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We study the dispersion properties of electron plasma waves, or plasmons,which can be excited in quantum plasmas in the nonlinear regime. In order todescribe nonlinear electron response to finite amplitude plasmons, we apply theVolkov approach to non-relativistic electrons. For that purpose, we use theSchr\"odinger equation and describe the electron population of a quantum plasmaas a mixture of quantum states. Within the kinetic framework that we are ableto derive from the Volkov solutions, we discuss the role of the wave amplitudeon the nonlinear plasma response. Finally, we focus on the quantum propertiesof nonlinear Landau damping and study the contributions of multi-plasmonabsorption and emission processes.

Plasmon dispersion and Landau damping in the nonlinear quantum regime