TY - GEN UR - http://lib.ugent.be/catalog/pug01:1044750 ID - pug01:1044750 LA - eng TI - Analytically solvable quantum Hamiltonians and relations to orthogonal polynomials PY - 2010 SN - 9780735407886 SN - 0094-243X PB - Melville AU - Regniers, Gilles 002003345747 AU - Van der Jeugt, Joris WE02 801000490010 0000-0003-1387-1676 AU - Dobrev, Vladimir editor AB - Quantum systems consisting of a linear chain of n harmonic oscillators coupled by a quadratic nearest-neighbour interaction are considered. We investigate when such a system is analytically solvable, in the sense that the eigenvalues and eigenvectors of the interaction matrix have analytically closed expressions. This leads to a relation with Jacobi matrices of systems of discrete orthogonal polynomials. Our study is first performed in the case of canonical quantization. Then we consider these systems under Wigner quantization, leading to solutions in terms of representations of Lie superalgebras. Finally, we show how such analytically solvable Hamiltonians also play a role in another application, that of spin chains used as communication channels in quantum computing. In this context, the analytic solvability leads to closed form expressions for certain transition amplitudes. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 1044750 | ||
005 | 20180813140504.0 | ||
008 | 100922s2010------------------------eng-- | ||
020 | a 9780735407886 | ||
022 | a 0094-243X | ||
024 | a 000282673700009 2 wos | ||
024 | a 1854/LU-1044750 2 handle | ||
024 | a 10.1063/1.3460184 2 doi | ||
040 | a UGent | ||
245 | a Analytically solvable quantum Hamiltonians and relations to orthogonal polynomials | ||
260 | a Melville, NY, USA b American Institute of Physics (AIP) c 2010 | ||
520 | a Quantum systems consisting of a linear chain of n harmonic oscillators coupled by a quadratic nearest-neighbour interaction are considered. We investigate when such a system is analytically solvable, in the sense that the eigenvalues and eigenvectors of the interaction matrix have analytically closed expressions. This leads to a relation with Jacobi matrices of systems of discrete orthogonal polynomials. Our study is first performed in the case of canonical quantization. Then we consider these systems under Wigner quantization, leading to solutions in terms of representations of Lie superalgebras. Finally, we show how such analytically solvable Hamiltonians also play a role in another application, that of spin chains used as communication channels in quantum computing. In this context, the analytic solvability leads to closed form expressions for certain transition amplitudes. | ||
598 | a P1 | ||
100 | a Regniers, Gilles 0 002003345747 0 802000306089 | ||
700 | a Van der Jeugt, Joris u WE02 0 801000490010 0 0000-0003-1387-1676 | ||
700 | a Dobrev, Vladimir e editor | ||
650 | a Mathematics and Statistics | ||
653 | a quantum computation | ||
653 | a Wigner quantization | ||
653 | a quantum system | ||
653 | a canonical quantization | ||
653 | a transition amplitude | ||
653 | a discrete orthogonal polynomial | ||
653 | a Lie superalgebra | ||
653 | a Jacobi matrices | ||
653 | a analytically solvable quantum Hamiltonian | ||
653 | a spin chains | ||
653 | a harmonic oscillator | ||
773 | t 8th International workshop on Lie Theory and its Applications in Physics g AIP Conf. Proc. 2010. American Institute of Physics (AIP). 1243 p.99-114 q 1243:<99 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/1044750/file/1044760 z [ugent] y LT8-VanderJeugt.pdf | ||
920 | a confcontrib | ||
852 | x WE b WE02 | ||
922 | a UGENT-WE |
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