Hi Everyone, Dr. Humberto Laguna will be giving group meeting this week at 2:00pm on Thursday in the Division Room (our new time for the summer). His talk details are included below. Title: Statistical correlations, localization and interactions in model quantum systems Abstract: Correlation is a key factor in understanding a variety of chemical and physical phenomena. There are three clear sources of statistical correlations in quantum systems: (1) that which arises from the indistinguishability restriction on the wave function; (2) that which originates from the interaction between particles through a potential; (3) and that which is due to the uncertainty principle as a result of the noncommutativity of operators. These statistical correlations manifest themselves through the nonseparability of the distribution functions describing the systems. In the first two cases (indistinguishability and interaction), the problem can be addressed, in position space (correlation between $x_{1}$ and $x_{2}$) or in momentum space (correlation between $p_{1}$ and $p_{2}$), by analyzing the nonseparability of the pair density distributions of the system. The differences between the relative strength of correlation in the two different spaces are discussed and related to the symmetry of the wave function and the strength of the interparticle potential. In the case of position-momentum correlation (which also occurs in one-particle systems), the problem must be formulated in terms of the Wigner function, a quantum phase-space representation of the system. Proposals to distinguish between the different kinds of statistical correlations are of fundamental importance to determine their effects on the behavior of a system. Additionally, there is the question of how one kind of correlation is related to another, e.g. how the position-momentum correlation is affected by the presence of an interparticle potential. Analyses of statistical correlation are made with the measures provided by Information Theory, i.e. mutual information, which is defined in terms of the Shannon entropies of the corresponding one- and two-particle densities. Also are discussed the delocalization phenomena in the distributions from analysis of their Shannon entropies. The problem is addressed in one-particle and two-particle models. -- Ryan Babbush | PhD Student in Physics (949) 331-3943 | babbush(a)fas.harvard.edu Harvard University | Aspuru-Guzik Group 12 Oxford Street | Cambridge, MA 02138 _______________________________________________ Aspuru-meetings-list mailing list Aspuru-meetings-list(a)lists.fas.harvard.edu https://lists.fas.harvard.edu/mailman/listinfo/aspuru-meetings-list