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Search Results: 1 - 10 of 198188 matches for " N. Debergh "
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On the relation between polynomial deformations of sl(2,R) and quasi-exactly solvability
N. Debergh
Physics , 2000, DOI: 10.1088/0305-4470/33/40/308
Abstract: A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the finite-dimensional representations and differential realizations of such deformations is illustrated on the sextic oscillator as well as on the second harmonic generation.
On the exact solutions of the Lipkin-Meshkov-Glick model
N. Debergh,Fl. Stancu
Physics , 2001, DOI: 10.1088/0305-4470/34/15/305
Abstract: We present the many-particle Hamiltonian model of Lipkin, Meshkov and Glick in the context of deformed polynomial algebras and show that its exact solutions can be easily and naturally obtained within this formalism. The Hamiltonian matrix of each $j$ multiplet can be split into two submatrices associated to two distinct irreps of the deformed algebra. Their invariant subspaces correspond to even and odd numbers of particle-hole excitations.
On realizations of nonlinear Lie algebras by differential operators
J. Beckers,Y. Brihaye,N. Debergh
Physics , 1998, DOI: 10.1088/0305-4470/32/15/008
Abstract: We study realizations of polynomial deformations of the sl(2,R)- Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear, quadratic and cubic cases are explicitly visited but the method works for arbitrary degrees in the polynomial functions. Multi-boson Hamiltonians are studied in the context of these ``nonlinear'' Lie algebras and some examples dealing with quantum optics are pointed out.
On oscillatorlike Hamiltonians and squeezing
J. Beckers,N. Debergh,F. H. Szafraniec
Physics , 2000,
Abstract: Generalizing a recent proposal leading to one-parameter families of Hamiltonians and to new sets of squeezed states, we construct larger classes of physically admissible Hamiltonians permitting new developments in squeezing. Coherence is also discussed.
Realizations of the Lie superalgebra q(2) and applications
N. Debergh,J. Van der Jeugt
Physics , 2001, DOI: 10.1088/0305-4470/34/39/311
Abstract: The Lie superalgebra q(2) and its class of irreducible representations V_p of dimension 2p (p being a positive integer) are considered. The action of the q(2) generators on a basis of V_p is given explicitly, and from here two realizations of q(2) are determined. The q(2) generators are realized as differential operators in one variable x, and the basis vectors of V_p as 2-arrays of polynomials in x. Following such realizations, it is observed that the Hamiltonian of certain physical models can be written in terms of the q(2) generators. In particular, the models given here as an example are the sphaleron model, the Moszkowski model and the Jaynes-Cummings model. For each of these, it is shown how the q(2) realization of the Hamiltonian is helpful in determining the spectrum.
On oscillatorlike developments and further improvements in squeezing
J. Beckers,N. Debergh,F. H. Szafraniec
Physics , 1999, DOI: 10.1103/PhysRevA.65.042112
Abstract: A recent proposal of new sets of squeezed states is seen as a particular case of a general context admitting realistic physical Hamiltonians. Such improvements reveal themselves helpful in the study of associated squeezing effects. Coherence is also considered.
On a Lie algebraic approach of quasi-exactly solvable potentials with two known eigenstates
Y. Brihaye,N. Debergh,J. Ndimubandi
Physics , 2001, DOI: 10.1142/S0217732301004479
Abstract: We compare two recent approaches of quasi-exactly solvable Schr\" odinger equations, the first one being related to finite-dimensional representations of $sl(2,R)$ while the second one is based on supersymmetric developments. Our results are then illustrated on the Razavy potential, the sextic oscillator and a scalar field model.
Quasi exactly solvable quantum lattice solitons
Y. Brihaye,N. Debergh,A. Nininahazwe
Physics , 2004, DOI: 10.1142/S0217751X06025316
Abstract: We extend the exactly solvable Hamiltonian describing $f$ quantum oscillators considered recently by J. Dorignac et al. by means of a new interaction which we choose as quasi exactly solvable. The properties of the spectrum of this new Hamiltonian are studied as function of the new coupling constant. This Hamiltonian as well as the original one are also related to adequate Lie structures.
Parasupersymmetric Quantum Mechanics with Generalized Deformed Parafermions
J. Beckers,N. Debergh,C. Quesne
Mathematics , 1996,
Abstract: A superposition of bosons and generalized deformed parafermions corresponding to an arbitrary paraquantization order $p$ is considered to provide deformations of parasupersymmetric quantum mechanics. New families of parasupersymmetric Hamiltonians are constructed in connection with two examples of su(2) nonlinear deformations such as introduced by Polychronakos and Ro\v cek.
On supersymmetries in nonrelativistic quantum mechanics
J. Beckers,N. Debergh,A. G. Nikitin
Mathematics , 2005, DOI: 10.1063/1.529954
Abstract: One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed out. The study of even supersymmetries is particularly enlightened through the already known symmetries of the corresponding Schr\"odinger equation. Three tables collect the even, odd, and total supersymmetries as well as the invariance (super)algebras.
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