On Stability of a Nonlinear Pendulum

Kengne, E.

doi:10.1023/b:nono.0000007821.77162.59

Cited by 1 publication

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“…The semidiscrete approximation means that the continuum approximation is only introduced for the envelope while a completely discrete description is used for the carrier wave, the wave-vector of which can range over the entire Brillouin zone. We follow Taniuti and Yajima and other [36][37][38][39] and seek a first-order uniform expansion by using both the method of multiple scales and the semi-discrete approximation method in the form…”

Section: Derivation Of the Modified Cubic-quintic Cglementioning

confidence: 99%

Dynamics of Modulated Wave Trains in a Discrete Nonlinear-Dispersive Dissipative Bi-inductance Transmission Line

Kengne

Bame

2005

Phys. Scr.

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The Dicke model describes an ensemble of N identical two-level atoms (qubits) coupled to a single quantized mode of a bosonic field. The fermion Dicke model should be obtained by changing the atomic pseudo-spin operators by a linear combination of Fermi operators. The generalized fermion Dicke model is defined introducing different coupling constants between the single mode of the bosonic field and the reservoir, g 1 and g 2 for rotating and counter-rotating terms, respectively. In the limit N → ∞, the thermodynamic of the fermion Dicke model can be analyzed using the path integral approach with the functional method. The system exhibits a second-order phase transition from normal to superradiance at some critical temperature with the presence of a condensate. We evaluate the critical transition temperature and present the spectrum of the collective bosonic excitations for the general case (g 1 = 0 and g 2 = 0). There is a quantum critical behavior when the coupling constants g 1 and g 2 satisfy g 1 + g 2 = (ω 0 ) 1 2 , where ω 0 is the frequency of the mode of the field and is the energy gap between the energy eigenstates of the qubits. Two particular situations are analyzed. First, we present the spectrum of the collective bosonic excitations, in the case g 1 = 0 and g 2 = 0, recovering the well-known results. Second, the case g 1 = 0 and g 2 = 0 is studied. In this last case, it is possible to have a superradiant phase when only virtual processes are introduced in the interaction Hamiltonian. Here also appears a quantum phase transition at the critical coupling g 2 = (ω 0 ) 1 2 , and for larger values for the critical coupling, the system enter in this superradiant phase with a Goldstone mode.

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Section: Derivation Of the Modified Cubic-quintic Cglementioning

confidence: 99%