Connection between the<i>su</i>(3) algebraic and configuration spaces: bending modes of linear molecules

Estévez-Fregoso, M. M.; Lemus, R.

doi:10.1080/00268976.2018.1487599

Cited by 14 publications

(12 citation statements)

References 48 publications

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“…In this section we shall follow the general approach presented in [26][27][28] where given a U(ν+1) unitary group space a procedure to establish a correspondence between operators in configuration and algebraic spacesis given. We start by establishing the mapping…”

Section: Minimization Approachmentioning

confidence: 99%

“…This is a non trivial result due to the fact that the receipt existing in second quantization to construct an observable in Fock space from configuration space does not work anymore in models where the s boson is involved. In order to reinforce the resulting connection between algebraic and configuration spaces we proceed to set up the connection from a formal point of view using a general minimization approach previously presented [26][27][28]. In addition the connection with the Holsteim-Primakoff transformation is given.The search for this mappingleads to identify three bases, corresponding to the energy, coordinate and momentum representations without any reference to an specific potential.…”

Section: Introductionmentioning

confidence: 99%

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A simple approach to solve the time independent Schröedinger equation for 1D systems

Lemus

2019

J. Phys. Commun.

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A simple algebraic approach based on the well known angular momentum SU(2) algebra is presented to describe 1D systems for arbitrary potentials. The approach is based on the dimension increase of the 1D harmonic oscillator space through the addition of a scalar boson, keeping constant the total number of bosons. In this new space the realization of the coordinate and momentum correspond to components of the angular momentum algebra, which in turn define the coordinate and momentum representation bases. This remarkable result allows the Hamiltonian matrix representationto be expressed in terms of a diagonal matrix characterizing the potential we are considering. The solutions are obtained as an expansion of harmonic oscillator functions by purely algebraic means. As an example of our approach the Morse and asymmetric double Morse potentials are considered.

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Section: Minimization Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A simple approach to solve the time independent Schröedinger equation for 1D systems

Lemus

2019

J. Phys. Commun.

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“…We will provide a detailed numerical study in a bosonic algebraic quantum model based on the u(3) algebra. This model has been originally introduced to describe bending modes of linear polyatomic molecules [54][55][56][57]. Later it has been successfully used to investigate purely theoretical concepts, such as quantum monodromy and quantum critical effects [58][59][60].…”

Section: Introductionmentioning

confidence: 99%

Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator

Novotný¹,

Stránský²

2023

Preprint

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A detailed numerical study reveals that the asymptotic values of the standard deviation-to-mean ratio of the out-of-time-ordered correlator can be successfully used as a measure of the quantum chaoticity of the system. We employ a finite-size fully connected quantum system with two degrees of freedom, namely the algebraic u(3) model, and demonstrate a clear correspondence between the relative oscillations of the correlators and the ratio of the chaotic part of the volume of phase space in the classical limit of the system. We also show how the relative oscillations scale with the system size and conjecture that the scaling exponent can also serve as a robust chaos indicator.

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“…In this scheme, it is through the transformation brackets connecting the different bases that makes it possible to obtain the representation of the Hamiltonian matrix in a simple form in terms of diagonal matrices, a feature characterizing a DVR approach. This approach has been called the unitary group approach (UGA), and it has been presented in detail for nD potentials [43][44][45][46][47][48]. A natural alternative to this approach consists in projecting the harmonic oscillator basis to a subspace of finite dimension.…”

Section: Introductionmentioning

confidence: 99%

Algebraic DVR Approaches Applied to Piecewise Potentials: Symmetry and Degeneracy

2022

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Algebraic discrete variable representation (DVR) methods that have been recently proposed are applied to describe 1D and 2D piecewise potentials. First, it is shown that it is possible to use a DVR approach to describe 1D square well potentials testing the wave functions with exact results. Thereafter, Morse and Pöschl-Teller (PT) potentials are described with multistep piecewise potentials in order to explore the sensibility of the potential to reproduce the transition from a pure square well energy pattern to an anharmonic energy spectrum. Once the properties of the different algebraic DVR approaches are identified, the 2D square potential as a function of the potential depth is studied. We show that this system displays natural degeneracy, accidental degeneracy and systematic accidental degeneracy. The latter appears only for a confined potential, where the symmetry group is identified and irreducible representations are constructed. One particle confined in a rectangular well potential with commensurate sides is also analyzed. It is proved that the systematic accidental degeneracy appearing in this system is removed for finite potential depth.

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Connection between thesu(3) algebraic and configuration spaces: bending modes of linear molecules

Cited by 14 publications

References 48 publications

A simple approach to solve the time independent Schröedinger equation for 1D systems

A simple approach to solve the time independent Schröedinger equation for 1D systems

Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator

Algebraic DVR Approaches Applied to Piecewise Potentials: Symmetry and Degeneracy

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