Impact of Temperature Gradients and Thermal Diffusion on Rayleigh-Taylor Instability in Strongly Coupled Quantum Plasmas

We have investigated the linear Rayleigh-Taylor instability driven by a temperature gradient in a thermally diffusive, strongly coupled quantum plasma under the incompressible limit. The heat diffusion equation, incorporating the background temperature gradient, is coupled with the transport dynamics of the self-gravitating quantum fluid. The resulting dispersion relation is analyzed in both the kinetic and hydrodynamic limits. In both regimes, the temperature gradient enhances the R-T instability, exhibiting features reminiscent of Rayleigh-Bénard convection. However, the system becomes unstable only when the temperature gradient exceeds a critical threshold. In the kinetic limit, the instability is always present, although viscosity and thermal diffusivity act to suppress its growth. Similarly, in the hydrodynamic limit, these dissipative effects can substantially diminish or even completely suppress the instability at higher wavenumbers.