Interlacing relaxation and first-passage phenomena in reversible discrete and continuous space Markovian dynamics

Hartich, David; Godec, Aljaž

doi:10.1088/1742-5468/ab00df

Cited by 49 publications

(66 citation statements)

References 91 publications

(220 reference statements)

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“…Moreover, the poles have no accumulation point in the left half plane Ã ( | ) are those zeroes of P x s a ,( | ), which are different from the zeroes of P x s x , 0 ( | ). Generally, P x s x , 0 ( | )and P x s a ,( | ) have infinitely many coinciding zeroes alongside the distinct ones (see proof in [59]), because the region beyond a cannot affect the first passage time from x 0 , whereas it must affect the relaxation. However, all common zeroes result in a vanishing residue.…”

Section: First Passage Time Density From the Relaxation Spectrummentioning

confidence: 99%

“…One can prove that setting x = a in equations (2) and ( [59]). Based on the interlacing in equation (4) we are now in the position to determine the entire first passage time statistics from the relaxation eigenspectrum,…”

Section: First Passage Time Density From the Relaxation Spectrummentioning

confidence: 99%

“…The calculation becomes rather involved and is sketched in the appendix (see also [59]), here we simply state the result. Introducing…”

Section: First Passage Time Density From the Relaxation Spectrummentioning

confidence: 99%

“…Using equation (7) the determinant k det n  ( ) of the almost triangular matrix with elements (6) is fully characterized, which in turn determines the first passage eigenvalue equation (5). It is now easy to obtain t x a 0 Ã ( | ) by inverting the Laplace transform in equation (3) using Cauchy's residue theorem yielding [59]…”

Section: First Passage Time Density From the Relaxation Spectrummentioning

confidence: 99%

“…Using standard Green's function theory [59] it can be shown after some straightforward but tedious algebra that…”

Section: First Passage Time Density From the Relaxation Spectrummentioning

confidence: 99%

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Duality between relaxation and first passage in reversible Markov dynamics: rugged energy landscapes disentangled

Hartich

Godec

2018

New J. Phys.

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Relaxation and first passage processes are the pillars of kinetics in condensed matter, polymeric and single-molecule systems. Yet, an explicit connection between relaxation and first passage time-scales so far remained elusive. Here we prove a duality between them in the form of an interlacing of spectra. In the basic form the duality holds for reversible Markov processes to effectively one-dimensional targets. The exploration of a triple-well potential is analyzed to demonstrate how the duality allows for an intuitive understanding of first passage trajectories in terms of relaxational eigenmodes. More generally, we provide a comprehensive explanation of the full statistics of reactive trajectories in rugged potentials, incl. the so-called 'few-encounter limit'. Our results are required for explaining quantitatively the occurrence of diseases triggered by protein misfolding. 1 l -, the longest relaxation time, and the mean first passage time to surmount the highest barrier in the landscape [7][8][9][10][11]56]. However, in spite of the

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Section: First Passage Time Density From the Relaxation Spectrummentioning

confidence: 99%

Section: First Passage Time Density From the Relaxation Spectrummentioning

confidence: 99%

“…The calculation becomes rather involved and is sketched in the appendix (see also [59]), here we simply state the result. Introducing…”

Section: First Passage Time Density From the Relaxation Spectrummentioning

confidence: 99%

Section: First Passage Time Density From the Relaxation Spectrummentioning

confidence: 99%

“…Using standard Green's function theory [59] it can be shown after some straightforward but tedious algebra that…”

Section: First Passage Time Density From the Relaxation Spectrummentioning

confidence: 99%

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Duality between relaxation and first passage in reversible Markov dynamics: rugged energy landscapes disentangled

Hartich

Godec

2018

New J. Phys.

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Pair-Correlation Effects in Many-Body Systems

Blom

2023

Springer Theses

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While pursuing a Ph.D. in the Mathematical bioPhysics Group in Göttingen I got acquainted with many great people, who have contributed in their own way to this work, and to the person I have become. It remains a difficult task to acknowledge all of these people with concise wording, and therefore I consider my attempt below also far from complete.First and foremost I thank my supervisor Aljaž Godec. I can say with great confidence that I could not have gotten a better supervisor. His office door has always been open for a discussion, a coffee, or a good Chuck Norris fact. Without his guidance, and constant desire for a deeper understanding, I would not have been able to produce the work presented in this thesis. The way Aljaž thinks in terms of inequalities and counterexamples has been of great influence on my way of thinking. I also thank Aljaž's family who has shown great hospitality to me.Secondly, I would like to thank my colleagues -those in the past and present -in the Mathematical bioPhysics Group. Alessio Lapolla and David Hartich were the first two colleagues I met, and I thank you both for your kindness and inspiring work attitude. Alessio convinced me to join his sports wrestling courses, which were a lot of fun, despite his superior strength. With David and his family I share many warm memories, and the visit to Esslingen was a highlight that hopefully will soon take place again. Together with Maximilian Vossel I started my doctorate. Being the barista in our group, he has made many delicious espressos, and I thank you for your thoughtfulness and for the great moments we share. I thank Cai Dieball for his sharp questions, fruitful discussions, dry humor, and the rounds of tennis we played during the summer. With Janik Schüttler I had many enjoyable moments on the running track, where he often pushed me to do an extra round. I thank you for your friendliness and positive spirit, hopefully we can once meet again in Cambridge. Finally, I thank Rick Bebon and Gerrit Wellecke for being such pleasant colleagues, who are always open to a discussion. Rick has extensively read every chapter of my thesis, and provided me with great feedback. All in all, I am thankful for my colleagues who made/make the Mathematical bioPhysics Group a great place to work. V Within the Theoretical and Computational Biophysics department there were/are also many colleagues to thank. Special thanks go to Lars Bock, Sara Gabrielli, Gabor Nagy, Florian Leidner, Wojciech Kopec, and Peleg Sapir who have been thoughtful, friendly, and open to me. It was a pleasure to have lunch with you, meet for leisure time, or to have a little chat in the office. I thank Ansgar Esztermann and Martin Fechner for teaching me the ins and outs of computer cluster usage, which I initially did not use correctly. Furthermore, I thank Eveline Heinemann, Stefanie Teichmann, and Petra Kellers for the administrative assistance and their fast support during times I was rather late with my conference applications. Finally, I would like to thank Helmut Grubmüller ...

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Criticality in Cell Adhesion

Blom¹

2023

Springer Theses

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Interlacing relaxation and first-passage phenomena in reversible discrete and continuous space Markovian dynamics

Cited by 49 publications

References 91 publications

Duality between relaxation and first passage in reversible Markov dynamics: rugged energy landscapes disentangled

Duality between relaxation and first passage in reversible Markov dynamics: rugged energy landscapes disentangled

Pair-Correlation Effects in Many-Body Systems

Criticality in Cell Adhesion

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