Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation

Pereira, Lucas Carvalho; Nascimento, Valter Aragão do

doi:10.3390/ma13102236

Cited by 3 publications

(3 citation statements)

References 42 publications

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“…We can obtain the evolution of classical observables, and also determine the spreading ∆(x 2 ), ∆(p 2 ) of the initial wave function (11), just as in [17]. Actually, this can be extended to more general interactions driven by different trapping potentials.…”

Section: General Variance ρ Effective Potentialmentioning

confidence: 99%

Effective Semiclassical Evolution of Bose Einstein Condensates

Hernandez Hernandez

2024

East Eur. J. Phys.

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In this work we analyze the effective evolution of a one dimensional Bose-Einstein Condensate (BEC) within a semiclassical description of quantum systems based on expectation values of quantum dispersions and physical observables, known as momentous quantum mechanics. We show that the most prominent features and physical parameters of the system can be determined from the dynamics of the corresponding semiclassical system, consisting of an extended phase space including original classical observables and quantum dispersions, and we also show that particle trajectories for expectation values of observables are a particular characteristic in this framework. We also demonstrate that interactions with several potentials can be implemented in an intuitive way.

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Section: General Variance ρ Effective Potentialmentioning

confidence: 99%

Effective Semiclassical Evolution of Bose Einstein Condensates

Hernandez Hernandez

2024

East Eur. J. Phys.

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“…In the absence of contact interactions and DDI, infrared-divergent components are exactly eliminated in the Hartree-Fock-Bogoliubov (HFB) shift of the single particle excitation energy [34]. In addition to dipolar and coulomb interactions, another long-range potential called PT interactions between atoms has been studied [35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Collective excitation of quantum droplet with different ranges of the interaction of Pöschl-Teller potential

Banerjee,

Majumder

2024

Phys. Scr.

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In this article, we studied quantum droplet with the Pöschl-Teller (PT) interaction potential between the Bose atoms. The Gross–Pitaevskii (GP) equation governs the system. The range and strength of the PT interaction can be adjusted. First, we studied the quantum droplet’s density variation for various PT interaction parameters by the imaginary-time split-step Crank-Nicolson (CN) method. We then used the Bogoliubov theory to examine the collective excitation spectra. We observed that sharp roton forms and phonon modes are missing during long-range interactions. There is a gap at the zero momentum zone due to the long-range PT interaction, which increases with the range and strength of the interaction.

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“…We will use EGP, within the scope of mean field theory, to describe the BEC of magnons. In order to solve the GPE, we will use two distinct approaches: an analytical approach (variational method) [ 13 , 14 ] and a numerical approach (split-step Crank-Nicolson method) [ 14 , 15 ].…”

Section: Introductionmentioning

confidence: 99%

Stability of Spin-Wave Solitons in Bose-Einstein Condensates of Magnons: A Possible Application in Ferromagnetic Films

Pereira

Nascimento

2022

Materials

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In this paper, we theoretically investigate the stability of spin-wave solitons in Bose-Einstein condensates of repulsive magnons, confined by an inhomogeneous external magnetic field described by a Gaussian well. For this purpose, we use the quasi-one-dimensional Gross-Pitaevskii equation to describe the behavior of the condensate. In order to solve the Gross-Pitaevskii equation, we used two different approaches: one analytical (variational method) and another numerical (split-step Crank-Nicolson method). The stability of the solutions and the validation of the numerical results were confirmed, respectively, through the anti-VK criterion and the virial theorem. Furthermore, the simulations described the behavior of physical quantities of interest such as chemical potential, energy per magnon and central density as a function of the nonlinearity of the model (magnon-magnon interactions). The theoretical results provide subsidies for a better understanding of the nonlinear phenomena related to the Bose-Einstein condensates of magnons in ferromagnetic films.

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Dynamics of Bose–Einstein Condensates Subject to the Pöschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation

Cited by 3 publications

References 42 publications

Effective Semiclassical Evolution of Bose Einstein Condensates

Effective Semiclassical Evolution of Bose Einstein Condensates

Collective excitation of quantum droplet with different ranges of the interaction of Pöschl-Teller potential

Stability of Spin-Wave Solitons in Bose-Einstein Condensates of Magnons: A Possible Application in Ferromagnetic Films

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