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Solid State Communications

The system of interacting polaritons: Classical versus quantum kinetic equation

Ivan Andreevich Shelykh, G. Malpuech, R. Johne, Alexey Vitalievich Kavokin

Published Aug 20, 2007• 1 citation
Publisher
DOI
10.1016/j.ssc.2007.07.042

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We derive quantum kinetic equations describing a system of interacting polaritons relaxing the Markovian approximation. We demonstrate the crucial role played by the nonclassical four-particle correlators in the dynamics. The decoherence process is shown to be responsible for the transition from the quantum limit to the classical limit. The general formalism is applied to the description of the dynamics of the polariton parametric oscillator. It allows accounting self-consistently for both signal-idler correlations and pump depletion.
A quasiclassical expression for the kinetic energy of interacting quantum many-body systems is derived from the full quantum expression for the kinetic energy as derived by means of the Fourier path integral representation of the canonical many-body density matrix of such systems. This quasiclassical form of the kinetic energy may be cast in the shape of thermodynamic expectation values w.r.t. to the classical Boltzmann distribution of the many-body system, which involves only the many-body interaction in contrast to the full Fourier path integral quantum distribution, which carries contributions also from the many-body kinetic energy operator. The quasiclassical quantum correction terms to the classical Boltzmann equipartition value are valid when the product of temperature and particle mass is large and then lead to significant technical simplifications and increase of speed of Monte Carlo computations of the quantum kinetic energy. The formal findings are tested numerically in quantum Fourier path integral versus classical Monte Carlo simulations.