On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential
Само за регистроване кориснике
2020
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
We have investigated the dynamics of a quantum particle in the optical lattice potential. Initially, the quantum particle was represented by a Gaussian wave packet, located in the center of the well. The corresponding Schrödinger equation was solved explicitly by the method of the Chebyshev global propagation. Obtained solutions were also used for the construction of the Wigner functions. We found a great number of local abrupt changes of the solution shape. To explain this behavior, we used the fact that structurally stable systems, which form the largest class of the low dimensional dynamical systems, can be modeled and classified according to the catastrophe theory. All important features of the exact solution were explained on the basis of the mathematical properties of the catastrophic model. Such an approach enabled us to extract relevant information out of numerical solutions without employing any kind of approximations. We have investigated the influence of the Wigner catastrop...hes on the details of the quantum-classical correspondence breakdown. The wave packet was found to expand rapidly, filling the whole classically available area of the phase space. It was found that its self-interference pattern saturates quickly. A region of the phase space emerges in which the Wigner function oscillations transform into the singularity driven fluctuations. Once this region covers the whole area of the phase space, a wave packet dynamics enters into the new regime where its Wigner function fluctuates around the ergodic average. It will be shown that all mentioned processes are caused by the proliferation of the catastrophes and their mutual interactions
Кључне речи:
theoretical study / oscillation / cell proliferation / disasterИзвор:
Chaos, 2020, 30, 10, 103107-Финансирање / пројекти:
- Ministry of Education, Science and Technological Development of the Republic of Serbia
DOI: 10.1063/1.5140528
ISSN: 1054-1500
PubMed: 33138471
WoS: 000582502600003
Scopus: 2-s2.0-85092491067
Институција/група
VinčaTY - JOUR AU - Ćosić, Marko AU - Petrović, Srđan M. AU - Bellucci, Stefano PY - 2020 UR - https://vinar.vin.bg.ac.rs/handle/123456789/9680 AB - We have investigated the dynamics of a quantum particle in the optical lattice potential. Initially, the quantum particle was represented by a Gaussian wave packet, located in the center of the well. The corresponding Schrödinger equation was solved explicitly by the method of the Chebyshev global propagation. Obtained solutions were also used for the construction of the Wigner functions. We found a great number of local abrupt changes of the solution shape. To explain this behavior, we used the fact that structurally stable systems, which form the largest class of the low dimensional dynamical systems, can be modeled and classified according to the catastrophe theory. All important features of the exact solution were explained on the basis of the mathematical properties of the catastrophic model. Such an approach enabled us to extract relevant information out of numerical solutions without employing any kind of approximations. We have investigated the influence of the Wigner catastrophes on the details of the quantum-classical correspondence breakdown. The wave packet was found to expand rapidly, filling the whole classically available area of the phase space. It was found that its self-interference pattern saturates quickly. A region of the phase space emerges in which the Wigner function oscillations transform into the singularity driven fluctuations. Once this region covers the whole area of the phase space, a wave packet dynamics enters into the new regime where its Wigner function fluctuates around the ergodic average. It will be shown that all mentioned processes are caused by the proliferation of the catastrophes and their mutual interactions T2 - Chaos T1 - On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential VL - 30 IS - 10 SP - 103107 DO - 10.1063/1.5140528 ER -
@article{ author = "Ćosić, Marko and Petrović, Srđan M. and Bellucci, Stefano", year = "2020", abstract = "We have investigated the dynamics of a quantum particle in the optical lattice potential. Initially, the quantum particle was represented by a Gaussian wave packet, located in the center of the well. The corresponding Schrödinger equation was solved explicitly by the method of the Chebyshev global propagation. Obtained solutions were also used for the construction of the Wigner functions. We found a great number of local abrupt changes of the solution shape. To explain this behavior, we used the fact that structurally stable systems, which form the largest class of the low dimensional dynamical systems, can be modeled and classified according to the catastrophe theory. All important features of the exact solution were explained on the basis of the mathematical properties of the catastrophic model. Such an approach enabled us to extract relevant information out of numerical solutions without employing any kind of approximations. We have investigated the influence of the Wigner catastrophes on the details of the quantum-classical correspondence breakdown. The wave packet was found to expand rapidly, filling the whole classically available area of the phase space. It was found that its self-interference pattern saturates quickly. A region of the phase space emerges in which the Wigner function oscillations transform into the singularity driven fluctuations. Once this region covers the whole area of the phase space, a wave packet dynamics enters into the new regime where its Wigner function fluctuates around the ergodic average. It will be shown that all mentioned processes are caused by the proliferation of the catastrophes and their mutual interactions", journal = "Chaos", title = "On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential", volume = "30", number = "10", pages = "103107", doi = "10.1063/1.5140528" }
Ćosić, M., Petrović, S. M.,& Bellucci, S.. (2020). On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential. in Chaos, 30(10), 103107. https://doi.org/10.1063/1.5140528
Ćosić M, Petrović SM, Bellucci S. On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential. in Chaos. 2020;30(10):103107. doi:10.1063/1.5140528 .
Ćosić, Marko, Petrović, Srđan M., Bellucci, Stefano, "On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential" in Chaos, 30, no. 10 (2020):103107, https://doi.org/10.1063/1.5140528 . .