Moments expansion study of the Rabi Hamiltonian

Fessatidis, Vassilios; Mancini, Jay D.; Bowen, Samuel P.

doi:10.1016/s0375-9601(02)00263-3

Cited by 18 publications

(31 citation statements)

References 32 publications

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“…(12) of the paper by Fessatidis et al [14]. We have verified that this discrepancy was not merely a misprint so that their results and conclusions may be incorrect.…”

Section: The Cumulant or -Expansionmentioning

confidence: 54%

“…To this end we resorted to the symbolic operations provided by available computer algebra software like Mathematica and wrote a code that produces the desired moments and connected moments in a reasonably short time. On the other hand, Fessatidis et al [14] only derived the first five moments of the Rabi Hamiltonian, a fact which considerably limited the accuracy of their results as well as the 1 …”

Section: The Cumulant or -Expansionmentioning

confidence: 99%

“…The CMX is quite appealing because it provides approximate values for the ground-state energy of a quantum system directly in terms of a finite number of connected mo-ments. This may be the reason why the CMX and its variants [4,6,7] were applied to several simple physical problems [5,6,[8][9][10][11][12][13][14][15] in spite of its limitations [4,6,7,12,13,[16][17][18]. In order to overcome some of the drawbacks of the CMX several authors have proposed alternative strategies like the generalized moment expansion (GMX) [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…Numerical experiments proved that the RRK converges more smoothly and is therefore more reliable than the CMX when both methods are applied to the simple models so far chosen for testing the latter [26,27]. Some time ago Fessatidis et al [14] applied the CMX and one of its variants, the alternative moments expansion (AMX), to a non-trivial problem with many physical applications: the Rabi Hamiltonian. Because they only considered low order expansions there is no clear indication about the convergence of the moments expansions for that important model.…”

Section: Introductionmentioning

confidence: 99%

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High-order connected moments expansion for the Rabi Hamiltonian

2011

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Ê Ú ¼ ÇØÓ Ö ¾¼½½ ÔØ ¾½ ÇØÓ Ö ¾¼½½ ×ØÖ ØWe analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large-order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.

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“…(12) of the paper by Fessatidis et al [14]. We have verified that this discrepancy was not merely a misprint so that their results and conclusions may be incorrect.…”

Section: The Cumulant or -Expansionmentioning

confidence: 54%

Section: The Cumulant or -Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High-order connected moments expansion for the Rabi Hamiltonian

2011

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“…In an attempt to overcome those difficulties some authors proposed variants of the CMX [8][9][10][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Further analysis of the connected moments expansion

Amore¹,

Fernández²,

Rodríguez³

2011

J. Phys. A: Math. Theor.

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Further analysis of the connected moments expansion 2 Abstract. By means of simple quantum-mechanical models we show that under certain conditions the main assumptions of the connected moments expansion (CMX) are no longer valid. In particular we consider two-level systems, the harmonic oscillator and the pure quartic oscillator. Although derived from such simple models, we think that the results of this investigation may be of utility in future applications of the approach to realistic problems. We show that a straightforward analysis of the CMX exponential parameters may provide a clear indication of the success of the approach.

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Epoxy‐silica nanocomposites: Preparation, experimental characterization, and modeling

Bondioli

Cannillo

Fabbri

et al. 2005

J of Applied Polymer Sci

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ABSTRACT:Silica nanoparticles having different sizes were obtained by the sol-gel process and characterized. The prepared nanoparticles were subsequently used as reinforcing fillers to prepare epoxy-based composites with a silica content ranging from 1 to 5 wt %. SEM analysis and tensile tests carried out on the silica-epoxy nanocomposites indicated the absence of particle aggregation and a reinforcing effect in terms of increased elastic modulus. Mechanical properties were also modeled by using a finite element code able to construct a numerical model from a microstructural image of the material. A more reliable model was prepared by considering the presence of an interphase layer surrounding the particles with intermediate elastic properties between the epoxy and the inclusions and a characteristic size proportional to the particle radius.

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Moments expansion study of the Rabi Hamiltonian

Cited by 18 publications

References 32 publications

High-order connected moments expansion for the Rabi Hamiltonian

High-order connected moments expansion for the Rabi Hamiltonian

Further analysis of the connected moments expansion

Epoxy‐silica nanocomposites: Preparation, experimental characterization, and modeling

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