We study a dynamic boundary, e.g. a mobile impurity, coupled to N independent Tomonaga-Luttinger liquids (TLLs) each with interaction parameter K. We demonstrate that for N>2 there is a quantum phase transition at K>1/2, where the TLL phases lock tog
ether at the particle position, resulting in a non-zero transconductance equal to e^2/Nh. The transition line terminates for strong coupling at K=1- 1/N, consistent with results at large N. Another type of a dynamic boundary is a superconducting (or Bose-Einstein condensate) grain coupled to N>2 TLLs, here the transition signals also the onset of a relevant Josephson coupling.
We study zero temperature spin dynamics of a particle confined to a ring in presence of spin orbit coupling and Ohmic electromagnetic fluctuations. We show that the dynamics of the angular position $theta(t)$ are decoupled from the spin dynamics and
that the latter is mapped to certain correlations of a spinless particle. We find that the spin correlations in the $z$ direction (perpendicular to the ring) are finite at long times, i.e. do not dephase. The parallel (in plane) components for spin $half$ do not dephase at weak dissipation but they probably decay as a power law with time at strong dissipation.
We present 3D numerical simulation results of moving vortex lattices in presence of 1D correlated disorder at zero temperature. Our results with field tilting confirm the theoritical predictions of a moving Bose glass phase, characterized by transver
se pinning and dynamical transverse Meissner effect, the moving flux lines being localized along the correlated disorder direction. Beyond a critical transverse field, vortex lines exhibit along all their length a kink structure resulting from an effective static tin roof pinning potential in the transverse direction.
