Sub-Planck spots of Schroedinger cats and quantum decoherence

Heisenberg's principle$^1$ states that the product of uncertainties of position and momentum should be no less than Planck's constant $\hbar$. This is usually taken to imply that phase space structures associated with sub-Planck ($\ll \hbar$) scales do not exist, or, at the very least, that they do not matter. I show that this deeply ingrained prejudice is false: Non-local "Schr\"odinger cat" states of quantum systems confined to phase space volume characterized by `the classical action' $A \gg \hbar$ develop spotty structure on scales corresponding to sub-Planck $a = \hbar^2 / A \ll \hbar$. Such structures arise especially quickly in quantum versions of classically chaotic systems (such as gases, modelled by chaotic scattering of molecules), that are driven into nonlocal Schr\"odinger cat -- like superpositions by the quantum manifestations of the exponential sensitivity to perturbations$^2$. Most importantly, these sub-Planck scales are physically significant: $a$ determines sensitivity of a quantum system (or of a quantum environment) to perturbations. Therefore sub-Planck $a$ controls the effectiveness of decoherence and einselection caused by the environment$^{3-8}$. It may also be relevant in setting limits on sensitivity of Schr\"odinger cats used as detectors.Comment: Published in Nature 412, 712-717 (2001

Anatomy of quantum chaotic eigenstates

The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The levels of description are macroscopic (one wants to understand the quantum averages of smooth observables), and microscopic (one wants informations on maxima of eigenfunctions, "scars" of periodic orbits, structure of the nodal sets and domains, local correlations), and often focusses on statistical results. Various models of "random wavefunctions" have been introduced to understand these statistical properties, with usually good agreement with the numerical data. We also discuss some specific systems (like arithmetic ones) which depart from these random models.Comment: Corrected typos, added a few references and updated some result

An Evaluation of the Large‐Scale Atmospheric Circulation and Its Variability in CESM2 and Other CMIP Models

The Community Earth System Model 2 (CESM2) is the latest Earth System Model developed by the National Center for Atmospheric Research in collaboration with the university community and is significantly advanced in most components compared to its predecessor (CESM1). Here, CESM2's representation of the large‐scale atmospheric circulation and its variability is assessed. Further context is providedthrough comparison to the CESM1 large ensemble and other models from the Coupled Model Intercomparison Project (CMIP5 and CMIP6). This includes an assessment of the representation of jet streams and storm tracks, stationary waves, the global divergent circulation, the annular modes, the North Atlantic Oscillation, and blocking. Compared to CESM1, CESM2 is substantially improved in the representation of the storm tracks, Northern Hemisphere (NH) stationary waves, NH winter blocking and the global divergent circulation. It ranks within the top 10% of CMIP class models in many of these features. Some features of the Southern Hemisphere (SH) circulation have degraded, such as the SH jet strength, stationary waves, and blocking, although the SH jet stream is placed at approximately the correct location. This analysis also highlights systematic deficiencies in these features across the new CMIP6 archive, such as the continued tendency for the SH jet stream to be placed too far equatorward, the North Atlantic westerlies to be too strong over Europe, the storm tracks as measured by low‐level meridional wind variance to be too weak and a lack of blocking in the North Atlantic sector

Radiative and chemical response to interactive stratospheric sulfate aerosols in fully coupled CESM1(WACCM)

We present new insights into the evolution and interactions of stratospheric aerosol using an updated version of the Whole Atmosphere Community Climate Model (WACCM). Improved horizontal resolution, dynamics, and chemistry now produce an internally generated quasi-biennial oscillation and significant improvements to stratospheric temperatures and ozone compared to observations. We present a validation of WACCM column ozone and climate calculations against observations. The prognostic treatment of stratospheric sulfate aerosols accurately represents the evolution of stratospheric aerosol optical depth and perturbations to solar and longwave radiation following the June 1991 eruption of Mount Pinatubo. We confirm the inclusion of interactive OH chemistry as an important factor in the formation and initial distribution of aerosol following large inputs of sulfur dioxide (SO2) to the stratosphere. We calculate that depletion of OH levels within the dense SO2 cloud in the first weeks following the Pinatubo eruption significantly prolonged the average initial e-folding decay time for SO2 oxidation to 47 days. Previous observational and model studies showing a 30 day decay time have not accounted for the large (30–55%) losses of SO2 on ash and ice within 7–9 days posteruption and have not correctly accounted for OH depletion. We examine the variability of aerosol evolution in free-running climate simulations due to meteorology, with comparison to simulations nudged with specified dynamics. We assess calculated impacts of volcanic aerosols on ozone loss with comparisons to observations. The completeness of the chemistry, dynamics, and aerosol microphysics in WACCM qualify it for studies of stratospheric sulfate aerosol geoengineering

Experimental Observation of Quantum Chaos in a Beam of Light

The manner in which unpredictable chaotic dynamics manifests itself in quantum mechanics is a key question in the field of quantum chaos. Indeed, very distinct quantum features can appear due to underlying classical nonlinear dynamics. Here we observe signatures of quantum nonlinear dynamics through the direct measurement of the time-evolved Wigner function of the quantum-kicked harmonic oscillator, implemented in the spatial degrees of freedom of light. Our setup is decoherence-free and we can continuously tune the semiclassical and chaos parameters, so as to explore the transition from regular to essentially chaotic dynamics. Owing to its robustness and versatility, our scheme can be used to experimentally investigate a variety of nonlinear quantum phenomena. As an example, we couple this system to a quantum bit and experimentally investigate the decoherence produced by regular or chaotic dynamics.Comment: 7 pages, 5 figure

Evolution under Fluctuating Environments Explains Observed Robustness in Metabolic Networks

A high level of robustness against gene deletion is observed in many organisms. However, it is still not clear which biochemical features underline this robustness and how these are acquired during evolution. One hypothesis, specific to metabolic networks, is that robustness emerges as a byproduct of selection for biomass production in different environments. To test this hypothesis we performed evolutionary simulations of metabolic networks under stable and fluctuating environments. We find that networks evolved under the latter scenario can better tolerate single gene deletion in specific environments. Such robustness is underlined by an increased number of independent fluxes and multifunctional enzymes in the evolved networks. Observed robustness in networks evolved under fluctuating environments was “apparent,” in the sense that it decreased significantly as we tested effects of gene deletions under all environments experienced during evolution. Furthermore, when we continued evolution of these networks under a stable environment, we found that any robustness they had acquired was completely lost. These findings provide evidence that evolution under fluctuating environments can account for the observed robustness in metabolic networks. Further, they suggest that organisms living under stable environments should display lower robustness in their metabolic networks, and that robustness should decrease upon switching to more stable environments

Health promotion through self-care and community participation: Elements of a proposed programme in the developing countries

BACKGROUND: The concepts of health promotion, self-care and community participation emerged during 1970s, primarily out of concerns about the limitation of professional health system. Since then there have been rapid growth in these areas in the developed world, and there is evidence of effectiveness of such interventions. These areas are still in infancy in the developing countries. There is a window of opportunity for promoting self care and community participation for health promotion. DISCUSSION: A broad outline is proposed for designing a health promotion programme in developing countries, following key strategies of the Ottawa Charter for health promotion and principles of self care and community participation. Supportive policies may be framed. Self care clearinghouses may be set up at provincial level to co-ordinate the programme activities in consultation with district and national teams. Self care may be promoted in the schools and workplaces. For developing personal skills of individuals, self care information, generated through a participatory process, may be disseminated using a wide range of print and audio-visual tools and information technology based tools. One such potential tool may be a personally held self care manual and health record, to be designed jointly by the community and professionals. Its first part may contain basic self care information and the second part may contain outlines of different personally-held health records to be used to record important health and disease related events of an individual. Periodic monitoring and evaluation of the programme may be done. Studies from different parts of the world indicate the effectiveness and cost-effectiveness of self care interventions. The proposed outline has potential for health promotion and cost reduction of health services in the developing countries, and may be adapted in different situations. SUMMARY: Self care, community participation and health promotion are emerging but dominant areas in the developed countries. Elements of a programme for health promotion in the developing countries following key principles of self care and community participation are proposed. Demonstration programmes may be initiated to assess the feasibility and effectiveness of this programme before large scale implementation