Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

Abstract

Abstract.The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of solution is given, by recasting the known solution of the Dirac oscillator into matrix form; there one notices, that a block-diagonal form arises in a Hamiltonian formulation. The blocks are two-dimensional. Choosing couplings that do not affect the block structure, these blow up the 2×2 matrices to 4×4 matrices, thus conserving solvability. The result can be cast again in covariant form. By way of example we apply this exact solution to calculate the evolution of entanglement.

Quantum phase transitions in the noncommutative Dirac oscillator

“…The Dirac oscillator on the other hand is one of the very few relativistic systems which is exactly solvable [15][16][17][18][19][20][21][22]. In mathematical physics the Dirac oscillator has become a paradigm for the realization of covariant quantum models and it has found applications both in nuclear [23][24][25] and subnuclear [26,27] physics as well as in quantum optics [28][29][30].…”

A Novel Exact Solution of the 2+1-Dimensional Radial Dirac Equation for the Generalized Dirac Oscillator with the Inverse Potentials

“…Now, the purpose of our study is to obtain the analytical properties of the scattering amplitude about singular potential. So, the corresponding 2+1-dimensional radial Dirac equation with inverse quartic power potential is given by equation (7)   (20) In order to deal with the question, the appropriate asymptotic behavior of the wave function   (21) where the parameter is set 2…”

“…Moreover, many phenomena in Quantum Optics [17][18][19][20][21] could also be explained by this model. The investigation of the relationship between Dirac oscillator and relativistic Jaynes-Cummings model [4,[20][21] bridges the two unrelated fields of Relativistic Quantum Mechanics and Quantum Optics [22][23]. In addition, this model can also be used to explain some new phenomena in condensed matter physics [16][17][24][25], such as the Quantum Hall Effect and Fractional Statistics.…”

Quantum phase transitions of the Dirac oscillator in the anti-Snyder model

“…The Dirac oscillator [16][17][18][19][20][21] in the presence of a homogeneous magnetic field is one of the few exactly solvable problems in relativistic quantum mechanics [22]. This combined system is known to exhibit a quantum chirality phase transition whenever the magnetic field strength exceeds a critical value [23][24][25].…”