On the microlocal phase-space concentration of Wigner distributions associated with Schrödinger evolutions
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914313331015680 |
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| author | Giacchi, Gianluca Tramontana, Davide |
| author_facet | Giacchi, Gianluca Tramontana, Davide |
| contents | In this work, we investigate the microlocal properties of the evolutions of Schrödinger equations using metaplectic Wigner distributions. So far, only restricted classes of metaplectic Wigner distributions, satisfying particular structural properties, have allowed the analysis of microlocal properties. We first extend the microlocal results to all metaplectic Wigner distributions, including the well-known Kohn-Nirenberg quantization, and examine these findings in the framework of Fourier integral operators with quadratic phase. Finally, we analyze the phase space concentration of the (cross) Wigner distribution arising from the interaction of two states, with particular attention to interactions generated by certain Schrödinger evolutions. These contributions enable a more refined study of the so-called ghost frequencies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the microlocal phase-space concentration of Wigner distributions associated with Schrödinger evolutions Giacchi, Gianluca Tramontana, Davide Analysis of PDEs Quantum Algebra Quantum Physics 35A18, 35J10, 35Q40, 35S10, 47G30, 70S20, 81S10, 81S30 In this work, we investigate the microlocal properties of the evolutions of Schrödinger equations using metaplectic Wigner distributions. So far, only restricted classes of metaplectic Wigner distributions, satisfying particular structural properties, have allowed the analysis of microlocal properties. We first extend the microlocal results to all metaplectic Wigner distributions, including the well-known Kohn-Nirenberg quantization, and examine these findings in the framework of Fourier integral operators with quadratic phase. Finally, we analyze the phase space concentration of the (cross) Wigner distribution arising from the interaction of two states, with particular attention to interactions generated by certain Schrödinger evolutions. These contributions enable a more refined study of the so-called ghost frequencies. |
| title | On the microlocal phase-space concentration of Wigner distributions associated with Schrödinger evolutions |
| topic | Analysis of PDEs Quantum Algebra Quantum Physics 35A18, 35J10, 35Q40, 35S10, 47G30, 70S20, 81S10, 81S30 |
| url | https://arxiv.org/abs/2511.19733 |