`Quantum phase transitions' in classical nonequilibrium processes

Eldad Bettelheim; Oded Agam; Nadav M. Shnerb

doi:10.1016/S1386-9477(00)00268-X

`Quantum phase transitions' in classical nonequilibrium processes

Eldad Bettelheim
, Oded Agam
, Nadav M. Shnerb

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

Diffusion-limited reaction of the Lotka-Volterra type is analyzed taking into account the discrete nature of the reactants. In the continuum approximation, the dynamics is dominated by an elliptic fixed point. This fixed point becomes unstable due to discretization effects, a scenario similar to quantum phase transitions. As a result, the long-time asymptotic behavior of the system changes and the dynamics flows into a limit cycle. The results are verified by numerical simulations.

Original language	English
Pages (from-to)	600-608
Number of pages	9
Journal	Physica E: Low-Dimensional Systems and Nanostructures
Volume	9
Issue number	3
DOIs	https://doi.org/10.1016/S1386-9477(00)00268-X
State	Published - Mar 2001
Externally published	Yes

Bibliographical note

Funding Information:
This research was supported by The Israel Science Foundation founded by The Israel Academy of Science and Humanities, and by Grant No. 9800065 from the USA–Israel Binational Science Foundation (BSF).

Funding

This research was supported by The Israel Science Foundation founded by The Israel Academy of Science and Humanities, and by Grant No. 9800065 from the USA–Israel Binational Science Foundation (BSF).

Funders	Funder number
United States-Israel Binational Science Foundation
Israel Academy of Sciences and Humanities	9800065
Israel Science Foundation

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10.1016/S1386-9477(00)00268-X

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abstract = "Diffusion-limited reaction of the Lotka-Volterra type is analyzed taking into account the discrete nature of the reactants. In the continuum approximation, the dynamics is dominated by an elliptic fixed point. This fixed point becomes unstable due to discretization effects, a scenario similar to quantum phase transitions. As a result, the long-time asymptotic behavior of the system changes and the dynamics flows into a limit cycle. The results are verified by numerical simulations.",

author = "Eldad Bettelheim and Oded Agam and Shnerb, \{Nadav M.\}",

note = "Funding Information: This research was supported by The Israel Science Foundation founded by The Israel Academy of Science and Humanities, and by Grant No. 9800065 from the USA–Israel Binational Science Foundation (BSF). ",

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AU - Bettelheim, Eldad

AU - Agam, Oded

AU - Shnerb, Nadav M.

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PY - 2001/3

Y1 - 2001/3

N2 - Diffusion-limited reaction of the Lotka-Volterra type is analyzed taking into account the discrete nature of the reactants. In the continuum approximation, the dynamics is dominated by an elliptic fixed point. This fixed point becomes unstable due to discretization effects, a scenario similar to quantum phase transitions. As a result, the long-time asymptotic behavior of the system changes and the dynamics flows into a limit cycle. The results are verified by numerical simulations.

AB - Diffusion-limited reaction of the Lotka-Volterra type is analyzed taking into account the discrete nature of the reactants. In the continuum approximation, the dynamics is dominated by an elliptic fixed point. This fixed point becomes unstable due to discretization effects, a scenario similar to quantum phase transitions. As a result, the long-time asymptotic behavior of the system changes and the dynamics flows into a limit cycle. The results are verified by numerical simulations.

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ER -

`Quantum phase transitions' in classical nonequilibrium processes

Abstract

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