Relaxation of Shannon entropy for trapped interacting bosons with dipolar interactions

We study the quantum many-body dynamics and entropy production triggered by an interaction quench of few dipolar bosons in an external harmonic trap. We solve the time-dependent many-body Schrodinger equation by using an in-principle numerically exact many-body method called the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We study the dynamical measures with high level of accuracy. We monitor the time evolution of the occupation in the natural orbitals and normalized first- and second-order Glauber's correlation functions. In particular, we focus on the relaxation dynamics of the Shannon entropy. Comparison with the corresponding results for contact interactions is presented. We observe significant effects coming from the presence of the non-local part of the dipolar interaction. The relaxation process is very fast for dipolar bosons with a clear signature of a truly saturated maximum entropy state. We also discuss the connection between the entropy production and the occurrence of correlations and loss of coherence in the system. We identify the long-time relaxed state as a many-body state retaining only diagonal correlations in the first-order correlation function and building up anti-bunching effect in the second-order correlation function.