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Princeton University Press eBooks

Power of Degeneracy

Published Jun 5, 2018• 0 citations
Publisher
DOI
10.2307/j.ctvc77gwd.20

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The two-level quantum heat engines have been studied extensively. Before that, the optimization of most heat engines was mainly concentrated in non-degenerate cases. We consider the level degeneracy, then calculate the maximum operation time and the irreversible dissipation coefficient of the two-level system under the scheme of linear tuned levels. In the high-temperature limit, we find that the level degeneracy affects the maximum power of the two-level heat engine. Especially in the case of the same degeneracy of the ground state and the excited state, the influence is the greatest. In addition, we also show that the degeneracy does not affect the efficiency at maximum power and the consistent relation of the two-level Carnot-like heat engine.

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An exact diagonalization of the XXX one-dimensional Heisenberg model a magnet with the single-node 1/2 reveals a specific degeneracy in the sector of r = 3 reversed spins at the centre k = 0 of the Brillouin zone. The degeneracy manifests itself by the second power (i.e. the double degeneracy) of a factor of the characteristic polynomial of the related secular matrix. The factor, treated as a polynomial in the variable x being an eigenenergy, is indecomposable over the field Q of rationals, and its roots correspond to appropriate rigged configurations of strings. The degeneracy is associated with the fact that quasimomenta of the two-string and the one-string are conserved independently each of the other, which is a particular consequence of integrability of the system.

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Degeneracy of the eigenvalues of hermitian matrices is analyzed in terms of algebraic relations between the matrix elements. Only finite-dimensional matrices are considered, representing Hamiltonians of spin systems in particular.The analysis is in terms of linear relations in the space of 'diagonal' operators, i.e. a complete set of powers of the Hamiltonian. A relation is found with the theorem formulated by Von Neumann and Wigner that only the variation of three parameters of the Hamiltonian may result in a 'crossing' or degeneracy of two eigenvalues.

Journal of Physics Conference Series•Mar 1, 2008•4 citations
The two-level quantum heat engines have been studied extensively. Before that, the optimization of most heat engines was mainly concentrated in non-degenerate cases. We consider the level degeneracy, then calculate the maximum operation time and the irreversible dissipation coefficient of the two-level system under the scheme of linear tuned levels. In the high-temperature limit, we find that the level degeneracy affects the maximum power of the two-level heat engine. Especially in the case of the same degeneracy of the ground state and the excited state, the influence is the greatest. In addition, we also show that the degeneracy does not affect the efficiency at maximum power and the consistent relation of the two-level Carnot-like heat engine.
An exact diagonalization of the XXX one-dimensional Heisenberg model a magnet with the single-node 1/2 reveals a specific degeneracy in the sector of r = 3 reversed spins at the centre k = 0 of the Brillouin zone. The degeneracy manifests itself by the second power (i.e. the double degeneracy) of a factor of the characteristic polynomial of the related secular matrix. The factor, treated as a polynomial in the variable x being an eigenenergy, is indecomposable over the field Q of rationals, and its roots correspond to appropriate rigged configurations of strings. The degeneracy is associated with the fact that quasimomenta of the two-string and the one-string are conserved independently each of the other, which is a particular consequence of integrability of the system.
Degeneracy of the eigenvalues of hermitian matrices is analyzed in terms of algebraic relations between the matrix elements. Only finite-dimensional matrices are considered, representing Hamiltonians of spin systems in particular.The analysis is in terms of linear relations in the space of 'diagonal' operators, i.e. a complete set of powers of the Hamiltonian. A relation is found with the theorem formulated by Von Neumann and Wigner that only the variation of three parameters of the Hamiltonian may result in a 'crossing' or degeneracy of two eigenvalues.