On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates

Paolo Antonelli; Peter A. Markowich; Ryan Obermeyer; Jesus Sierra; CHRISTOF SPARBER

doi:10.1088/1361-6544/ab2bc1

On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates

Paolo Antonelli, Peter A. Markowich, Ryan Obermeyer, Jesus Sierra, CHRISTOF SPARBER

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Abstract

We study a generalized dissipative Gross-Pitaevskii-type model arising in the description of exciton-polariton condensates. We derive global in-time existence results and various a priori estimates for this model posed on the one-dimensional torus. Moreover, we analyze in detail the long-time behavior of spatially homogenous solutions and their respective steady states and present numerical simulations in the case of more general initial data. We also study the convergence to the corresponding adiabatic regime, which results in a single damped-driven Gross-Pitaveskii equation.

Original language	English (US)
Pages (from-to)	4317-4345
Number of pages	29
Journal	Nonlinearity
Volume	32
Issue number	11
DOIs	https://doi.org/10.1088/1361-6544/ab2bc1
State	Published - Oct 2 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors are grateful to the anonymous referee for helpful suggestions to improve upon an earlier version of this paper: in particular, we are grateful for pointing out the pointwise L∞-bound on n (see lemma 2.4) and for suggesting a Lyapunov-type functional similar to the one introduced in proposition 2.6.

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10.1088/1361-6544/ab2bc1

https://repository.kaust.edu.sa/bitstream/10754/660402/1/EPcondensate12.pdf

Cite this

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title = "On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates",

abstract = "We study a generalized dissipative Gross-Pitaevskii-type model arising in the description of exciton-polariton condensates. We derive global in-time existence results and various a priori estimates for this model posed on the one-dimensional torus. Moreover, we analyze in detail the long-time behavior of spatially homogenous solutions and their respective steady states and present numerical simulations in the case of more general initial data. We also study the convergence to the corresponding adiabatic regime, which results in a single damped-driven Gross-Pitaveskii equation.",

author = "Paolo Antonelli and Markowich, {Peter A.} and Ryan Obermeyer and Jesus Sierra and CHRISTOF SPARBER",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: The authors are grateful to the anonymous referee for helpful suggestions to improve upon an earlier version of this paper: in particular, we are grateful for pointing out the pointwise L∞-bound on n (see lemma 2.4) and for suggesting a Lyapunov-type functional similar to the one introduced in proposition 2.6.",

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AU - Antonelli, Paolo

AU - Markowich, Peter A.

AU - Obermeyer, Ryan

AU - Sierra, Jesus

AU - SPARBER, CHRISTOF

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: The authors are grateful to the anonymous referee for helpful suggestions to improve upon an earlier version of this paper: in particular, we are grateful for pointing out the pointwise L∞-bound on n (see lemma 2.4) and for suggesting a Lyapunov-type functional similar to the one introduced in proposition 2.6.

PY - 2019/10/2

Y1 - 2019/10/2

N2 - We study a generalized dissipative Gross-Pitaevskii-type model arising in the description of exciton-polariton condensates. We derive global in-time existence results and various a priori estimates for this model posed on the one-dimensional torus. Moreover, we analyze in detail the long-time behavior of spatially homogenous solutions and their respective steady states and present numerical simulations in the case of more general initial data. We also study the convergence to the corresponding adiabatic regime, which results in a single damped-driven Gross-Pitaveskii equation.

AB - We study a generalized dissipative Gross-Pitaevskii-type model arising in the description of exciton-polariton condensates. We derive global in-time existence results and various a priori estimates for this model posed on the one-dimensional torus. Moreover, we analyze in detail the long-time behavior of spatially homogenous solutions and their respective steady states and present numerical simulations in the case of more general initial data. We also study the convergence to the corresponding adiabatic regime, which results in a single damped-driven Gross-Pitaveskii equation.

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DO - 10.1088/1361-6544/ab2bc1

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EP - 4345

JO - Nonlinearity

JF - Nonlinearity

IS - 11

ER -

On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates

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