{"682220":{"#nid":"682220","#data":{"type":"event","title":"PhD Defense by Han Liang","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ESchool of Physics Thesis Dissertation Defense\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EHan Liang\u003C\/strong\u003E\u003Cbr\u003EAdvisor: Dr. Predrag Cvitanovi\u0107,\u0026nbsp;School of Physics, Georgia Institute\u0026nbsp;of Technology\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u003Cbr\u003E\u003Cstrong\u003EA Deterministic Lattice Field Theory of Spatiotemporal Chaos\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003EDate: Monday, May 12, 2025\u003Cbr\u003ETime: 1:00 p.m.\u003Cbr\u003ELocation: Howey N201\/N202\u003Cbr\u003E\u003Cbr\u003E\u003Cstrong\u003EZoom link\u003C\/strong\u003E: \u0026nbsp;\u003Ca href=\u0022https:\/\/gatech.zoom.us\/j\/98851319184\u0022\u003Ehttps:\/\/gatech.zoom.us\/j\/98851319184\u003C\/a\u003E\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u003Cbr\u003E\u003Cstrong\u003ECommittee members:\u003C\/strong\u003E\u003Cbr\u003EDr. Elisabetta Matsumoto, \u0026nbsp;School of Physics, Georgia Institute\u0026nbsp;of Technology\u003C\/p\u003E\u003Cp\u003EDr. Martin Mourigal, \u0026nbsp;School of Physics, Georgia Institute\u0026nbsp;of Technology\u003C\/p\u003E\u003Cp\u003EDr. Zeb Rocklin, School of Physics, Georgia Institute of Technology\u003Cbr\u003EDr. Luca Dieci, School of Mathematics, Georgia Institute of Technology\u003C\/p\u003E\u003Cp\u003E\u003Cbr\u003E\u003Cstrong\u003EAbstract:\u003C\/strong\u003E\u003Cbr\u003ETraditional periodic orbit theory enables the evaluation of statistical properties of finite-dimensional chaotic dynamical systems through the\u003C\/p\u003E\u003Cp\u003Ehierarchy of their periodic orbits. However, this approach becomes impractical for spatiotemporally chaotic systems over large or infinite\u003C\/p\u003E\u003Cp\u003Espatial domains. As the spatial extents of these systems increase, the physical dimensions grow linearly, requiring exponentially more distinct\u003C\/p\u003E\u003Cp\u003Eperiodic orbits to describe the dynamics to the same accuracy. To address this challenge, we propose a novel approach, describing spatiotemporally\u003C\/p\u003E\u003Cp\u003Echaotic or turbulent systems using the chaotic field theories discretized over multi-dimensional spatiotemporal lattices. The `chaos theory\u0027 is\u003C\/p\u003E\u003Cp\u003Ehere recast in the language of statistical mechanics, field theory, and solid state physics, with traditional periodic orbit theory of\u003C\/p\u003E\u003Cp\u003Elow-dimensional, temporally chaotic dynamics a special, one-dimensional case.\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003EIn this field-theoretical formulation, there is no time evolution. Instead, by treating the temporal and spatial directions on equal footing,\u003C\/p\u003E\u003Cp\u003Eone determines the spatiotemporally periodic states that contribute to the theory\u0027s partition function, each a solution of the system\u0027s\u003C\/p\u003E\u003Cp\u003Edeterministic defining equations, with sums over time-periodic orbits of dynamical systems theory now replaced by sums of d-periodic states over\u003C\/p\u003E\u003Cp\u003Ed-dimensional spacetime geometries, weighted by their global orbit stabilities.\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003EThe orbit stability of each periodic state is evaluated using the determinant of its spatiotemporal orbit Jacobian matrix. We derive the\u003C\/p\u003E\u003Cp\u003EHill\u0027s formula, which relates the global orbit stability to the conventional low-dimensional forward-in-time evolution stability, and\u003C\/p\u003E\u003Cp\u003Eshow that the field-theoretical formulation is equivalent to the temporal periodic orbit theory for systems with fixed finite spatial extent. By\u003C\/p\u003E\u003Cp\u003Esumming the partition functions over different spacetime geometries, we extend the temporal periodic orbit theory to spatiotemporal systems. The\u003C\/p\u003E\u003Cp\u003Emultiple periodicities of spatiotemporally periodic states are described in the language of crystallography using Bravais lattices. Applying the\u003C\/p\u003E\u003Cp\u003EFloquet-Bloch theorem to evaluate the spectrum of orbit Jacobian operators of periodic states, we compute their multiplicative weights, leading to\u003C\/p\u003E\u003Cp\u003Ethe spatiotemporal zeta function formulation of the theory in terms of prime orbits. Hyperbolic shadowing of periodic orbits by pseudo orbits\u003C\/p\u003E\u003Cp\u003Eensures that the predictions of the theory are dominated by the prime periodic orbits with shortest spatiotemporal periods.\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E","summary":"","format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"\u003Cp\u003EA Deterministic Lattice Field Theory of Spatiotemporal Chaos\u003C\/p\u003E","format":"limited_html"}],"field_summary_sentence":[{"value":"A Deterministic Lattice Field Theory of Spatiotemporal Chaos"}],"uid":"27707","created_gmt":"2025-05-05 13:43:39","changed_gmt":"2025-05-05 13:43:39","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2025-05-12T13:00:00-04:00","event_time_end":"2025-05-12T15:00:00-04:00","event_time_end_last":"2025-05-12T15:00:00-04:00","gmt_time_start":"2025-05-12 17:00:00","gmt_time_end":"2025-05-12 19:00:00","gmt_time_end_last":"2025-05-12 19:00:00","rrule":null,"timezone":"America\/New_York"},"location":"Howey N201\/N202","extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78771","name":"Public"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}