If the diameter of the copper and quartz pipes are close you can use a short piece of silicone rubber tubing to connect the two pipes. After placing the tubing over the pipes you can secure with hose clamps or wrap with wire to hold in place.
Not sure what temperatures you are working at but silicone is stable to heat and is fairly inert.
For connecting quartz pipe with copper pipe “universal joint" method is useful. You need to prepare groove on quartz pipe where specially design universal joint can be used. If pipe diameter is standard one can go with standard universal joint available in market. Please refer US patents US5516159 for details where you can get some idea to join quartz pipe with copper pipe.