ASEP on a ring conditioned on enhanced flux

We show that in the asymmetric simple exclusion process (ASEP) on a ring, conditioned on carrying a large flux, the particle experiences an effective long-range potential which in the limit of very large flux takes the simple form U = -2 Sigma(i not equal j) log vertical bar sin pi(n(i)/L - nj/ L)vertical bar, where n1, n2, ..., nN are the particle positions, similar to the effective potential between the eigenvalues of the circular unitary ensemble in random matrices. Effective hopping rates and various quasi-stationary probabilities under such a conditioning are found analytically using the Bethe ansatz and determinantal free fermion techniques. Our asymptotic results extend to the limit of large current and large activity for a family of reaction-diffusion processes with on-site exclusion between particles. We point out an intriguing generic relation between classical stationary probability distributions for conditioned dynamics and quantum ground state wavefunctions, in particular in the case of exclusion processes, for free fermions.