Condensed Matter Theory

Abstract:

We report a method to control the positions of ellipsoidal magnets in flowing channels of rectangular or circular cross section at low Reynolds number. A static uniform magnetic field is used to pin the particle orientation and the particles move with translational drift velocities resulting from hydrodynamic interactions with the channel walls which can be described using Blake’s image tensor. Building on his insights, we are able to present a far-field theory predicting the particle motion in rectangular channels and validate the accuracy of the theory by comparing to numerical solutions using the boundary element method. We find that, by changing the direction of the applied magnetic field, the motion can be controlled so that particles move either to a curved focusing region or to the channel walls. We also use simulations to show that the particles are focused to a single line in a circular channel. Our results suggest ways to focus and segregate magnetic particles in lab-on-a-chip devices.

Abstract:

Quenched randomness can have a dramatic effect on the dynamics of isolated 1D quantum many-body systems, even for systems that thermalize. This is because transport, entanglement, and operator spreading can be hindered by “Griffiths” rare regions, which locally resemble the many-body-localized phase and thus act as weak links. We propose coarse-grained models for entanglement growth and for the spreading of quantum operators in the presence of such weak links. We also examine entanglement growth across a single weak link numerically. We show that these weak links have a stronger effect on entanglement growth than previously assumed: entanglement growth is subballistic whenever such weak links have a power-law probability distribution at low couplings, i.e., throughout the entire thermal Griffiths phase. We argue that the probability distribution of the entanglement entropy across a cut can be understood from a simple picture in terms of a classical surface growth model. We also discuss spreading of operators and conserved quantities. Surprisingly, the four length scales associated with (i) production of entanglement, (ii) spreading of conserved quantities, (iii) spreading of operators, and (iv) the width of the “front” of a spreading operator, are characterized by dynamical exponents that in general are all distinct. Our numerical analysis of entanglement growth between weakly coupled systems may be of independent interest.