Adrián A. Budini — Page 2

arXiv2017

Smoothed quantum-classical states in time-irreversible hybrid dynamics

We consider a quantum system continuously monitored in time which in turn is coupled to an arbitrary dissipative classical system (diagonal reduced density matrix). The quantum and classical dynamics can modify each other, being described by an arbitrary time-irreversible hybrid Lindblad equation. Given a measurement trajectory, a conditional bipartite stochastic state can be inferred by taking into account all previous recording information (filtering). Here, we demonstrate that the joint quantum-classical state can also be inferred by taking into account both past and future measurement results (smoothing). The smoothed hybrid state is estimated without involving information from unobserved measurement channels. Its average over recording realizations recovers the joint time-irreversible behavior. As an application we consider a fluorescent system monitored by an inefficient photon detector. This feature is taken into account through a fictitious classical two-level system. The average purity of the smoothed quantum state increases over that of the (mixed) state obtained from the standard quantum jump approach.

quant-ph↗

arXiv2013

Fluctuating observation time ensembles in the thermodynamics of trajectories

The dynamics of stochastic systems, both classical and quantum, can be studied by analysing the statistical properties of dynamical trajectories. The properties of ensembles of such trajectories for long, but fixed, times are described by large-deviation (LD) rate functions. These LD functions play the role of dynamical free-energies: they are cumulant generating functions for time-integrated observables, and their analytic structure encodes dynamical phase behaviour. This "thermodynamics of trajectories" approach is to trajectories and dynamics what the equilibrium ensemble method of statistical mechanics is to configurations and statics. Here we show that, just like in the static case, there is a variety of alternative ensembles of trajectories, each defined by their global constraints, with that of trajectories of fixed total time being just one of these. We show that an ensemble of trajectories where some time-extensive quantity is constant (and large) but where total observation time fluctuates, is equivalent to the fixed-time ensemble, and the LD functions that describe one ensemble can be obtained from those that describe the other. We discuss how the equivalence between generalised ensembles can be exploited in path sampling schemes for generating rare dynamical trajectories.

cond-mat.stat-mech↗