کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1856596 | 1529879 | 2013 | 11 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Quantum mechanical Hamiltonians with large ground-state degeneracy Quantum mechanical Hamiltonians with large ground-state degeneracy](/preview/png/1856596.png)
Nonrelativistic Hamiltonians with large, even infinite, ground-state degeneracy are studied by connecting the degeneracy to the property of a Dirac operator. We then identify a special class of Hamiltonians, for which the full space of degenerate ground states in any spatial dimension can be exhibited explicitly. The two-dimensional version of the latter coincides with the Pauli Hamiltonian, and recently-discussed models leading to higher-dimensional Landau levels are obtained as special cases of the higher-dimensional version of this Hamiltonian. But, in our framework, it is only the asymptotic behavior of the background ‘potential’ that matters for the ground-state degeneracy. We work out in detail the ground states of the three-dimensional model in the presence of a uniform magnetic field and such potential. In the latter case one can see degenerate stacking of all 2d Landau levels along the magnetic field axis.
► We study a class of nonrelativistic Hamiltonian which is a square of the Dirac operator.
► Some of them has a large number of degenerate ground states.
► 2-dim Pauli Hamiltonian and 3-dim Landau problem are a part of this class.
► In a version, all 2-dim Landau levels become degenerate ground states, stacking along the magnetic direction.
Journal: Annals of Physics - Volume 331, April 2013, Pages 258–268