Say a student is enrolled in a PhD program in the US and is in the first or 2nd year and has not started their thesis work but has only done coursework. The student has always been in the same lab (no rotations). Say such student for whatever reason wants to switch to a PhD program in Europe.
How should such a student handle contacting PhD advisors and other institutions? Should the student mention in the first e-mail that they are already enrolled in a PhD program or can this be mentioned in the first phone call? Or should it be mentioned at all? How much would this situation decrease the chances of getting accepted into a PhD program in Europe? Or should the student first quit the current PhD program before applying to any other program?