Dirac fermion in a time-dependent spherical box
Kuvonchbek MatchonovNational University of Uzbekistan, 4 University Str., 100174 Tashkent, UzbekistanD. U. MatrasulovTurin Polytechnic University in Tashkent, 17 Niyazov Str., 100095 Tashkent, Uzbekistan; Tashkent University of Architecture and Civil Engineering, Yangishahar Str. 9A, 100095 Tashkent, UzbekistanJ. DittrichCzech Academy of Sciences, Nuclear Physics Institute, 25068 Řež, Czech Republic
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Abstract
We consider a Dirac particle in a spherical box with a time-dependent radius. Analytical and numerical solutions of the time-dependent Dirac equation with time-dependent boundary (Dirichlet) conditions are obtained. Using the obtained solutions, physically observable characteristics of the dynamical confinement, such as the average kinetic energy (as a function of time) and average quantum force acting on the particle by the moving wall, are calculated. The trembling motion is analysed by computing the average coordinate of the Dirac particle as a function of time. The absence of the geometric phase is shown by direct calculation.
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