Finite element distributions in statistical theory of energy levels in quantum systems |
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| Affiliation: | 1. Institute of Physics, Jagellonian University, ulica Reymonta 4, 30-059 Cracow, Poland;2. Institute of Physics, Cracow University of Technology, ulica Podchorazych 1, 30-084 Cracow, Poland;1. Department of Tourism, Conventions and Event Management, IUPUI, USA;2. The School of Tourism Management, Sun Yat-sen University, Guangzhou, China;1. Coventry University, Coventry CV1 5DL, UK;2. University of Worcester, Worcester WR1 3AS, UK;3. Royal Agricultural University, Cirencester GL7 6JS, UK;1. Department of Mechanical Engineering, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur, India;2. Department of Electrical and Electronics Engineering, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur, India;3. School of Mechanical Engineering, Faculty of Engineering and Technology, Jain (Deemed to be University), Bangalore, India;1. Department of Pediatric Dentistry, College of Dentistry, University of Illinois-Chicago, Chicago, IL, USA;2. Department of Pediatric Dentistry, Guanghua School of Stomotology, Hospital of Stomatology, Sun Yat-sen University, Guangdong Provincial Key Laboratory of Stomatology, Guangzhou, China;3. Department of Restorative Dentistry, College of Dentistry, University of Illinois-Chicago, Chicago, IL, USA;4. Department of Oral Biology, College of Dentistry, University of Illinois-Chicago, Chicago, IL, USA;1. Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal;2. CERIS, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal;3. Department of Engineering and Applied Sciences, University of Bergamo, Viale G. Marconi 5, 24044 Dalmine (BG), Italy |
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| Abstract: | ![]()
The probability density functions of the three-point finite elements of the three adjacent energy levels for the three-level quantum system are introduced as a supplementary characteristics of quantum chaos. The three-level quantum system is studied. The probability density functions of the second difference and asymmetrical three-point first finite element are computed for the three-dimensional Gaussian orthogonal ensemble GOE(3), the three-dimensional Gaussian unitary ensemble GUE(3), the three-dimensional Gaussian symplectic ensemble GSE(3), as well as for the Poisson ensemble PE. |
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