We address the kinetics of long-lived excitations at zero temperature in an electronic quantum Hall system with filling factor \(\nu = 2\). The initial coherent state of spin-cyclotron magnetoexitons with two-dimensional wave vector \(q = 0\) resulting from laser pumping is stochastized over time due to emission of acoustic phonons. The elementary emission process requires participation of two magnetoexitons, so the effective rate of phonon emission is proportional to the excitation density squared, and the stochastization process occurs nonexponentially with time. The final distribution of magnetoexitons over two-dimensional momenta, established as a result of stochastization, is compared with equilibrium distribution at finite temperature.
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Notes
This statement concerns also special phonon modes (optical or acoustic) arising in the GaAs/AlGaAs interface.
For the first time this operator was used in [6].
In this calculation one used the fact that the expectation \(\left\langle {0{\text{|}}{{{({{\mathcal{Q}}_{0}})}}^{{N + 1}}}{{{(\mathcal{Q}_{0}^{\dag })}}^{{N - 1}}}\mathcal{Q}_{{ - {{\mathbf{q}}_{1}}}}^{\dag }\mathcal{Q}_{{{{\mathbf{q}}_{1}}}}^{\dag }{\text{|}}0} \right\rangle \) at \({{\mathbf{q}}_{1}} \ne 0\) is independent of \({{\mathbf{q}}_{1}}\).
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ACKNOWLEDGMENTS
We are grateful to L.V. Kulik for useful discussions.
Funding
This work was supported by the Russian Science Foundation, project no. 21-12-00386.
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Dickmann, S., Kaysin, B.D. Stochastization of Long Living Spin-Cyclotron Excitations in a Spin-Unpolarised Quantum Hall System. Jetp Lett. 114, 585–592 (2021). https://doi.org/10.1134/S002136402122001X
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DOI: https://doi.org/10.1134/S002136402122001X