Small-scale properties of the KPZ equation and dynamical symmetry breaking |
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| Institution: | 1. Laboratorio de Astrofísica Espacial y Física Fundamental, Apartado 50727, 28080 Madrid, Spain;2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;3. Physics Department, Washington University, Saint Louis, MO 63130-4899, USA;4. Centro de Astrobiologı́a, INTA-CSIC, Ctra. Ajalvir, Km. 4, 28850 Torrejón, Madrid, Spain;1. School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou 510006, Guangdong, China;2. Department of Civil Engineering, Tsinghua University, Beijing 100084, China;3. School of New Energy and Materials, Southwest Petroleum University, Chengdu 610500, Sichuan, China;4. School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo 454003, Henan, China;5. Shenzhen Yichuang International Design Co., Ltd, Shenzhen 518000, China;6. Guangzhou Metro Design & Research Institution Co., Ltd., Guangzhou 510010, Guangdong, China;1. College of Material, Chemistry and Chemical Engineering, Key Laboratory of Organosilicon Chemistry and Material Technology, Ministry of Education, Hangzhou Normal University, Hangzhou, 311121, PR China;2. School of Earth, Energy and Environmental Engineering, Kitami Institute of Technology, 165 Koen-cho, Kitami, Hokkaido, 090-8507, Japan;3. Department of Applied Chemistry and Chemical Engineering, Graduate School of Science and Technology, Niigata University, Ikarashi 2-8050, Nishi-ku, Niigata, 950-2181, Japan;1. Department of Applied Chemistry, Tokyo University of Science, Kagurazaka, Shinjuku-ku, Tokyo, 162-8601 Japan;2. Research Organization for Nano & Life Innovation, Waseda University, Wasedatsurumaki-cho, Shinjuku-ku, Tokyo, 162-0041 Japan |
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| Abstract: | A functional integral technique is used to study the ultraviolet or short distance properties of the Kardar–Parisi–Zhang (KPZ) equation with white Gaussian noise. We apply this technique to calculate the one-loop effective potential for the KPZ equation. The effective potential is (at least) one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, but non-renormalizable in 4 or higher space dimensions. This potential is intimately related to the probability distribution function (PDF) for the spacetime averaged field. For the restricted class of field configurations considered here, the KPZ equation exhibits dynamical symmetry breaking (DSB) via an analog of the Coleman–Weinberg mechanism in 1 and 2 space dimensions, but not in 3 space dimensions. |
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