5,728 research outputs found

    Convexity at finite temperature and non-extensive thermodynamics

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    Assuming that tunnel effect between two degenerate bare minima occurs, in a scalar field theory at finite volume, this article studies the consequences for the effective potential, to all loop orders. Convexity is achieved only if the two bare minima are taken into account in the path integral, and a new derivation of the effective potential is given, in the large volume limit. The effective potential has then has a universal form, it is suppressed by the space time volume, and does not feature spontaneous symmetry breaking as long as the volume is finite. The finite temperature analysis leads to surprising thermal properties, following from the non-extensive expression for the free energy. Although the physical relevance of these results is not clear, the potential application to ultra-light scalar particles is discussed.Comment: 17 page

    Autofocusing and self-healing of partially blocked circular Airy derivative beams

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    We numerically and experimentally study the autofocusing and self-healing of partially blocked circular Airy derivative beams (CADBs). The CADB consists of multiple rings, and partial blocking of CADB with different kinds is achieved by using symmetric and asymmetric binary amplitude masks, enabling blocking of inner/outer rings and sectorially. The CADB blocked with different types possesses the ability to autofocus, however, the required propagation distance for abrupt autofocusing vary with the amount and types of blocking. The abrupt autofocusing is quantified by a maximum k-value, and how fast it changes around the autofocusing distance (zafz_{af}). In particular, CADB blocked with inner rings (first/two/three) exhibits an abrupt autofocusing, as the k-value sharply increases [decreases] just before [after] zafz_{af}. The maximum k-value always occurs at zafz_{af}, which decreases as the number of blocked inner rings increases. For CADB blocked with outer rings, the k-value gradually changes around zafz_{af}, indicating a lack of abrupt autofocusing. The value of zafz_{af} increases with the number of blocked outer rings. This suggests that although outer rings contain low intensities, these play an important role in autofocusing. A sectorially blocked CADB possesses an abrupt autofocusing, and maximum k-value depends on the amount of blocking. The CADB blocked with different types possesses good self-healing abilities, where blocked parts reappear as a result of redistribution of intensity. The maximum self-healing occurs at zafz_{af}, where an overlap integral approaches a maximum value. Finally, we have compared ideal CADB and partially blocked CADB having the same radii, and found that an ideal CADB possesses better abrupt autofocusing. We have found a good agreement between the numerical simulations and experimental results.Comment: 16 pages, 20 figure

    Introducing symplectic billiards

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    In this article we introduce a simple dynamical system called symplectic billiards. As opposed to usual/Birkhoff billiards, where length is the generating function, for symplectic billiards symplectic area is the generating function. We explore basic properties and exhibit several similarities, but also differences of symplectic billiards to Birkhoff billiards.Comment: 41 pages, 16 figure
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