It is generally believed that collisions of particles reduce the self-diffusion coefficient. Here we show that in odd-diffusive systems, which are characterized by diffusion tensors with antisymmetric elements, collisions surprisingly can enhance the self-diffusion. In these systems, due to an inherent curving effect, the motion of particles is facilitated, instead of hindered by collisions leading to a mutual rolling effect. Using a geometric model, we analytically predict the enhancement of the self-diffusion coefficient with increasing density. This counterintuitive behavior is demonstrated in the archetypal odd-diffusive system of Brownian particles under Lorentz force. We validate our findings by many-body Brownian dynamics simulations in dilute systems.

Equilibrium properties of a system of passive diffusing particles in an external magnetic field are unaffected by Lorentz force. In contrast, active Brownian particles exhibit steady-state phenomena that depend on both the strength and the polarity of the applied magnetic field. The intriguing effects of the Lorentz force, however, can only be observed when out-of-equilibrium density gradients are maintained in the system. To this end, we use the method of stochastic resetting on active Brownian particles in two dimensions by resetting them to the line x = 0 at a constant rate and periodicity in the y direction. Under stochastic resetting, an active system settles into a nontrivial stationary state which is characterized by an inhomogeneous density distribution, polarization and bulk fluxes perpendicular to the density gradients. We show that whereas for a uniform magnetic field the properties of the stationary state of the active system can be obtained from its passive counterpart, novel features emerge in the case of an inhomogeneous magnetic field which have no counterpart in passive systems. In particular, there exists an activity-dependent threshold rate such that for smaller resetting rates, the density distribution of active particles becomes non-monotonic. We also study the mean first-passage time to the x axis and find a surprising result: it takes an active particle more time to reach the target from any given point for the case when the magnetic field increases away from the axis. The theoretical predictions are validated using Brownian dynamics simulations.

We study the motion of a Brownian particle subjected to Lorentz force due to an external magnetic field. Each spatial degree of freedom of the particle is coupled to a different thermostat. We show that the magnetic field results in correlation between different velocity components in the stationary state. Integrating the velocity autocorrelation matrix, we obtain the diffusion matrix that enters the Fokker–Planck equation for the probability density. The eigenvectors of the diffusion matrix do not align with the temperature axes. As a consequence the Brownian particle performs spatially correlated diffusion. We further show that in the presence of an isotropic confining potential, an unusual, flux-free steady state emerges which is characterized by a non-Boltzmann density distribution, which can be rotated by reversing the magnetic field. The nontrivial steady state properties of our system result from the Lorentz force induced coupling of the spatial degrees of freedom which cease to exist in equilibrium corresponding to a single-temperature system.

In systems with overdamped dynamics, the Lorentz force reduces the diffusivity of a Brownian particle in the plane perpendicular to the magnetic field. The anisotropy in diffusion implies that the Fokker-Planck equation for the probability distribution of the particle acquires a tensorial coefficient. The tensor, however, is not a typical diffusion tensor due to the antisymmetric elements, which account for the fact that Lorentz force curves the trajectory of a moving charged particle. This gives rise to unusual dynamics with features such as additional Lorentz fluxes and a nontrivial density distribution, unlike a diffusive system. The equilibrium properties are, however, unaffected by the Lorentz force. Here we show that by stochastically resetting the Brownian particle, a nonequilibrium steady state can be created that preserves the hallmark features of dynamics under Lorentz force. We then consider a minimalistic example of a spatially inhomogeneous magnetic field, which shows how Lorentz fluxes fundamentally alter the boundary conditions giving rise to an unusual stationary state.

The Fokker-Planck equation provides a complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial coefficient, which reflects the anisotropy of the particle's motion. This tensor, however, cannot be interpreted as a diffusion tensor; there are antisymmetric terms which give rise to fluxes perpendicular to the density gradients. Here, we show that for an inhomogeneous magnetic field these nondiffusive fluxes have finite divergence and therefore affect the density evolution of the system. Only in the special cases of a uniform magnetic field or carefully chosen initial condition with the same full rotational symmetry as the magnetic field can these fluxes be ignored in the density evolution.

Thermally activated escape of a Brownian particle over a potential barrier is well understood within Kramers theory. When subjected to an external magnetic field, the Lorentz force slows down the escape dynamics via a rescaling of the diffusion coefficient without affecting the exponential dependence on the barrier height. Here, we study the escape dynamics of a charged Brownian particle from a two-dimensional truncated harmonic potential under the influence of Lorentz force due to an external magnetic field. The particle is driven anisotropically by subjecting it to noises with different strengths along different spatial directions. We show that the escape time can largely be tuned by the anisotropic driving. While the escape process becomes anisotropic due to the two different noises, the spatial symmetry is restored in the limit of large magnetic fields. This is attributed to the Lorentz-force–induced coupling between the spatial degrees of freedom which makes the difference between two noises irrelevant at high magnetic fields. The theoretical predictions are verified by Brownian dynamics simulations. In principle, our predictions can be tested by experiments with a Brownian gyrator in the presence of a magnetic field.