Coupled forward-backward trajectory approach for non-equilibrium electron-ion dynamics

We introduce a simple ansatz for the wavefunction of a many-body system based on coupled forward and backward-propagating semiclassical trajectories. This method is primarily aimed at, but not limited to, treating nonequilibrium dynamics in electron-phonon systems. The time-evolution of the system is obtained from the Euler-Lagrange variational principle, and we show that this ansatz yields Ehrenfest mean field theory in the limit that the forward and backward trajectories are orthogonal, and in the limit that they coalesce. We investigate accuracy and performance of this method by simulating electronic relaxation in the spin-boson model and the Holstein model. Although this method involves only pairs of semiclassical trajectories, it shows a substantial improvement over mean field theory, capturing quantum coherence of nuclear dynamics as well as electron-nuclear correlations. This improvement is particularly evident in nonadiabatic systems, where the accuracy of this coupled trajectory method extends well beyond the perturbative electron-phonon coupling regime. This approach thus provides an attractive route forward to the ab-initio description of relaxation processes, such as thermalization, in condensed phase systems

Rebuilding our Neighborhoods: Improving New York State Housing Policy to Better Meet Upstate Needs

New York faces a wide variety of housing challenges. While in the New York City region, where the population is growing, availability and affordability are the most pressing concerns, upstate regions have a different set of problems stemming from population loss, housing vacancy, abandonment, and deterioration. To address the full range of issues, state housing policy needs a variety of tools in its tool box. This policy brief discusses four ways that state housing policy can better address the needs of upstate regions such as Buffalo: Support holistic neighborhood revitalization, using Buffalo’s award-winning Green Development Zone as a model; Restore and enhance funding streams for small projects and housing repairs; Adjust New York’s Low Income Housing Tax Credit Qualified Allocation Plan to better address upstate needs; and Revise the DHCR Design Handbook to better facilitate rehabilitation projects

Mapping quantum-classical Liouville equation: projectors and trajectories

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.Comment: 4 figure