Quantum Dynamics in a Comb Geometry: Green Function Solutions with Nonlocal and Fractional Potentials
We investigate a generalized quantum Schrödinger equation in a comb-like structure that imposes geometric constraints on spatial variables. The model is extended by the introduction of nonlocal and fractional potentials to capture memory effects in both space and time. We consider four distinct scen...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-07-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/7/446 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849406858161291264 |
|---|---|
| author | Enrique C. Gabrick Ervin K. Lenzi Antonio S. M. de Castro José Trobia Antonio M. Batista |
| author_facet | Enrique C. Gabrick Ervin K. Lenzi Antonio S. M. de Castro José Trobia Antonio M. Batista |
| author_sort | Enrique C. Gabrick |
| collection | DOAJ |
| description | We investigate a generalized quantum Schrödinger equation in a comb-like structure that imposes geometric constraints on spatial variables. The model is extended by the introduction of nonlocal and fractional potentials to capture memory effects in both space and time. We consider four distinct scenarios: (i) a time-dependent nonlocal potential, (ii) a spatially nonlocal potential, (iii) a combined space–time nonlocal interaction with memory kernels, and (iv) a fractional spatial derivative, which is related to distributions asymptotically governed by power laws and to a position-dependent effective mass. For each scenario, we propose solutions based on the Green’s function for arbitrary initial conditions and analyze the resulting quantum dynamics. Our results reveal distinct spreading regimes, depending on the type of non-locality and the fractional operator applied to the spatial variable. These findings contribute to the broader generalization of comb models and open new questions for exploring quantum dynamics in backbone-like structures. |
| format | Article |
| id | doaj-art-a59f2ab3c8f449a0b3ec3fe87801ab7a |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-a59f2ab3c8f449a0b3ec3fe87801ab7a2025-08-20T03:36:14ZengMDPI AGFractal and Fractional2504-31102025-07-019744610.3390/fractalfract9070446Quantum Dynamics in a Comb Geometry: Green Function Solutions with Nonlocal and Fractional PotentialsEnrique C. Gabrick0Ervin K. Lenzi1Antonio S. M. de Castro2José Trobia3Antonio M. Batista4Institute of Physics, University of São Paulo, São Paulo 05508-090, SP, BrazilGraduate Program in Science, State University of Ponta Grossa, Ponta Grossa 84030-900, PR, BrazilGraduate Program in Science, State University of Ponta Grossa, Ponta Grossa 84030-900, PR, BrazilDepartment of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa 84030-900, PR, BrazilGraduate Program in Science, State University of Ponta Grossa, Ponta Grossa 84030-900, PR, BrazilWe investigate a generalized quantum Schrödinger equation in a comb-like structure that imposes geometric constraints on spatial variables. The model is extended by the introduction of nonlocal and fractional potentials to capture memory effects in both space and time. We consider four distinct scenarios: (i) a time-dependent nonlocal potential, (ii) a spatially nonlocal potential, (iii) a combined space–time nonlocal interaction with memory kernels, and (iv) a fractional spatial derivative, which is related to distributions asymptotically governed by power laws and to a position-dependent effective mass. For each scenario, we propose solutions based on the Green’s function for arbitrary initial conditions and analyze the resulting quantum dynamics. Our results reveal distinct spreading regimes, depending on the type of non-locality and the fractional operator applied to the spatial variable. These findings contribute to the broader generalization of comb models and open new questions for exploring quantum dynamics in backbone-like structures.https://www.mdpi.com/2504-3110/9/7/446comb modelsquantum dynamicsGreen’s function |
| spellingShingle | Enrique C. Gabrick Ervin K. Lenzi Antonio S. M. de Castro José Trobia Antonio M. Batista Quantum Dynamics in a Comb Geometry: Green Function Solutions with Nonlocal and Fractional Potentials Fractal and Fractional comb models quantum dynamics Green’s function |
| title | Quantum Dynamics in a Comb Geometry: Green Function Solutions with Nonlocal and Fractional Potentials |
| title_full | Quantum Dynamics in a Comb Geometry: Green Function Solutions with Nonlocal and Fractional Potentials |
| title_fullStr | Quantum Dynamics in a Comb Geometry: Green Function Solutions with Nonlocal and Fractional Potentials |
| title_full_unstemmed | Quantum Dynamics in a Comb Geometry: Green Function Solutions with Nonlocal and Fractional Potentials |
| title_short | Quantum Dynamics in a Comb Geometry: Green Function Solutions with Nonlocal and Fractional Potentials |
| title_sort | quantum dynamics in a comb geometry green function solutions with nonlocal and fractional potentials |
| topic | comb models quantum dynamics Green’s function |
| url | https://www.mdpi.com/2504-3110/9/7/446 |
| work_keys_str_mv | AT enriquecgabrick quantumdynamicsinacombgeometrygreenfunctionsolutionswithnonlocalandfractionalpotentials AT ervinklenzi quantumdynamicsinacombgeometrygreenfunctionsolutionswithnonlocalandfractionalpotentials AT antoniosmdecastro quantumdynamicsinacombgeometrygreenfunctionsolutionswithnonlocalandfractionalpotentials AT josetrobia quantumdynamicsinacombgeometrygreenfunctionsolutionswithnonlocalandfractionalpotentials AT antoniombatista quantumdynamicsinacombgeometrygreenfunctionsolutionswithnonlocalandfractionalpotentials |