Orbital magnetism of an active particle in viscoelastic suspension

We consider an active (self-propelling) particle in a viscoelastic fluid. The particle is charged and constrained to move in a two-dimensional harmonic trap. Its dynamics is coupled to a constant magnetic field applied perpendicular to its plane of motion via Lorentz force. Due to the finite activity, the generalized fluctuation-dissipation relation (GFDR) breaks down, driving the system away from equilibrium. While breaking GFDR, we have shown that the system can have finite classical orbital magnetism only when the dynamics of the system contains finite inertia. The orbital magnetic moment has been calculated exactly. Remarkably, we find that when the elastic dissipation timescale of the medium is larger (smaller) than the persistence timescale of the self-propelling particle, it is diamagnetic (paramagnetic). Therefore, for a given strength of the magnetic field, the system undergoes a transition from diamagnetic to paramagnetic state (and vice versa) simply by tuning the timescales of underlying physical processes, such as active fluctuations and viscoelastic dissipation. Interestingly, we also find that the magnetic moment, which vanishes at equilibrium, behaves nonmonotonically with respect to increasing persistence of self-propulsion, which drives the system out of equilibrium.

Figure 1

$\langle M\left(\infty \right)\rangle$ [Eq. (10)] as a function of $t_c$ and $t_c^{\prime }$: (a) with ${\omega }_c=1$, ${\omega }_0=1$, and $\mathrm{\Gamma }=1$, (b) with ${\omega }_c=1.5$, ${\omega }_0=1$, $\mathrm{\Gamma }=1$, (c) with ${\omega }_0=1.5$, ${\omega }_c=1$, $\mathrm{\Gamma }=1$, and (d) with $\mathrm{\Gamma }=3$, ${\omega }_0=1$, ${\omega }_c=1$. Both $K_{B}T$ and $\frac{\left|q\right|}{mc}$ are assumed to be unity.

Figure 2

$M_r$ [Eq. (15)] is plotted with $t_c$ (at $t_c^{\prime }\to 0$ limit) from analytics (solid lines) as well as from numerical simulation (solid points) for (a) various values of ${\omega }_0$, keeping ${\omega }_c$ and $\mathrm{\Gamma }$ to be fixed as unity, and (b) for various values of ${\omega }_c$, keeping ${\omega }_0$ and $\mathrm{\Gamma }$ as fixed to unity. Both $K_{B}T$ and $\frac{\left|q\right|}{mc}$ are also assumed to be unity.

Figure 3

$M_r$ [Eq. (15)] is plotted with ${\omega }_c$ (a) for different $t_c$ and (b) for different $\mathrm{\Gamma }$, keeping other parameters fixed at unity.