Canonical form of master equations and characterization of non-Markovianity

Master equations govern the time evolution of a quantum system interacting with an environment, and may be written in a variety of forms. Time-independent or memoryless master equations, in particular, can be cast in the well-known Lindblad form. Any time-local master equation, Markovian or non-Markovian, may in fact also be written in a Lindblad-like form. A diagonalisation procedure results in a unique, and in this sense canonical, representation of the equation, which may be used to fully characterize the non-Markovianity of the time evolution. Recently, several different measures of non-Markovianity have been presented which reflect, to varying degrees, the appearance of negative decoherence rates in the Lindblad-like form of the master equation. We therefore propose using the negative decoherence rates themselves, as they appear in the canonical form of the master equation, to completely characterize non-Markovianity. The advantages of this are especially apparent when more than one decoherence channel is present. We show that a measure proposed by Rivas et al. is a surprisingly simple function of the canonical decoherence rates, and give an example of a master equation that is non-Markovian for all times t>0, but to which nearly all proposed measures are blind. We also give necessary and sufficient conditions for trace distance and volume measures to witness non-Markovianity, in terms of the Bloch damping matrix.Comment: v2: Significant update, with many new results and one new author. 12 pages; v3: Minor clarifications, to appear in PRA; v4: matches published versio

Modification of the simple mass balance equation for calculation of critical loads of acidity.

Over the last few years, the simple mass balance equation for the calculation of critical loads of acidity has been gradually modified as the underlying critical load concepts have developed and as problems with particular forms of the equation have been identified, through application in particular countries. The first major update of the equation took place following a workshop held in Vienna, Austria (Hojesky et al. 1993). The workshop was held to discuss problems which had been identified when the then current form of the equation was applied in countries with high rainfall. The problems had largely arisen because of simplifications and assumptions incorporated into the early formulation of the equation. The equation was reformulated to overcome the problems identified at the workshop. However, further problems were identified when the reformulated equation was applied in the UK in situations with a combination of high rainfall, large marine inputs and widespread occurrence of organic soils. A small workshop was, therefore held in Grange-over-Sands, UK in late 1993 to dicuss the problems and to further re-evaluate the equation. The problems had arisen in the UK because of simplifications and assumptions made in the formulation concerning, in particular, cation leaching and uptake. As a result, a more rigorous treatment of these variables was incorporated into the equation. The reformulation of the equation, as derived at the September 1993 workshop is described below

Quantum probability rule : a generalization of the theorems of Gleason and Busch

Buschs theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleasons theorem. Here we show that a further generalization is possible by reducing the number of quantum postulates used by Busch. We do not assume that the positive measurement outcome operators are effects or that they form a probability operator measure. We derive a more general probability rule from which the standard rule can be obtained from the normal laws of probability when there is no measurement outcome information available, without the need for further quantum postulates. Our general probability rule has prediction-retrodiction symmetry and we show how it may be applied in quantum communications and in retrodictive quantum theory

The development of an approach to assess critical loads of acidity for woodland habitats in Great Britain

International audienceAlongside other countries that are signatories to the UNECE Convention Long Range Transboundary on Air Pollution, the UK is committed to reducing the impact of air pollution on the environment. To advise and guide this policy in relation to atmospheric emissions of sulphur and nitrogen, a critical load approach has been developed. To assess the potential impact of these pollutants on woodland habitats a steady state, simple mass balance model has been parameterised. For mineral soils, a Ca:Al ratio in soil solution has been used as the critical load indicator for potential damage. For peat and organic soils critical loads have been set according to a pH criterion. Together these approaches have been used with national datasets to examine the potential scale of acidification in woodland habitats across the UK. The results can be mapped to show the spatial variability in critical loads of the three principal woodland habitat types (managed coniferous, managed broadleaved/ mixed woodland and unmanaged woodland). The results suggest that there is a wide range of critical loads. The most sensitive (lowest) critical loads are associated with managed coniferous followed by unmanaged woodland on peat soils. Calculations indicate that at steady state, acid deposition inputs reported for 1995?1997 result in a large proportion of all the woodland habitats identified receiving deposition loads in excess of their critical load; i.e. critical loads are exceeded. These are discussed in relation to future modelled depositions for 2010. Whilst significant widespread negative impacts of such deposition on UK woodland habitats have not been reported, the work serves to illustrate that if acid deposition inputs were maintained and projected emissions reductions not achieved, the long-term sustainability of large areas of woodland in the UK could be compromised. Keywords: critical loads, acid deposition, acidification, woodland, simple mass balance model, sustainabilit

Single microwave photon detection in the micromaser

High efficiency single photon detection is an interesting problem for many areas of physics, including low temperature measurement, quantum information science and particle physics. For optical photons, there are many examples of devices capable of detecting single photons with high efficiency. However reliable single photon detection of microwaves is very difficult, principally due to their low energy. In this paper we present the theory of a cascade amplifier operating in the microwave regime that has an optimal quantum efficiency of 93%. The device uses a microwave photon to trigger the stimulated emission of a sequence of atoms where the energy transition is readily detectable. A detailed description of the detector's operation and some discussion of the potential limitations of the detector are presented.Comment: 8 pages, 5 figure

Test of the quantumness of atom-atom correlations in a bosonic gas

It is shown how the quantumness of atom-atom correlations in a trapped bosonic gas can be made observable. Application of continuous feedback control of the center of mass of the atomic cloud is shown to generate oscillations of the spatial extension of the cloud, whose amplitude can be directly used as a characterization of atom-atom correlations. Feedback parameters can be chosen such that the violation of a Schwarz inequality for atom-atom correlations can be tested at noise levels much higher than the standard quantum limit

Nitrogen cycle disruption through the application of de-icing salts on upland highways

It is hypothesized that episodic introductions of road salt severely disrupt the soil nitrogen cycle at a range of spatial and temporal scales. A field-scale study has confirmed impacts on the nitrogen cycle in soil, soil solution and river samples. There is evidence that ammonium-N retention on cation exchange sites has been reduced by the presence of sodium ions, and that ammonium-N has been flushed from the exchange sites. Increases in soil pH have been caused in naturally acidic uplands. These have enhanced mineralization of organic-N, especially nitrification, leading to a reduction in the mineralizable-N pool of roadside soils. There is evidence to support the hypothesis that organic matter content has been lowered over decades either through desorption or dispersal processes. Multiple drivers are identified that contribute to the disruption of nitrogen cycling processes, but their relative importance is difficult to quantify unequivocally. The influence of road salt on soil and soil solution declines with distance from the highway, but impacts on water chemistry in a local stream are still strongly evident at some distance from the road

Local in time master equations with memory effects: Applicability and interpretation

Non-Markovian local in time master equations give a relatively simple way to describe the dynamics of open quantum systems with memory effects. Despite their simple form, there are still many misunderstandings related to the physical applicability and interpretation of these equations. Here we clarify these issues both in the case of quantum and classical master equations. We further introduce the concept of a classical non-Markov chain signified through negative jump rates in the chain configuration.Comment: Special issue on loss of coherence and memory effects in quantum dynamics, J. Phys. B., to appea

Completely positive maps with memory

The prevailing description for dissipative quantum dynamics is given by the Lindblad form of a Markovian master equation, used under the assumption that memory effects are negligible. However, in certain physical situations, the master equation is essentially of a non-Markovian nature. This paper examines master equations that possess a memory kernel, leading to a replacement of white noise by colored noise. The conditions under which this leads to a completely positive, trace-preserving map are discussed for an exponential memory kernel. A physical model that possesses such an exponential memory kernel is presented. This model contains a classical, fluctuating environment based on random telegraph signal stochastic variables.Comment: 4 page