{"title":"自引力玻色气体中的波湍流与非局部非线性光学","authors":"J. Skipp, V. L’vov, S. Nazarenko","doi":"10.1103/physreva.102.043318","DOIUrl":null,"url":null,"abstract":"We develop the theory of weak wave turbulence in systems described by the Schr\\\"odinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schr\\\"odinger equation, and the Schr\\\"odinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schr\\\"odinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. The inverse cascade we interpret as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the Schr\\\"odinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schr\\\"odinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterise such \"warm cascade\" states.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics\",\"authors\":\"J. Skipp, V. L’vov, S. Nazarenko\",\"doi\":\"10.1103/physreva.102.043318\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We develop the theory of weak wave turbulence in systems described by the Schr\\\\\\\"odinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schr\\\\\\\"odinger equation, and the Schr\\\\\\\"odinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schr\\\\\\\"odinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. The inverse cascade we interpret as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the Schr\\\\\\\"odinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schr\\\\\\\"odinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterise such \\\"warm cascade\\\" states.\",\"PeriodicalId\":8473,\"journal\":{\"name\":\"arXiv: Statistical Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-10-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Statistical Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1103/physreva.102.043318\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Statistical Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1103/physreva.102.043318","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics
We develop the theory of weak wave turbulence in systems described by the Schr\"odinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schr\"odinger equation, and the Schr\"odinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schr\"odinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. The inverse cascade we interpret as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the Schr\"odinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schr\"odinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterise such "warm cascade" states.