Landau quantization for an electric quadrupole moment of position-dependent mass quantum particles interacting with electromagnetic fields

Abstract

Analogous to Landau quantization related to a neutral particle possessing an electric quadrupole moment, we generalize such a Landau quantization to include position-dependent mass (PDM) neutral particles. Using cylindrical coordinates, the exact solvability of PDM neutral particles with an electric quadrupole moment moving in electromagnetic fields is reported. The interaction between the electric quadrupole moment of a PDM neutral particle and a magnetic field in the absence of an electric field is analyzed for two different radial cylindrical PDM settings. Next, two particular cases of radial electric fields ( − → E = λ ρ ρ and − → E = λρ 2 ρ) are considered to investigate their influence on the Landau quantization (of this system using the same models of PDM settings). The exact eigenvalues and eigenfunctions for each case are analytically obtained.

PDM Klein-Gordon oscillators in cosmic string spacetime in magnetic and Aharonov-Bohm flux fields within the Kaluza-Klein theory

“…Moreover, we have observed that square the energies in (18) (i.e., E 2 ) resembles the Landau-type energies-squared with an irrational magnetic quantum number γ that indulges within the Aharonov-Bohm flux field effect. We may argue, therefore, that the additional compact dimension of the Kaluza-Klein theory offers quasi-Landau energy levels (e.g., [6,64,67]). Hereby, the behaviour of the energy levels E nr ,ℓ is found to follow two different trends of clustering and batching up for the curvature parameter α ≈ 0 and α ≫ 1.…”

“…It is interesting to know that this is manifestly introduced by the coupling between the compact Kaluza-Klein fifth-dimension u and the ϕ coordinate. As such, we may argue that the additional compact dimension of the Kaluza-Klein theory offers quasi-Landau energy levels (e.g., [6,64,67]). Moreover, one should be aware that the four possible KG-oscillators' settings discussed above, with some straightforward parametric substitutions, admit exact solvability as in (18) and (19).…”

Isochronous $n$-dimensional nonlinear PDM-oscillators: linearizability, invariance and exact solvability

“…This would consequently enrich the class of exactly solvable dynamical systems within the standard Lagrangian/Hamiltonian settings. Moreover, one should be aware that when equation ( 35) is multiplied by qi and summed over i = 1, 2, • • • , n, it would yield (43) or equivalently (45).…”

“…Which is, in fact, a very interesting equation for both physics and mathematics [1][2][3][4][5][6][7][8][9][10][11]. The linearizability and isochronicity of which have invited a vast number of interesting research studies in many fields (c.f., e.g., [35][36][37][38][39][40][41][42][43][44][45]). Tiwari et al [2] and Lakshmanan and Chandrasekar [3], for example, have used Lie point symmetries and asserted that in the case of eight parameter symmetry group, the one-dimensional quadratic Liénard type equation ( 3) is linearizable and isochronic.…”

Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass

“…In addition, it is also shown the coherent states for the harmonic oscillator satisfy the minimization of the Heisenberg's uncertainty principle. 16 Complementary, another important issue in quantum mechanics is the concept of position-dependent mass (PDM), which has attracted the attention along the decades due its wide applicability in: semiconductor heterostructures, [17][18][19][20][21][22][23][24] nonlinear optics, 25 quantum liquids, 26 many-body theory, 27 molecular physics, 28 Wigner functions, 29 quantum information, 30 relativistic quantum mechanics, 31 Dirac equation, 32 superintegrable systems, 33 nuclear physics, 34 magnetic monopoles, 35 Landau quantization, 36 factorization and supersymmetry methods, [37][38][39][40][41] coherent states, [42][43][44][45] etc.…”