A Brief Study on Chemical Potential

Brian K. Kendrick, N. Balakrishnan

The role of the geometric phase effect in chemical reaction dynamics has long been a topic of active experimental and theoretical investigations. The topic has received renewed interest in recent years in cold and ultracold chemistry where it was shown to play a decisive role in state-to-state chemical dynamics. We provide a brief review of these developments focusing on recent studies of O + OH and hydrogen exchange in the H + H 2 and D + HD reactions at cold and ultracold temperatures. Non-adiabatic effects in ultracold chemical dynamics arising from the conical intersection between two electronic potential energy surfaces are also briefly discussed. By taking the hydrogen exchange reaction as an illustrative example it is shown that the inclusion of the geometric phase effect captures the essential features of non-adiabatic dynamics at collision energies below the conical intersection.

Philippe A. Martin

Sebastian F. Keller, Markus Reiher

The Density Matrix Renormalization Group (DMRG) algorithm has been a rising star for the accurate ab initio exploration of Born-Oppenheimer potential energy surfaces in theoretical chemistry. However, owing to its iterative numerical nature, pitfalls that can affect the accuracy of DMRG energies need to be circumvented. Here, after a brief introduction into this quantum chemical method, we discuss criteria that determine the accuracy of DMRG calculations.

Giancarlo Calvanese Strinati

This chapter provides a concise account of the salient features of the BCS–BEC crossover. After a brief historical review of the topic, the key features of the BCS–BEC crossover are recalled. In particular, the BCS wave function for the ground state is shown to contain the BEC state of composite bosons as a limiting situation, and the special role played in this context by the chemical potential is pointed out. The need for pairing fluctuations beyond mean field is also emphasized, together with the occurrence of two (coupling and temperature dependent) lengths, which measure the correlation either within a pair of fermions with opposite spins or among different pairs. The limiting physical situations corresponding to the Ginzburg–Landau and Gross–Pitaevskii equations are finally considered.

Volker Schmidt