In this talk we report our study on the thermal modifications of charmonia and bottomonia from spatial correlation functions at zero and nonzero momenta in quenched QCD. To accommodate the heavy quarks on the lattice we performed simulations on very fine lattices at a fixed beta value corresponding to a lattice spacing $a^{-1}\sim $22 GeV on $192^3\times 32$, $192^3\times 48$, $192^3\times 64$ and $192^3\times 96$ lattices using clover-improved Wilson fermions. These lattices correspond to temperatures at $2.25T_c$, $1.50T_c$, $1.10T_c$ and $0.75T_c$. To increase the signal to noise ratio in the axial-vector and scalar channels we used multi-sources for the measurement of spatial correlation functions. By investigating on the differences between spatial and temporal correlators as well as the temperature dependence of screening masses we will discuss the thermal effects in different channels of quarkonium states. Besides this the dispersion relation of the screening mass at different momenta is also discussed.

Nonzero Temperature and Density