Path integral in position-deformed Heisenberg algebra with maximal length uncertainty

Lawson, Latévi M.; Osei, Prince K.; Sodoga, Komi; Soglohu, Fred

doi:10.1016/j.aop.2023.169389

Cited by 3 publications

(2 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the EUP leads to a bounded dense domain of the infinite-dimensional Hilbert space  due to the maximum length constraint [30]. Consequently, instead of studying the entire Hilbert space…”

Section: Null Potential [V(x) = 0]mentioning

confidence: 99%

“…Similarly to the free case, we can compute ΔX and ΔP along with the validation of EUP as illustrated in figure 4. Furthermore, by plotting the effective Hamiltonian as a function of K for different values of α (see figure5), we observe that equation(30) displays local minima at specific values of K. Inserting these values into the soliton ansatz yields profiles of the bright soliton depicted in figure 5(a).…”

mentioning

confidence: 93%

See 1 more Smart Citation

One dimensional Bose–Einstein condensate under the effect of the extended uncertainty principle

Benhadjira,

Benkrane,

Bentouila

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

In this study, an analytical investigation was conducted to assess the effects of the extended uncertainty principle (EUP) on a Bose-Einstein condensate (BEC) described by the deformed one-dimensional Gross-Pitaevskii equation (GPE). Analytical solutions were derived for null potential, while, we used variational and numerical methods for harmonic oscillator potential. Subsequently, we analyzed the probability density, position, and momentum uncertainties as functions of the deformation parameter α

show abstract

Section: Null Potential [V(x) = 0]mentioning

confidence: 99%

mentioning

confidence: 93%

One dimensional Bose–Einstein condensate under the effect of the extended uncertainty principle

Benhadjira,

Benkrane,

Bentouila

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

Study of Bose–Einstein condensate in the presence of the extended uncertainty principle: infinite potential well

Benkrane,

Benhadjira

2024

Phys. Scr.

View full text Add to dashboard Cite

This paper investigates the inﬂuence of the extended uncertainty principle (EUP) and non-linearity on Bose-Einstein condensate (BEC) conﬁned within an inﬁnite potential well, described by a deformed one-dimensional Gross-Pitaevskii equation (GPE). Exact solutions are derived, and the impact of the EUP and the parameter of interaction g is explored through solution, position and momentum uncertainties plots. The study reveals signiﬁcant changes in the probability density and energy spectra, depending on the deformation and non-linearity parameters.

show abstract

Position-dependent mass from noncommutativity and its statistical descriptions

Lawson,

Amouzouvi,

Sodoga

et al. 2024

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

A set of position-dependent noncommutative algebra in two dimension (2D) that describes the space near the Planck scale had been introduced [J. Phys. A: Math. Theor. 53 (2020) 115303]. This algebra predicted the existence of maximal length of graviton measurable at low energy. From this algebra, we deduce in the present paper, a new noncommutative algebra that is compatible with the deformed algebra proposed by Costa Filho et al. [Phys. Rev. A 84 (2011) 050102] to describe the Position-Dependent Mass (PDM) system in 1D. To this aim, we derive from the momentum operators, the Schrödinger-like equation which describes PDM system in null quantum well potential. The spectrum of this system is asymetrically deformed and exhibits different behaviours from the one obtained by Costa Filho et al. Thus, we observe that by increasing the PDM, the energy decreases and this decrease is more pronounced as the quantum number increases. Finally, we evaluate the thermodynamic quantities within the canonical ensemble and we show that these results are consistent with the ones recently obtained by Bensalem and Bouaziz [Phys. A Stat. Mech. Appl. 523 (2019) 583–592].

show abstract

Path integral in position-deformed Heisenberg algebra with maximal length uncertainty

Cited by 3 publications

References 24 publications

One dimensional Bose–Einstein condensate under the effect of the extended uncertainty principle

One dimensional Bose–Einstein condensate under the effect of the extended uncertainty principle

Study of Bose–Einstein condensate in the presence of the extended uncertainty principle: infinite potential well

Position-dependent mass from noncommutativity and its statistical descriptions

Contact Info

Product

Resources

About