorder strength, for static disorder
models described by stable distributions with stability index {\alpha}<1. The
main points of the Comment are that the outliers introduced by heavy tails in
the disorder distribution (i) do not lead to deviations from the conventional
scaling law for the half width at half maximum (HWHM) of the absorption
spectrum and (ii) do not lead to non-universality of the distribution of
localization lengths. We show below that the findings reported by us in the
Letter are correct and that the wrong conclusions of the Comment arise from
focusing on small {\sigma} values.Comment: Based on our response submitted to Physical Review Letters on January
  20, 2012. We now also take into account the modifications made to the Comment
  upon resubmission of the Comment. The Reply has been accepted in Physical
  Review Letter

Eisfeld, A.

Knoester, J.

Malyshev, V. A.

Möbius, S.

Vlaming, S. M.

Physical Review Letters

English

arXiv

Moebius, S.

Malyshev, V.A.

NARCIS 

Comment on "Excitons in Molecular Aggregates with Levy-Type Disorder: Anomalous Localization and Exchange Broadening of Optical Spectra" Reply

A. Eisfeld

S. M. Vlaming

S. Möbius

V. A. Malyshev

J. Knoester

Crossref

Eisfeld<i>et al.</i>Reply:

ARTS repository - University of Groningen

   University of GroningenComment on "Excitons in Molecular Aggregates with Levy-Type DisorderEisfeld, A.; Vlaming, S. M.; Moebius, S.; Malyshev, V.A.; Knoester, J.Published in:Physical Review LettersDOI:10.1103/PhysRevLett.109.259702IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2012Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Eisfeld, A., Vlaming, S. M., Moebius, S., Malyshev, V. A., & Knoester, J. (2012). Comment on "Excitons inMolecular Aggregates with Levy-Type Disorder: Anomalous Localization and Exchange Broadening ofOptical Spectra" Reply. Physical Review Letters, 109(25), 259702-1-259702-1. [259702].https://doi.org/10.1103/PhysRevLett.109.259702CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 07-06-2022Eisfeld et al. Reply: The authors of the precedingComment [1] questioned our statement regarding the un-conventional disorder scalings of the HWHM and thenonuniversality of the localization length (LL) distributionreported by us our Letter [2]. We attributed these findingsto originate from segmentation caused by the occurrence ofoutliers [2]. We demonstrate here that our conclusions arecorrect and that the criticism in Ref. [1] is a consequence offocusing on small values of the disorder strength .The conventional  scaling for the HWHM (derived inRef. [2] for linear chains with site disorder drawn fromgeneral symmetric -stable distributions) reads HWHMJð=JÞ2=ð1þÞ, J being the intersite nearest neighbor in-teraction. Here, segmentation is not taken into account.Outliers become more abundant for smaller . By equatingN and Nseg from Eqs. (3) and (4) in Ref. [2], one canestimate the value of  above which segmentation starts toplay a role [see shaded region in Fig. 1(a)].For  & J (values of interest for many molecular sys-tems), deviations from the conventional HWHM  scalingare not seen for  ¼ 2 and 1 (Gaussian and Lorentziandisorder, respectively). However, for  & 0:5, we foundclear deviations.This is shown in Figs. 1(b) and 1(c), where for  * 0:4the conventional scaling (solid red lines) clearly breaksdown. Moreover, the data points show kinks at which theHWHM suddenly jumps. This is not noise. It can beattributed to structure in the high-energy wing of theabsorption spectrum, which grows upon increasing , asa consequence of segmentation [2]. Both effects becomemore pronounced for smaller . The data also show thatthese features cannot be adequately fitted by a power law.Finally, we point out that the straight reference line inFig. 2 of Ref. [2] is irrelevant and has no effect on theconclusion of the existence of exchange broadening of theabsorption spectrum.Next, we demonstrate the nonuniversality of the LLdistribution due to segmentation by outliers. Figure 2 dis-plays the normalized LL distributions obtained for ¼ 0:5using the same scaling of the energy interval as inRefs. [1,3]. In Fig. 2(a), small   0:1J are considered,as in Ref. [1]. Segmentation is irrelevant here and thenormalized LL distributions are nearly identical. Yet, al-ready for  ¼ 0:1J, deviations become visible in the ap-pearance of sharp peaks at small LL. Upon increasing [Fig. 2(b)], the deviations become more pronounced, andthe nonuniversal character of the LL distribution is clear.This is the effect of outliers. In Ref. [1] it is stated that theconventional scalings break down at high  values, onlybecause Nloc approaches unity: a trivial effect. We havedemonstrated that the breakdown of scalings found by us ismore subtle and is related to a frequent occurrence ofoutliers when  & 0:5.A. Eisfeld,1 S.M. Vlaming,2,3 S. Möbius,1V. A. Malyshev,2 and J. Knoester21Max Planck Institute for Physics of Complex SystemsNöthnitzer Strasse 38, D-01187 Dresden, Germany2Centre for Theoretical Physicsand Zernike Institute for Advanced MaterialsUniversity of GroningenNijenborgh 4, 9747 AG Groningen, The Netherlands3Department of ChemistryMassachusetts Institute of Technology77 Massachusetts AvenueCambridge, Massachusetts 02139, USAReceived 27 August 2012; published 21 December 2012DOI: 10.1103/PhysRevLett.109.259702PACS numbers: 78.30.Ly, 71.35.Aa, 73.20.Mf[1] A. Werpachowska and A. Olaya-Castro, precedingComment, Phys. Rev. Lett. 109, 259701 (2012).[2] A. Eisfeld, S.M. Vlaming, V.A. Malyshev, and J.Knoester, Phys. Rev. Lett. 105, 137402 (2010).[3] S.M. Vlaming, V. A. Malyshev, and J. Knoester, Phys.Rev. B 79, 205121 (2009).(a)(b) (c)FIG. 1 (color online). (a) Diagram showing for which (, )the chain segmentation dominates localization (shaded area). (b),(c) HWHM  scaling of the absorption peak. Data (þ), resultsof numerical simulations (N ¼ 200); red curves, conventionalscaling law.locloc loc loc locloclocloc(a) (b)FIG. 2 (color online). Normalized LL distributions calculatedfor  ¼ 0:5 (N ¼ 200). In (b), the curves have different verticaloffsets to better show their distinction.PRL 109, 259702 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending21 DECEMBER 20120031-9007=12=109(25)=259702(1) 259702-1  2012 American Physical Society

Comment on "Excitons in Molecular Aggregates with Levy-Type Disorder:Anomalous Localization and Exchange Broadening of Optical Spectra" Reply

Vlaming, S.

Malyshev, V.

MPG.PuRe

   University of GroningenComment on "Excitons in Molecular Aggregates with Levy-Type DisorderEisfeld, A.; Vlaming, S. M.; Moebius, S.; Malyshev, V.A.; Knoester, J.Published in:Physical Review LettersDOI:10.1103/PhysRevLett.109.259702IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2012Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Eisfeld, A., Vlaming, S. M., Moebius, S., Malyshev, V. A., & Knoester, J. (2012). Comment on "Excitons inMolecular Aggregates with Levy-Type Disorder: Anomalous Localization and Exchange Broadening ofOptical Spectra" Reply. Physical Review Letters, 109(25), 259702-1-259702-1. Article 259702.https://doi.org/10.1103/PhysRevLett.109.259702CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 05-12-2023Eisfeld et al. Reply: The authors of the precedingComment [1] questioned our statement regarding the un-conventional disorder scalings of the HWHM and thenonuniversality of the localization length (LL) distributionreported by us our Letter [2]. We attributed these findingsto originate from segmentation caused by the occurrence ofoutliers [2]. We demonstrate here that our conclusions arecorrect and that the criticism in Ref. [1] is a consequence offocusing on small values of the disorder strength .The conventional  scaling for the HWHM (derived inRef. [2] for linear chains with site disorder drawn fromgeneral symmetric -stable distributions) reads HWHMJð=JÞ2=ð1þÞ, J being the intersite nearest neighbor in-teraction. Here, segmentation is not taken into account.Outliers become more abundant for smaller . By equatingN and Nseg from Eqs. (3) and (4) in Ref. [2], one canestimate the value of  above which segmentation starts toplay a role [see shaded region in Fig. 1(a)].For  & J (values of interest for many molecular sys-tems), deviations from the conventional HWHM  scalingare not seen for  ¼ 2 and 1 (Gaussian and Lorentziandisorder, respectively). However, for  & 0:5, we foundclear deviations.This is shown in Figs. 1(b) and 1(c), where for  * 0:4the conventional scaling (solid red lines) clearly breaksdown. Moreover, the data points show kinks at which theHWHM suddenly jumps. This is not noise. It can beattributed to structure in the high-energy wing of theabsorption spectrum, which grows upon increasing , asa consequence of segmentation [2]. Both effects becomemore pronounced for smaller . The data also show thatthese features cannot be adequately fitted by a power law.Finally, we point out that the straight reference line inFig. 2 of Ref. [2] is irrelevant and has no effect on theconclusion of the existence of exchange broadening of theabsorption spectrum.Next, we demonstrate the nonuniversality of the LLdistribution due to segmentation by outliers. Figure 2 dis-plays the normalized LL distributions obtained for ¼ 0:5using the same scaling of the energy interval as inRefs. [1,3]. In Fig. 2(a), small   0:1J are considered,as in Ref. [1]. Segmentation is irrelevant here and thenormalized LL distributions are nearly identical. Yet, al-ready for  ¼ 0:1J, deviations become visible in the ap-pearance of sharp peaks at small LL. Upon increasing [Fig. 2(b)], the deviations become more pronounced, andthe nonuniversal character of the LL distribution is clear.This is the effect of outliers. In Ref. [1] it is stated that theconventional scalings break down at high  values, onlybecause Nloc approaches unity: a trivial effect. We havedemonstrated that the breakdown of scalings found by us ismore subtle and is related to a frequent occurrence ofoutliers when  & 0:5.A. Eisfeld,1 S.M. Vlaming,2,3 S. Möbius,1V. A. Malyshev,2 and J. Knoester21Max Planck Institute for Physics of Complex SystemsNöthnitzer Strasse 38, D-01187 Dresden, Germany2Centre for Theoretical Physicsand Zernike Institute for Advanced MaterialsUniversity of GroningenNijenborgh 4, 9747 AG Groningen, The Netherlands3Department of ChemistryMassachusetts Institute of Technology77 Massachusetts AvenueCambridge, Massachusetts 02139, USAReceived 27 August 2012; published 21 December 2012DOI: 10.1103/PhysRevLett.109.259702PACS numbers: 78.30.Ly, 71.35.Aa, 73.20.Mf[1] A. Werpachowska and A. Olaya-Castro, precedingComment, Phys. Rev. Lett. 109, 259701 (2012).[2] A. Eisfeld, S.M. Vlaming, V.A. Malyshev, and J.Knoester, Phys. Rev. Lett. 105, 137402 (2010).[3] S.M. Vlaming, V. A. Malyshev, and J. Knoester, Phys.Rev. B 79, 205121 (2009).(a)(b) (c)FIG. 1 (color online). (a) Diagram showing for which (, )the chain segmentation dominates localization (shaded area). (b),(c) HWHM  scaling of the absorption peak. Data (þ), resultsof numerical simulations (N ¼ 200); red curves, conventionalscaling law.locloc loc loc locloclocloc(a) (b)FIG. 2 (color online). Normalized LL distributions calculatedfor  ¼ 0:5 (N ¼ 200). In (b), the curves have different verticaloffsets to better show their distinction.PRL 109, 259702 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending21 DECEMBER 20120031-9007=12=109(25)=259702(1) 259702-1  2012 American Physical Society

University of Groningen

   University of GroningenComment on "Excitons in Molecular Aggregates with Levy-Type DisorderEisfeld, A.; Vlaming, S. M.; Moebius, S.; Malyshev, V.A.; Knoester, J.Published in:Physical Review LettersDOI:10.1103/PhysRevLett.109.259702IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2012Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Eisfeld, A., Vlaming, S. M., Moebius, S., Malyshev, V. A., & Knoester, J. (2012). Comment on "Excitons inMolecular Aggregates with Levy-Type Disorder: Anomalous Localization and Exchange Broadening ofOptical Spectra" Reply. Physical Review Letters, 109(25), 259702-1-259702-1. [259702].https://doi.org/10.1103/PhysRevLett.109.259702CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 26-04-2023Eisfeld et al. Reply: The authors of the precedingComment [1] questioned our statement regarding the un-conventional disorder scalings of the HWHM and thenonuniversality of the localization length (LL) distributionreported by us our Letter [2]. We attributed these findingsto originate from segmentation caused by the occurrence ofoutliers [2]. We demonstrate here that our conclusions arecorrect and that the criticism in Ref. [1] is a consequence offocusing on small values of the disorder strength .The conventional  scaling for the HWHM (derived inRef. [2] for linear chains with site disorder drawn fromgeneral symmetric -stable distributions) reads HWHMJð=JÞ2=ð1þÞ, J being the intersite nearest neighbor in-teraction. Here, segmentation is not taken into account.Outliers become more abundant for smaller . By equatingN and Nseg from Eqs. (3) and (4) in Ref. [2], one canestimate the value of  above which segmentation starts toplay a role [see shaded region in Fig. 1(a)].For  & J (values of interest for many molecular sys-tems), deviations from the conventional HWHM  scalingare not seen for  ¼ 2 and 1 (Gaussian and Lorentziandisorder, respectively). However, for  & 0:5, we foundclear deviations.This is shown in Figs. 1(b) and 1(c), where for  * 0:4the conventional scaling (solid red lines) clearly breaksdown. Moreover, the data points show kinks at which theHWHM suddenly jumps. This is not noise. It can beattributed to structure in the high-energy wing of theabsorption spectrum, which grows upon increasing , asa consequence of segmentation [2]. Both effects becomemore pronounced for smaller . The data also show thatthese features cannot be adequately fitted by a power law.Finally, we point out that the straight reference line inFig. 2 of Ref. [2] is irrelevant and has no effect on theconclusion of the existence of exchange broadening of theabsorption spectrum.Next, we demonstrate the nonuniversality of the LLdistribution due to segmentation by outliers. Figure 2 dis-plays the normalized LL distributions obtained for ¼ 0:5using the same scaling of the energy interval as inRefs. [1,3]. In Fig. 2(a), small   0:1J are considered,as in Ref. [1]. Segmentation is irrelevant here and thenormalized LL distributions are nearly identical. Yet, al-ready for  ¼ 0:1J, deviations become visible in the ap-pearance of sharp peaks at small LL. Upon increasing [Fig. 2(b)], the deviations become more pronounced, andthe nonuniversal character of the LL distribution is clear.This is the effect of outliers. In Ref. [1] it is stated that theconventional scalings break down at high  values, onlybecause Nloc approaches unity: a trivial effect. We havedemonstrated that the breakdown of scalings found by us ismore subtle and is related to a frequent occurrence ofoutliers when  & 0:5.A. Eisfeld,1 S.M. Vlaming,2,3 S. Möbius,1V. A. Malyshev,2 and J. Knoester21Max Planck Institute for Physics of Complex SystemsNöthnitzer Strasse 38, D-01187 Dresden, Germany2Centre for Theoretical Physicsand Zernike Institute for Advanced MaterialsUniversity of GroningenNijenborgh 4, 9747 AG Groningen, The Netherlands3Department of ChemistryMassachusetts Institute of Technology77 Massachusetts AvenueCambridge, Massachusetts 02139, USAReceived 27 August 2012; published 21 December 2012DOI: 10.1103/PhysRevLett.109.259702PACS numbers: 78.30.Ly, 71.35.Aa, 73.20.Mf[1] A. Werpachowska and A. Olaya-Castro, precedingComment, Phys. Rev. Lett. 109, 259701 (2012).[2] A. Eisfeld, S.M. Vlaming, V.A. Malyshev, and J.Knoester, Phys. Rev. Lett. 105, 137402 (2010).[3] S.M. Vlaming, V. A. Malyshev, and J. Knoester, Phys.Rev. B 79, 205121 (2009).(a)(b) (c)FIG. 1 (color online). (a) Diagram showing for which (, )the chain segmentation dominates localization (shaded area). (b),(c) HWHM  scaling of the absorption peak. Data (þ), resultsof numerical simulations (N ¼ 200); red curves, conventionalscaling law.locloc loc loc locloclocloc(a) (b)FIG. 2 (color online). Normalized LL distributions calculatedfor  ¼ 0:5 (N ¼ 200). In (b), the curves have different verticaloffsets to better show their distinction.PRL 109, 259702 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending21 DECEMBER 20120031-9007=12=109(25)=259702(1) 259702-1  2012 American Physical Society

   University of GroningenComment on "Excitons in Molecular Aggregates with Levy-Type DisorderEisfeld, A.; Vlaming, S. M.; Moebius, S.; Malyshev, V.A.; Knoester, J.Published in:Physical Review LettersDOI:10.1103/PhysRevLett.109.259702IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2012Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Eisfeld, A., Vlaming, S. M., Moebius, S., Malyshev, V. A., & Knoester, J. (2012). Comment on "Excitons inMolecular Aggregates with Levy-Type Disorder: Anomalous Localization and Exchange Broadening ofOptical Spectra" Reply. Physical Review Letters, 109(25), 259702-1-259702-1. [259702].https://doi.org/10.1103/PhysRevLett.109.259702CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 12-11-2019Eisfeld et al. Reply: The authors of the precedingComment [1] questioned our statement regarding the un-conventional disorder scalings of the HWHM and thenonuniversality of the localization length (LL) distributionreported by us our Letter [2]. We attributed these findingsto originate from segmentation caused by the occurrence ofoutliers [2]. We demonstrate here that our conclusions arecorrect and that the criticism in Ref. [1] is a consequence offocusing on small values of the disorder strength .The conventional  scaling for the HWHM (derived inRef. [2] for linear chains with site disorder drawn fromgeneral symmetric -stable distributions) reads HWHMJð=JÞ2=ð1þÞ, J being the intersite nearest neighbor in-teraction. Here, segmentation is not taken into account.Outliers become more abundant for smaller . By equatingN and Nseg from Eqs. (3) and (4) in Ref. [2], one canestimate the value of  above which segmentation starts toplay a role [see shaded region in Fig. 1(a)].For  & J (values of interest for many molecular sys-tems), deviations from the conventional HWHM  scalingare not seen for  ¼ 2 and 1 (Gaussian and Lorentziandisorder, respectively). However, for  & 0:5, we foundclear deviations.This is shown in Figs. 1(b) and 1(c), where for  * 0:4the conventional scaling (solid red lines) clearly breaksdown. Moreover, the data points show kinks at which theHWHM suddenly jumps. This is not noise. It can beattributed to structure in the high-energy wing of theabsorption spectrum, which grows upon increasing , asa consequence of segmentation [2]. Both effects becomemore pronounced for smaller . The data also show thatthese features cannot be adequately fitted by a power law.Finally, we point out that the straight reference line inFig. 2 of Ref. [2] is irrelevant and has no effect on theconclusion of the existence of exchange broadening of theabsorption spectrum.Next, we demonstrate the nonuniversality of the LLdistribution due to segmentation by outliers. Figure 2 dis-plays the normalized LL distributions obtained for ¼ 0:5using the same scaling of the energy interval as inRefs. [1,3]. In Fig. 2(a), small   0:1J are considered,as in Ref. [1]. Segmentation is irrelevant here and thenormalized LL distributions are nearly identical. Yet, al-ready for  ¼ 0:1J, deviations become visible in the ap-pearance of sharp peaks at small LL. Upon increasing [Fig. 2(b)], the deviations become more pronounced, andthe nonuniversal character of the LL distribution is clear.This is the effect of outliers. In Ref. [1] it is stated that theconventional scalings break down at high  values, onlybecause Nloc approaches unity: a trivial effect. We havedemonstrated that the breakdown of scalings found by us ismore subtle and is related to a frequent occurrence ofoutliers when  & 0:5.A. Eisfeld,1 S.M. Vlaming,2,3 S. Mo¨bius,1V. A. Malyshev,2 and J. Knoester21Max Planck Institute for Physics of Complex SystemsNo¨thnitzer Strasse 38, D-01187 Dresden, Germany2Centre for Theoretical Physicsand Zernike Institute for Advanced MaterialsUniversity of GroningenNijenborgh 4, 9747 AG Groningen, The Netherlands3Department of ChemistryMassachusetts Institute of Technology77 Massachusetts AvenueCambridge, Massachusetts 02139, USAReceived 27 August 2012; published 21 December 2012DOI: 10.1103/PhysRevLett.109.259702PACS numbers: 78.30.Ly, 71.35.Aa, 73.20.Mf[1] A. Werpachowska and A. Olaya-Castro, precedingComment, Phys. Rev. Lett. 109, 259701 (2012).[2] A. Eisfeld, S.M. Vlaming, V.A. Malyshev, and J.Knoester, Phys. Rev. Lett. 105, 137402 (2010).[3] S.M. Vlaming, V. A. Malyshev, and J. Knoester, Phys.Rev. B 79, 205121 (2009).(a)(b) (c)FIG. 1 (color online). (a) Diagram showing for which (, )the chain segmentation dominates localization (shaded area). (b),(c) HWHM  scaling of the absorption peak. Data (þ), resultsof numerical simulations (N ¼ 200); red curves, conventionalscaling law.locloc loc loc locloclocloc(a) (b)FIG. 2 (color online). Normalized LL distributions calculatedfor  ¼ 0:5 (N ¼ 200). In (b), the curves have different verticaloffsets to better show their distinction.PRL 109, 259702 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending21 DECEMBER 20120031-9007=12=109(25)=259702(1) 259702-1  2012 American Physical Society

University of GroningenComment on "Excitons in Molecular Aggregates with Levy-Type DisorderEisfeld, A.; Vlaming, S. M.; Moebius, S.; Malyshev, V.A.; Knoester, J.Published in:Physical Review LettersDOI:10.1103/PhysRevLett.109.259702IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2012Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Eisfeld, A., Vlaming, S. M., Moebius, S., Malyshev, V. A., & Knoester, J. (2012). Comment on "Excitons inMolecular Aggregates with Levy-Type Disorder: Anomalous Localization and Exchange Broadening ofOptical Spectra" Reply. Physical Review Letters, 109(25), 259702-1-259702-1. Article 259702.https://doi.org/10.1103/PhysRevLett.109.259702CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 30-12-2025Eisfeld et al. Reply: The authors of the precedingComment [1] questioned our statement regarding the un-conventional disorder scalings of the HWHM and thenonuniversality of the localization length (LL) distributionreported by us our Letter [2]. We attributed these findingsto originate from segmentation caused by the occurrence ofoutliers [2]. We demonstrate here that our conclusions arecorrect and that the criticism in Ref. [1] is a consequence offocusing on small values of the disorder strength .The conventional  scaling for the HWHM (derived inRef. [2] for linear chains with site disorder drawn fromgeneral symmetric -stable distributions) reads HWHMJð=JÞ2=ð1þÞ, J being the intersite nearest neighbor in-teraction. Here, segmentation is not taken into account.Outliers become more abundant for smaller . By equatingN and Nseg from Eqs. (3) and (4) in Ref. [2], one canestimate the value of  above which segmentation starts toplay a role [see shaded region in Fig. 1(a)].For  & J (values of interest for many molecular sys-tems), deviations from the conventional HWHM  scalingare not seen for  ¼ 2 and 1 (Gaussian and Lorentziandisorder, respectively). However, for  & 0:5, we foundclear deviations.This is shown in Figs. 1(b) and 1(c), where for  * 0:4the conventional scaling (solid red lines) clearly breaksdown. Moreover, the data points show kinks at which theHWHM suddenly jumps. This is not noise. It can beattributed to structure in the high-energy wing of theabsorption spectrum, which grows upon increasing , asa consequence of segmentation [2]. Both effects becomemore pronounced for smaller . The data also show thatthese features cannot be adequately fitted by a power law.Finally, we point out that the straight reference line inFig. 2 of Ref. [2] is irrelevant and has no effect on theconclusion of the existence of exchange broadening of theabsorption spectrum.Next, we demonstrate the nonuniversality of the LLdistribution due to segmentation by outliers. Figure 2 dis-plays the normalized LL distributions obtained for ¼ 0:5using the same scaling of the energy interval as inRefs. [1,3]. In Fig. 2(a), small   0:1J are considered,as in Ref. [1]. Segmentation is irrelevant here and thenormalized LL distributions are nearly identical. Yet, al-ready for  ¼ 0:1J, deviations become visible in the ap-pearance of sharp peaks at small LL. Upon increasing [Fig. 2(b)], the deviations become more pronounced, andthe nonuniversal character of the LL distribution is clear.This is the effect of outliers. In Ref. [1] it is stated that theconventional scalings break down at high  values, onlybecause Nloc approaches unity: a trivial effect. We havedemonstrated that the breakdown of scalings found by us ismore subtle and is related to a frequent occurrence ofoutliers when  & 0:5.A. Eisfeld,1 S.M. Vlaming,2,3 S. Möbius,1V. A. Malyshev,2 and J. Knoester21Max Planck Institute for Physics of Complex SystemsNöthnitzer Strasse 38, D-01187 Dresden, Germany2Centre for Theoretical Physicsand Zernike Institute for Advanced MaterialsUniversity of GroningenNijenborgh 4, 9747 AG Groningen, The Netherlands3Department of ChemistryMassachusetts Institute of Technology77 Massachusetts AvenueCambridge, Massachusetts 02139, USAReceived 27 August 2012; published 21 December 2012DOI: 10.1103/PhysRevLett.109.259702PACS numbers: 78.30.Ly, 71.35.Aa, 73.20.Mf[1] A. Werpachowska and A. Olaya-Castro, precedingComment, Phys. Rev. Lett. 109, 259701 (2012).[2] A. Eisfeld, S.M. Vlaming, V.A. Malyshev, and J.Knoester, Phys. Rev. Lett. 105, 137402 (2010).[3] S.M. Vlaming, V. A. Malyshev, and J. Knoester, Phys.Rev. B 79, 205121 (2009).(a)(b) (c)FIG. 1 (color online). (a) Diagram showing for which (, )the chain segmentation dominates localization (shaded area). (b),(c) HWHM  scaling of the absorption peak. Data (þ), resultsof numerical simulations (N ¼ 200); red curves, conventionalscaling law.locloc loc loc locloclocloc(a) (b)FIG. 2 (color online). Normalized LL distributions calculatedfor  ¼ 0:5 (N ¼ 200). In (b), the curves have different verticaloffsets to better show their distinction.PRL 109, 259702 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending21 DECEMBER 20120031-9007=12=109(25)=259702(1) 259702-1  2012 American Physical Society

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