Abstract
Quantum effects on a Landau-type system associated with a moving atom with a magnetic quadrupole moment subject to confining potentials are analysed. It is shown that the spectrum of energy of the Landau-type system can be modified, where the degeneracy of the energy levels can be broken. In three particular cases, it is shown that the analogue of the cyclotron frequency is modified, and the possible values of this angular frequency of the system are determined by the quantum numbers associated with the radial modes and the angular momentum and by the parameters associated with confining potentials in order that bound states solutions can be achieved.
Highlights
It is well-known in the literature that the Landau quantization [1] takes place when the motion of a charged particle in a plane perpendicular to a uniform magnetic field acquires distinct orbits and the energy spectrum of this system becomes discrete and infinitely degenerate
With the aim of building a quantum system where the quantum Hall effect for neutral particles could be observed, a model has been proposed in [8] where the electric field that interacts with the permanent magnetic dipole moment of the neutral particle must satisfy specific conditions: there is absence of torque on the magnetic dipole moment of the neutral particle, the electric field must satisfy the electrostatic conditions, and there exists the presence of a uniform effective magnetic field given by B⃗eff = ∇⃗ × A⃗ eff, where A⃗ eff = σ⃗ × E⃗ corresponds to an effective vector potential, E⃗ is the electric field, and σ⃗ are the Pauli matrices
The Landau quantization for an atom with electric quadrupole moment has been proposed in [13] by imposing the notion that the electric quadrupole tensor must be symmetric and traceless and there exists the presence of a uniform effective magnetic field given by an effective vector potential defined as A⃗ eff = Q⃗ × B⃗, where Q⃗ is a vector associated with the electric quadrupole tensor [13, 14] and B⃗ is the magnetic field in the laboratory frame
Summary
It is well-known in the literature that the Landau quantization [1] takes place when the motion of a charged particle in a plane perpendicular to a uniform magnetic field acquires distinct orbits and the energy spectrum of this system becomes discrete and infinitely degenerate. It is important in studies of two-dimensional surfaces [2,3,4], the quantum Hall effect [5], and Bose-Einstein condensation [6, 7]. The structure of this paper is as follows: in Section 2, we introduce the Landau-type system associated with an atom with a magnetic quadrupole moment by using the single particle approximation of [47, 48]; in Section 3, we confine the Landau-type system to a hard-wall confining potential and analyse the bound states solutions; in Section 4, we discuss the Landau-type system subject to a Coulomb-type confining potential; in Section 5, we discuss the Landau-type system subject to a linear confining potential; in Section 6, we discuss the Landau-type system subject to a Coulomb-type and a linear confining potential; in Section 7, we present our conclusions
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