Abstract:We consider the magnetic Schrödinger operators on the Poincaré upper half plane with constant Gaussian curvature −1. We assume the magnetic field is given by the sum of a constant field and the Dirac δ measures placed on some lattice. We give a sufficient condition for each Landau level to be an infinitely degenerated eigenvalue. We also prove the lowest Landau level is not an eigenvalue if the above condition fails. In particular, the infinite degeneracy of the lowest Landau level is equivalent to the infinit… Show more
“…Landau levels in negative [14][15][16] and positive [14,17] curvature cases have been intensively studied in order to explore quantum Hall effect in these spaces [18][19][20][21][22][23]. Quantum Hall effect in a Lobachevsky plane was considered in ref.…”
In this paper we study the quantum dynamics of an electron/hole in a two-dimensional quantum ring within a spherical space. For this geometry, we consider a harmonic confining potential.Suggesting that the quantum ring is affected by the presence of an Aharonov-Bohm flux and an uniform magnetic field, we solve the Schrödinger equation for this problem and obtain exactly the eigenvalues of energy and corresponding eigenfunctions for this nanometric quantum system. Afterwards, we calculate the magnetization and persistent current are calculated, and discuss influence of curvature of space on these values.
“…Landau levels in negative [14][15][16] and positive [14,17] curvature cases have been intensively studied in order to explore quantum Hall effect in these spaces [18][19][20][21][22][23]. Quantum Hall effect in a Lobachevsky plane was considered in ref.…”
In this paper we study the quantum dynamics of an electron/hole in a two-dimensional quantum ring within a spherical space. For this geometry, we consider a harmonic confining potential.Suggesting that the quantum ring is affected by the presence of an Aharonov-Bohm flux and an uniform magnetic field, we solve the Schrödinger equation for this problem and obtain exactly the eigenvalues of energy and corresponding eigenfunctions for this nanometric quantum system. Afterwards, we calculate the magnetization and persistent current are calculated, and discuss influence of curvature of space on these values.
In this paper, we study the quantum dynamics of an electron/hole in a two-dimensional quantum ring within a spherical space. For this geometry, we consider a harmonic confining potential. Suggesting that the quantum ring is affected by the presence of an Aharonov–Bohm flux and a uniform magnetic field, we solve the Schrödinger equation for this problem and obtain exactly the eigenvalues of energy and corresponding eigenfunctions for this nanometric quantum system. Afterwards, we calculate the magnetization and persistent current are calculated, and discuss influence of curvature of space on these values.
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