Nuclear quantum effects in electronically adiabatic quantum time correlation functions : Application to the absorption spectrum of a hydrated electron

A general formalism for introducing nuclear quantum effects in the expression of the quantum time correlation function of an operator in a multi-level electronic system is presented in the adiabatic limit. The final formula includes the nuclear quantum time correlation functions of the operator matrix elements, of the energy gap, and their cross terms. These quantities can be inferred and evaluated from their classical analogs obtained by mixed quantum-classical molecular dynamics simulations. The formalism is applied to the absorption spectrum of a hydrated electron, expressed in terms of the time correlation function of the dipole operator in the ground electronic state. We find that both static and dynamic nuclear quantum effects distinctly influence the shape of the absorption spectrum, especially its high-energy tail related to transitions to delocalized electron states. Their inclusion does improve significantly the agreement between theory and experiment for both the low and high frequency edges of the spectrum. It does not appear sufficient, however, to resolve persistent deviations in the slow Lorentzian-like decay part of the spectrum in the intermediate 2-3 eV region

Thermal quenches in N=2* plasmas

We exploit gauge/gravity duality to study `thermal quenches' in a plasma of the strongly coupled N=2* gauge theory. Specifically, we consider the response of an initial thermal equilibrium state of the theory under variations of the bosonic or fermionic mass, to leading order in m/T<<1. When the masses are made to vary in time, novel new counterterms must be introduced to renormalize the boundary theory. We consider transitions the conformal super-Yang-Mills theory to the mass deformed gauge theory and also the reverse transitions. By construction, these transitions are controlled by a characteristic time scale \calt and we show how the response of the system depends on the ratio of this time scale to the thermal time scale 1/T. The response shows interesting scaling behaviour both in the limit of fast quenches with T\calt<<1 and slow quenches with T\calt>>1. In the limit that T\calt\to\infty, we observe the expected adiabatic response. For fast quenches, the relaxation to the final equilibrium is controlled by the lowest quasinormal mode of the bulk scalar dual to the quenched operator. For slow quenches, the system relaxes with a (nearly) adiabatic response that is governed entirely by the late time profile of the mass. We describe new renormalization scheme ambiguities in defining gauge invariant observables for the theory with time dependant couplings.Comment: 78 pages, 17 figure

Self-Consistent Projection Operator Theory in Nonlinear Quantum Optical Systems: A case study on Degenerate Optical Parametric Oscillators

Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. In this article we apply the recently developed self-consistent projection operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.Comment: Comments are welcom