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Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models. (arXiv:1707.01122v1 [hep-th] CROSS LISTED)
来源于:arXiv
A Hamiltonian formulation of generic many-body systems with balanced loss and
gain is presented. It is shown that a Hamiltonian formulation is possible only
if the balancing of loss and gain terms occur in a pairwise fashion. It is also
shown that with the choice of a suitable co-ordinate, the Hamiltonian can
always be reformulated in the background of a pseudo- Euclidean metric. If the
equations of motion of some of the well-known many-body systems like Calogero
models are generalized to include balanced loss and gain, it appears that the
same may not be amenable to a Hamiltonian formulation. A few exactly solvable
systems with balanced loss and gain, along with a set of integrals of motion is
constructed. The examples include a coupled chain of nonlinear oscillators and
a many-particle Calogero-type model with four-body inverse square plus two-body
pair-wise harmonic interactions. For the case of nonlinear oscillators, stable
solution exists even if the dissipation parameter has unbo 查看全文>>