Non-reciprocal phase transitions
Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter 1 – 6 , non-equilibrium systems 7 – 9 , networks of neurons 10 , 11 , social groups with conformist and contrarian members 12 , directional interface growth phenome...
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| Vydáno v: | Nature (London) Ročník 592; číslo 7854; s. 363 - 369 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
London
Nature Publishing Group UK
15.04.2021
Nature Publishing Group |
| Témata: | |
| ISSN: | 0028-0836, 1476-4687, 1476-4687 |
| On-line přístup: | Získat plný text |
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| Abstract | Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter
1
–
6
, non-equilibrium systems
7
–
9
, networks of neurons
10
,
11
, social groups with conformist and contrarian members
12
, directional interface growth phenomena
13
–
15
and metamaterials
16
–
20
. Although wave propagation in non-reciprocal media has recently been closely studied
1
,
16
–
20
, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points
21
. We describe the emergence of these phases using insights from bifurcation theory
22
,
23
and non-Hermitian quantum mechanics
24
,
25
. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle.
A theoretical study of non-reciprocity in collective phenomena reveals the emergence of time-dependent phases heralded by exceptional points in contexts ranging from synchronization and flocking to pattern formation. |
|---|---|
| AbstractList | Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter
, non-equilibrium systems
, networks of neurons
, social groups with conformist and contrarian members
, directional interface growth phenomena
and metamaterials
. Although wave propagation in non-reciprocal media has recently been closely studied
, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points
. We describe the emergence of these phases using insights from bifurcation theory
and non-Hermitian quantum mechanics
. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle. Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter 1 – 6 , non-equilibrium systems 7 – 9 , networks of neurons 10 , 11 , social groups with conformist and contrarian members 12 , directional interface growth phenomena 13 – 15 and metamaterials 16 – 20 . Although wave propagation in non-reciprocal media has recently been closely studied 1 , 16 – 20 , less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points 21 . We describe the emergence of these phases using insights from bifurcation theory 22 , 23 and non-Hermitian quantum mechanics 24 , 25 . Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle. A theoretical study of non-reciprocity in collective phenomena reveals the emergence of time-dependent phases heralded by exceptional points in contexts ranging from synchronization and flocking to pattern formation. Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter.sup.1-6, non-equilibrium systems.sup.7-9, networks of neurons.sup.10,11, social groups with conformist and contrarian members.sup.12, directional interface growth phenomena.sup.13-15 and metamaterials.sup.16-20. Although wave propagation in non-reciprocal media has recently been closely studied.sup.1,16-20, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points.sup.21. We describe the emergence of these phases using insights from bifurcation theory.sup.22,23 and non-Hermitian quantum mechanics.sup.24,25. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle. Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter.sup.1-6, non-equilibrium systems.sup.7-9, networks of neurons.sup.10,11, social groups with conformist and contrarian members.sup.12, directional interface growth phenomena.sup.13-15 and metamaterials.sup.16-20. Although wave propagation in non-reciprocal media has recently been closely studied.sup.1,16-20, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points.sup.21. We describe the emergence of these phases using insights from bifurcation theory.sup.22,23 and non-Hermitian quantum mechanics.sup.24,25. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle. A theoretical study of non-reciprocity in collective phenomena reveals the emergence of time-dependent phases heralded by exceptional points in contexts ranging from synchronization and flocking to pattern formation. Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter1-6, non-equilibrium systems7-9, networks of neurons10,11, social groups with conformist and contrarian members12, directional interface growth phenomena13-15 and metamaterials16-20. Although wave propagation in non-reciprocal media has recently been closely studied1,16-20, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points21. We describe the emergence of these phases using insights from bifurcation theory22,23 and non-Hermitian quantum mechanics24,25. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi) crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle. Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter1-6, non-equilibrium systems7-9, networks of neurons10,11, social groups with conformist and contrarian members12, directional interface growth phenomena13-15 and metamaterials16-20. Although wave propagation in non-reciprocal media has recently been closely studied1,16-20, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points21. We describe the emergence of these phases using insights from bifurcation theory22,23 and non-Hermitian quantum mechanics24,25. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle.Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter1-6, non-equilibrium systems7-9, networks of neurons10,11, social groups with conformist and contrarian members12, directional interface growth phenomena13-15 and metamaterials16-20. Although wave propagation in non-reciprocal media has recently been closely studied1,16-20, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points21. We describe the emergence of these phases using insights from bifurcation theory22,23 and non-Hermitian quantum mechanics24,25. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle. |
| Audience | Academic |
| Author | Vitelli, Vincenzo Fruchart, Michel Littlewood, Peter B. Hanai, Ryo |
| Author_xml | – sequence: 1 givenname: Michel surname: Fruchart fullname: Fruchart, Michel organization: James Franck Institute and Department of Physics, University of Chicago – sequence: 2 givenname: Ryo surname: Hanai fullname: Hanai, Ryo organization: James Franck Institute and Department of Physics, University of Chicago, Department of Physics, Osaka University, Pritzker School of Molecular Engineering, University of Chicago – sequence: 3 givenname: Peter B. surname: Littlewood fullname: Littlewood, Peter B. organization: James Franck Institute and Department of Physics, University of Chicago – sequence: 4 givenname: Vincenzo orcidid: 0000-0001-6328-8783 surname: Vitelli fullname: Vitelli, Vincenzo email: vitelli@uchicago.edu organization: James Franck Institute and Department of Physics, University of Chicago, Kadanoff Center for Theoretical Physics, University of Chicago |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/33854249$$D View this record in MEDLINE/PubMed |
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| Copyright | The Author(s), under exclusive licence to Springer Nature Limited 2021 COPYRIGHT 2021 Nature Publishing Group Copyright Nature Publishing Group Apr 15, 2021 |
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, non-equilibrium... Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter , non-equilibrium... Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter.sup.1-6,... Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter1-6, non-equilibrium... |
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| Title | Non-reciprocal phase transitions |
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