Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909177698320384 |
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| author | Mu, Sen Gong, Jiangbin Lemarié, Gabriel |
| author_facet | Mu, Sen Gong, Jiangbin Lemarié, Gabriel |
| contents | We identify the key features of Kardar-Parisi-Zhang universality class in the fluctuations of the wave density logarithm, in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit an algebraic scaling with distance characterized by an exponent of $1/3$, and a Tracy-Widom probability distribution of the fluctuations. Additionally, within a directed polymer picture of KPZ physics, we identify the dominant contribution of a directed path to the wave packet density and find that its transverse fluctuations are characterized by a roughness exponent $2/3$. Leveraging on this connection with KPZ physics, we verify that an Anderson localized wave packet in 2D exhibits a stretched-exponential correction to its well-known exponential localization. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_08272 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets Mu, Sen Gong, Jiangbin Lemarié, Gabriel Disordered Systems and Neural Networks Quantum Gases Statistical Mechanics Chaotic Dynamics Quantum Physics We identify the key features of Kardar-Parisi-Zhang universality class in the fluctuations of the wave density logarithm, in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit an algebraic scaling with distance characterized by an exponent of $1/3$, and a Tracy-Widom probability distribution of the fluctuations. Additionally, within a directed polymer picture of KPZ physics, we identify the dominant contribution of a directed path to the wave packet density and find that its transverse fluctuations are characterized by a roughness exponent $2/3$. Leveraging on this connection with KPZ physics, we verify that an Anderson localized wave packet in 2D exhibits a stretched-exponential correction to its well-known exponential localization. |
| title | Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets |
| topic | Disordered Systems and Neural Networks Quantum Gases Statistical Mechanics Chaotic Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2306.08272 |