Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system

We consider the exact reduced dynamics of a two-level system coupled to a bosonic reservoir, further obtaining the exact time-convolutionless and Nakajima-Zwanzig non-Markovian equations of motion. The considered system includes the damped and undamped Jaynes-Cummings model. The result is obtained by exploiting an expression of quantum maps in terms of matrices and a simple relation between the time evolution map and time-convolutionless generator as well as Nakajima-Zwanzig memory kernel. This non-perturbative treatment shows that each operator contribution in Lindblad form appearing in the exact time-convolutionless master equation is multiplied by a different time dependent function. Similarly, in the Nakajima-Zwanzig master equation each such contribution is convoluted with a different memory kernel. It appears that depending on the state of the environment the operator structures of the two set of equations of motion can exhibit important differences.Comment: 12 pages, no figure

The diffusion coefficient of propagating fronts with multiplicative noise

Recent studies have shown that in the presence of noise both fronts propagating into a metastable state and so-called pushed fronts propagating into an unstable state, exhibit diffusive wandering about the average position. In this paper we derive an expression for the effective diffusion coefficient of such fronts, which was motivated before on the basis of a multiple scale ansatz. Our systematic derivation is based on the decomposition of the fluctuating front into a suitably positioned average profile plus fluctuating eigenmodes of the stability operator. While the fluctuations of the front position in this particular decomposition are a Wiener process on all time scales, the fluctuations about the time averaged front profile relax exponentially.Comment: 4 page

Modelling of Energy-Crops in Agricultural Sector Models - A Review of Existing Methodologies

The present report provides an overview of the different methodologies applied in partial and general equilibrium models used to analyse biofuel policies in Europe, as well as their methodological pros and cons. While the LEITAP model is included as a general equilibrium model covering biofuel demand, partial equilibrium models are represented by ESIM, FAPRI, AGLINK/COSIMO, RAUMIS, AGMEMOD (agricultural models); POLES and PRIMES (energy sector); and EUFASOM/ENFA (forestry sector). The study is highly relevant for the current modelling work at IPTS, where models such as ESIM and AGLINK play an important role in the Integrated Modelling Platform for Agro-economic Commodity and Policy Analysis (iMAP) of the AGRILIFE Unit. Additionally, the POLES model is currently part of the model portfolio used by the Competitiveness & Sustainability Unit in several studies analysing possible technological pathways of energy production and demand for bioenergy in Europe, a result of implementing the biofuel directive. This compilation of information is also important since the implicit and explicit treatment of bioenergy, either as a demand shock to the processing of oilseeds or feedstock for bioethanol and biodiesel, or as the introduction of a biofuel-sector into a computational general equilibrium (CGE) is foreseen in the short-term by other economic models used at IPTS.JRC.J.5-Agriculture and Life Sciences in the Econom

Quantum interference induced by initial system-environment correlations

We investigate the quantum interference induced by a relative phase in the correlated initial state of a system which consists in a two-level atom interacting with a damped mode of the radiation field. We show that the initial relative phase has significant effects on both the evolution of the atomic excited-state population and the information flow between the atom and the reservoir, as quantified by the trace distance. Furthermore, by considering two two-level atoms interacting with a common damped mode of the radiation field, we highlight how initial relative phases can affect the subsequent entanglement dynamics.Comment: 13 pages, 3 figure

A novel method to investigate how the spatial correlation of the pump beam affects the purity of polarization entangled states

We present an innovative method to address the relation between the purity of type-I polarization entangled states and the spatial properties of the pump laser beam. Our all-optical apparatus is based on a spatial light modulator, and it offers unprecedented control on the spatial phase function of the entangled states. In this way, we demonstrate quantitatively the relation between the purity of the generated state and spatial correlation function of the pump beam.Comment: 3 pages, 3 figure