We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliar operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two previous levels. This happens, for example, for systems having the energy spectrum given by Fibonacci sequence. Moreover, the algebraic structure depends on tw...

We show that quantum optical systems preserving the total number of excitations admit a simple classification of possible resonant transitions (including effective), which can be classified by analizying the free Hamiltonian and the corresponding integrals of motion. Quantum systems not preserving the total number of excitations do not admit such a simple classification, so that an explicit for...

A closed SO(5) algebraic structure in the the mean-field form of the Hamiltonian the pure p-wave superconductivity is found that can help to diagonalized by making use of the Bogoliubov rotation instead of the Balian-Werthamer approach. we point out that the eigenstate is nothing but SO(5)-coherent state with fermionic realization. By applying the approach to the Hamiltonian with dipole interac...

We study the eeect of position and momentumprojectionsin the numericalintegrationof constrained Hamiltonian systems. We show theoretically and numerically that momentum projections are better and more eecient. They lead to smaller error growth rates and aaect the energy error much less, as they deene a canonical transformation. As a concrete example, the planar pendulum is treated. Let the Hami...

This paper concerns constrained dynamic optimization problems governed by delayed differentialalgebraic systems. Dynamic constraints in such systems, which are particularly important for engineering applications, are described by interconnected delay-differential inclusions and algebraic equations. We pursue a two-hold goal: to study variational stability of such control systems with respect to...

The carbon dioxide Raman spectrum is simulated within an algebraic approach based on curvilinear coordinates in a local representation. The two main advantages of the present algebraic approach are a possible connection with configuration space and the correct description of systems with either local or normal mode character. The system Hamiltonian and polarizability tensor are expanded in term...

Recently defect production was investigated during non-unitary dynamics due to non-Hermitian Hamiltonian. By ramping up the coupling linearly in time through an exceptional point, defects are produced much same way as approaching a Hermitian critical point. A generalized Kibble--Zurek scaling accounted for ensuing of density terms speed drive and corresponding exponents. Here we extend this set...