On tunnelling in the cubic potential

Wartak, Marek S.; Krzemiński, S.

doi:10.1088/0305-4470/22/21/006

Cited by 9 publications

(5 citation statements)

References 5 publications

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“…For example, a potential in the form V = 1 2 mω 2 x 2 − 1 3 bx 3 can be used to model decay of metastable states [32], and it also describes the global flow [33]. Further, the tunnelling rate in real time in the semiclassical limit may be found for arbitrary energy levels, while it's ground state agrees well with the result found by the instanton method [34]. It is therefore worth continue the present study in view of such an additive form in the cubic potential.…”

Section: Power Law Potential F (φ) = φ Nsupporting

confidence: 70%

Inflation with scalar-tensor theory of gravity

Saha¹,

Sanyal²,

Sanyal³

2020

Preprint

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The latest released data from Planck in 2018, put up tighter constraints on inflationary parameters. In the present article, the in-built symmetry of the non-minimally coupled scalar-tensor theory of gravity is used to fix the coupling parameter, the functional Brans-Dicke parameter, and the potential of the theory. It is found that all the three different power-law potentials and one exponential, pass these constraints comfortably, and also gracefully exit from inflation.

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Section: Power Law Potential F (φ) = φ Nsupporting

confidence: 70%

Inflation with scalar-tensor theory of gravity

Saha¹,

Sanyal²,

Sanyal³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…For example, a potential in the form V = 1 2 mω 2 x 2 − 1 3 bx 3 can be used to model decay of metastable states [55], and it also describes the global flow [56]. Further, the tunnelling rate in real time in the semiclassical limit may be found for arbitrary energy levels, while its ground state agrees well with the result found by the instanton method [57]. It is therefore worth to continue the present study in view of such an additive form in the cubic potential.…”

Section: Case-2supporting

confidence: 69%

Inflation with Scalar-Tensor Theory of Gravity

Saha

Sanyal

2020

Symmetry

View full text Add to dashboard Cite

The latest released data from Planck in 2018 put up tighter constraints on inflationary parameters. In the present article, the in-built symmetry of the non-minimally coupled scalar-tensor theory of gravity is used to fix the coupling parameter, the functional Brans–Dicke parameter, and the potential of the theory. It is found that all the three different power-law potentials and one exponential pass these constraints comfortably, and also gracefully exit from inflation.

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“…The first two terms in H m are the potential energy and the kinetic energy of the simple harmonic oscillator, respectively, the third term involving q 3 is the potential energy produced by the cubic mechanical nonlinearity, the parameter α is the strength of the mechanical nonlinearity. It is noted that many aspects of a cubic nonlinear oscillator have been studied, such as the behavior of the resonances [37], the quantum mechanical tunnelling [38], the Bender-Wu branch points [39], the real spectrum [40], the Stark effect [41], the periodic motion [42], and the homoclinic bifurcation [43]. Moreover, in the adiabatic limit of ω m πc/L (c is the speed of light in vacuum, L is the length of the cavity), the oscillation of the movable mirror is very slow, thus the scattering of the photons to the other cavity modes can be neglected, so there is only one cavity mode in the cavity [44].…”

Section: Modelmentioning

confidence: 99%

Normal Mode Splitting in a Cavity Optomechanical System with a Cubic Anharmonic Oscillator

2021

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The strong coupling between a macroscopic mechanical oscillator and a cavity field is essential for many quantum phenomena in a cavity optomechanical system. In this work, we discuss the normal mode splitting in a cavity optomechanical system with a cubic nonlinear movable mirror. We study how the mechanical nonlinearity affects the normal-mode splitting behavior of the movable mirror and the output field. We find that the mechanical nonlinearity can increase the peak separation in the spectra of the movable mirror and the output field. We also find that the heights and linewidths of the two peaks are very sensitive to the mechanical nonlinearity.

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On tunnelling in the cubic potential

Cited by 9 publications

References 5 publications

Inflation with scalar-tensor theory of gravity

Inflation with scalar-tensor theory of gravity

Inflation with Scalar-Tensor Theory of Gravity

Normal Mode Splitting in a Cavity Optomechanical System with a Cubic Anharmonic Oscillator

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