Quasi-exactly solvable models in nonlinear optics

Álvarez, Gabriel; Finkel, Federico; González‐López, A.; Rodrı́guez, Miguel Á.

doi:10.1088/0305-4470/35/41/305

Cited by 11 publications

(26 citation statements)

References 17 publications

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“…The coefficients B To summarize: the explicit expression for λ (2) (m, K) in the µ 5 approximation is given by eq. (18), with the above mean values N k .…”

Section: So In Calculating λmentioning

confidence: 99%

“…at |K| → ∞, constant T ) of the intercepts λ µ of the two-and three-particle correlation functions. Let us find the asymptotical expression for λ (2) µ within the order µ 5 approximation, see (18). With the account of relevant averages from Appendix A both in the numerator and in the denominator of (18), we derive the result λ (2) as…”

Section: Asymptotics Of Intercepts Of Two-and Three-particle Correlatmentioning

confidence: 99%

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Intercepts of the momentum correlation functions in the $ \mu$ -Bose gas model and their asymptotics

Gavrilik

Rebesh

2011

Eur. Phys. J. A

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The so-called µ-deformed oscillator (or µ-oscillator) introduced by A. Jannussis, though possesses rather exotic properties with respect to other better known deformed oscillator models, also has good potential for diverse physical applications. In this paper, the corresponding µ-Bose gas model based on µ-oscillators is developed. Within this model, the intercepts λ (2) (K) and λ (3) (K) of two-and three-particle momentum correlation functions are calculated with the goal of possible application for modeling the non-Bose type behavior of the intercepts of two-and three-pion correlations, observed in the experiments on relativistic heavy ion collisions. In derivation of intercepts, a fixed order of approximation in the deformation parameter µ is assumed. For the asymptotics of the intercepts λ (2) (K) and λ (3) (K), we derive exact analytical formulas. The results for λ (2) (K) are compared with experimental data, and with earlier known results drawn using other deformed Bose gas models.

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“…The coefficients B To summarize: the explicit expression for λ (2) (m, K) in the µ 5 approximation is given by eq. (18), with the above mean values N k .…”

Section: So In Calculating λmentioning

confidence: 99%

Section: Asymptotics Of Intercepts Of Two-and Three-particle Correlatmentioning

confidence: 99%

Intercepts of the momentum correlation functions in the $ \mu$ -Bose gas model and their asymptotics

Gavrilik

Rebesh

2011

Eur. Phys. J. A

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“…The algebraic form of the Hamiltonian can be obtained by combining (38) and the su (1, 1) realization, given in (30), yields…”

Section: Exactly Solvable Hamiltoniansmentioning

confidence: 99%

“…Consequently, their finite number of eigenvalues and associated eigenfunctions can be obtained in the closed form. These systems are said to be QES systems [24][25][26][27][28][29][30].…”

Section: Qes Hamiltoniansmentioning

confidence: 99%

Algebraic treatments of the problems of the spin-1/2 particles in the one- and two-dimensional geometry: A systematic study

et al. 2005

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We consider solutions of the 2 · 2 matrix Hamiltonians of the physical systems within the context of the su (2) and su (1, 1) Lie algebras. Our technique is relatively simple when compared with those of others and treats those Hamiltonians which can be treated in a unified framework of the Sp (4, R) algebra. The systematic study presented here reproduces a number of earlier results in a natural way as well as leads to a novel finding. Possible generalizations of the method are also suggested.

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“…Multiboson Hamiltonians studied in this paper were often identified as quasi-exactly solvable [29,30] with a close relation to the boson realizations of polynomial algebras [31,32]. Among the applicable physical scenarios, Bose-Einstein condensates and nonlinear optical systems are the most prominent.…”

Section: Introductionmentioning

confidence: 99%

Hiking a generalized Dyck path: A tractable way of calculating multimode boson evolution operators

Brádler

2015

Computer Physics Communications

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A time evolution operator in the interaction picture is given by exponentiating an interaction Hamiltonian H. Important examples of Hamiltonians, often encountered in quantum optics, condensed matter and high energy physics, are of a general form H = r(A † − A), where A is a multimode boson operator and r is the coupling constant. If no simple factorization formula for the evolution operator exists, the calculation of the evolution operator is a notoriously difficult problem. In this case the only available option may be to Taylor expand the operator in r and act on a state of interest ψ. But this brute-force method quickly hits the complexity barrier since the number of evaluated expressions increases exponentially. We relate a combinatorial structure called Dyck paths to the action of a boson word (monomial) and a large class of monomial sums on a quantum state ψ. This allows us to cross the exponential gap and make the problem of a boson unitary operator evaluation computationally tractable by achieving polynomial-time complexity for an extensive family of physically interesting multimode Hamiltonians. We further test our method on a cubic boson Hamiltonian whose Taylor series is known to diverge for all nonzero values of the coupling constant and an analytic continuation via a Padé approximant must be performed.

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Quasi-exactly solvable models in nonlinear optics

Cited by 11 publications

References 17 publications

Intercepts of the momentum correlation functions in the $ \mu$ -Bose gas model and their asymptotics

Intercepts of the momentum correlation functions in the $ \mu$ -Bose gas model and their asymptotics

Algebraic treatments of the problems of the spin-1/2 particles in the one- and two-dimensional geometry: A systematic study

Hiking a generalized Dyck path: A tractable way of calculating multimode boson evolution operators

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