3 research outputs found

    10th International Conference on Problems of Quantum Field Theory

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    A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model.

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    We introduce a geometric mechanism for di?usion in a priori unstable nearly integrable dynamical systems. It is based on the observation that resonances, besides destroying the primary KAM tori, create secondary tori and tori of lower dimension. We argue that these objects created by resonances can be incorporated in transition chains taking the place of the destroyed primary KAM tori. We establish rigorously the existence of this mechanism in a simple model that has been studied before. The main technique is to develop a toolkit to study, in a unified way, tori of different topologies and their invariant manifolds, their intersections as well as shadowing properties of these bi-asymptotic orbits. This toolkit is based on extending and unifying standard techniques. A new tool used here is the scattering map of normally hyperbolic invariant manifolds. The model considered is a one-parameter family, which for " = 0 is an integrable system. We give a small number of explicit conditions the jet of order 3 of the family that, if verified imply diffusion. The conditions are just that some explicitely constructed functionals do not vanish identically or have non-degenerate critical points, etc. An attractive feature of the mechanism is that the transition chains are shorter in the places where the heuristic intuition and numerical experimentation suggests that the diffusion is strongest

    Buddhist perspectives on sustainability : towards radical transformation of self and world

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    This thesis concerns the contribution of Buddhism to sustainability. It explores the impacts of Buddhism on the lives of nine individuals and the implications of these impacts for a sustainable world. This thesis regards sustainability as the most pressing issue at this junction in human history. It believes that the shift to sustainability requires profound individual and social transformations throughout the world and that such transformations necessitate the involvement of the spiritual traditions of the world. As one such tradition, Buddhism has the ability to impart principles and practices that have been applied in daily living for over 2,500 years to contemporary sustainability discourse. The modern idea of sustainability first became prominent in the international arena in 1980s when the Brundtland Commission enunciated its vision of the path to sustainability and referred to it as 'sustainable development'. However, this thesis contends that the concept of sustainable development was flawed from the beginning because it was founded on the idea of perpetual economic growth as the solution to environmental and social problems. Instead, the thesis forwards a holistic, systems approach to sustainability that regards human well-being as the ultimate goal. It adopts two theoretical conceptions of sustainability developed by Donella Meadows - the pyramidal framework for sustainability and the scheme of leverage points - as tools to analyse the contribution of Buddhism to sustainability. This thesis examines the literature on Buddhism and sustainability. It finds that Buddhism espouses many ecological and social values conducive to a sustainable philosophy of life. In addition, Buddhist economics has experienced rich theoretical developments in recent years and provides an alternative to mainstream economics based on growth. Buddhist economics has helped propel two Buddhist developmental paradigms - Bhutan's Gross National Happiness and Thailand's Sufficiency Economy - to the forefront of national agendas in their respective countries, thus demonstrating the renaissance of the application of Buddhist thinking in society. At the micro level, many communities around the world are attempting to translate the most fundamental principles of Buddhism into ways for harmonious living and in an attempt to combat the tide of environmental and social degradation. Thus, Buddhism is making an impact on sustainability at many levels around the world. However, this thesis finds little empirical evidence to demonstrate the effect of Buddhism on forms of personal transformation that leads to sustainable behaviour. This is despite the importance of the idea of transformation and personal growth in Buddhism. This empirical void leads to the aim of the thesis, which is to explore the ways in which the beliefs, practices and transformational tools within Buddhism can contribute to living sustainably. To achieve this aim, the methodology of mindful inquiry was employed. Mindful inquiry is a methodological union of East and West and integrates four perspectives: critical theory, hermeneutics, phenomenology and Buddhism. It is appropriate for a values-based research such as this one where the orientation of the researcher is critical to the outcome of the research. A method consistent with mindful inquiry is the basic interpretive qualitative study. The basic interpretive qualitative study used in this study combines elements from ethnography, case study, phenomenology and critical research. It was used to explore the lifeworlds of nine Buddhist participants in order to understand the impact of Buddhism on their lives. The major data gathering technique was in-depth interviews although participant observation and document collection were also used. Analysis of data proceeded through the constant comparative method. The findings from this thesis are divided into three themes. Firstly, the idea of personal sustainability is forwarded as a concept to help understand the impact of Buddhism. Personal sustainability concerns the psychological 'integratedness' of individuals to enable the achievement of higher levels of well-being. The findings suggest that Buddhism has significantly enhanced the personal sustainability level of all nine participants. Secondly, Meadows' ideas of paradigm shift and paradigm transcendence are explored. The findings suggest that paradigm shifts or paradigm transcendence have occurred among the participants through the adoption of Buddhist principles and meditative practices. Thirdly, the notions of happiness and purpose in life are investigated. The findings highlight radical changes in the participants' understandings of these notions and the nature of these understandings that are significantly different from conventional views. As a result of these findings, the thesis argues that the contribution of Buddhism to sustainability can be considerable because Buddhism contributes to the protection of natural capital, the enrichment of social and human capitals, and a deepened understanding of well-being, which is divorced from simplistic ideas such as material accumulation and sensual gratification. The thesis concludes by highlighting the potentials of Buddhism to instigate profound personal and social transformations that could lead to a sustainable world
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