In this work, we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation greatly s
implifies the original path-integral-based route to these equations and provides new insight into the physical features associated with high-dimensional liquids and glass formation. Most importantly, our construction provides a facile route to the exact dynamical analysis of important related dynamical problems, as well as a means to devise cluster generalizations of the exact solution in infinite dimensions. This latter fact opens the door to the construction of increasingly accurate theories of vitrification in three-dimensional liquids.
We show that the dynamics of (vertical) Franck-Condon excitations in the regime where Holstein-coupled vibrational modes mix strongly with electronic degrees of freedom sharply contrasts with the known self-localized behavior of vibrationally relaxed
excitations. Instead, the strongly-coupled modes are found to periodically induce resonances between interacting electronic sites, during which effective excitation transfer occurs, allowing Franck-Condon excitations to attain substantial mean square displacements under conditions where relaxed excitations are essentially trapped to a single site. In demonstrating this behavior, we employ a multi-set matrix product state formalism. We find this numerically exact technique to be a remarkably efficient approach to the notoriously difficult problem posed by the Holstein model in the regime where the electronic coupling, the vibrational quantum, and the vibrational reorganization energy are comparable in magnitude.
We study the applicability of the time-dependent variational principle in matrix product state manifolds for the long time description of quantum interacting systems. By studying integrable and nonintegrable systems for which the long time dynamics a
re known we demonstrate that convergence of long time observables is subtle and needs to be examined carefully. Remarkably, for the disordered nonintegrable system we consider the long time dynamics are in good agreement with the rigorously obtained short time behavior and with previous obtained numerically exact results, suggesting that at least in this case the apparent convergence of this approach is reliable. Our study indicates that while great care must be exercised in establishing the convergence of the method, it may still be asymptotically accurate for a class of disordered nonintegrable quantum systems.
We study transport through a quantum dot side-coupled to two parallel Luttinger liquid leads in the presence of a Coulombic dot-lead interaction. This geometry enables an exact treatment of the inter-lead Coulomb interactions. We find that for dots s
ymmetrically disposed between the two leads the correlation of charge fluctuations between the two leads can lead to an enhancement of the current at the Coulomb-blockade edge and even to a negative differential conductance. Moving the dot off center or separating the wires further converts the enhancement to a suppression.
