Hamiltonian dynamics of the double sine-Gordon kink

Willis, C. R.; El‐Batanouny, M.; Burdick, S.; Boesch, R.; Sodano, P.

doi:10.1103/physrevb.35.3496

Cited by 31 publications

(10 citation statements)

References 18 publications

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“…The parameter R(t) in [7a] and [7b] is now to be promoted to a dynamical variable R(t) in order to proceed with the development of a Hamiltonian formalism in which it becomes a canonical coordinate (8). The time derivative of (7) is…”

Section: Discussionmentioning

confidence: 99%

“…In this note, we shall treat, in terms of the Hamiltonian dynamic theory without the corrective terms of the first order, i.e., the radiation correction (8,9), the internal oscillations of three kinks in the double SGE with n = 3, and show that there is an exact stationary solution for the equation. The frequencies and the ratio between the frequencies of the internal oscillations are calculated.…”

Section: Introductionmentioning

confidence: 99%

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Hamiltonian dynamics of the general double sine-Gordon kinks

Zhang¹,

Huang²,

Hu³

1992

Can. J. Phys.

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We present a complete Hamiltonian treatment of the internal oscillations of a solitary wave solution in the general double sine-Gordon system with n = 3. The exact stationary solution for the system is found. The frequencies and the ratio between the frequencies of the internal oscillations are shown, and agree with numerical results.Nous presentons un traitement hamiltonien complet des oscillations internes d'une solution en onde solitaire dans le systkme gknkral double sine-Gordon avec n = 3. La solution stationnaire exacte pour le systkme a ete trouvee. Les frkquences et le rapport entre les frequences des oscillations internes ont ttC dCterminCes et sont en accord avec les rksultats numtriques.[Traduit par la rkdaction]Can.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hamiltonian dynamics of the general double sine-Gordon kinks

Zhang¹,

Huang²,

Hu³

1992

Can. J. Phys.

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“…However, it is possible to find a topologically stable 2π-kink solution for a range of parameter η, i.e., η > −1/4. For η ≥ 0, the 2π-kink solution can be constructed by a superposition of π-kink solutions when η → ∞, i.e., φ π (x) = 2 tan −1 exp(x) [9,10,11,12], and expressed as…”

Section: Double Sine-gordon Equation For Long Sfs Junctionmentioning

confidence: 99%

“…With a dynamical π-π kink pair, these two energies compete in time, resulting in a new type of dynamics. The π-π kink pair exhibits an internal oscillation related to the relative oscillations of two π kinks around the equilibrium separation [9,10,11,12]. It has been shown that the frequency of the π-π kink oscillation is below the lower edge of the continuum phonon band [10,13].…”

Section: Double Sine-gordon Equation For Long Sfs Junctionmentioning

confidence: 99%

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Mobile fluxon qubits in a long superconductor-ferromagnet-superconductor Josephson junction

Nishida

Fujii

Hatakenaka

2008

J. Phys.: Conf. Ser.

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Abstract. We propose a new type of mobile qubit that utilizes a bound pair of half fluxons in a long superconductor-ferromagnet-superconductor (SFS) Josephson junction. The qubit states are composed of the lowest two levels of the quantized nonlinear internal oscillation of the bound pair. The energy levels are estimated by the numerical quantization based on a collective coordinate method. The qubit operation scheme is discussed, showing an estimate of the interaction strength between a bound pair and a microcircuit. IntroductionA quantum computer is an innovative computer based on the principles of quantum mechanics. The fundamental unit of a quantum computer is a qubit, which is a quantum-mechanical superposition state of a two-state system. As regards solid-state qubits, the precise mechanism providing control of the interaction between an arbitrary pair of qubits remains unresolved. To overcome this problem, we proposed a mobile qubit [1, 2] using breather excitation in a conventional long Josephson junction. However, a breather is fragile with respect to background perturbations. In particular, a breather can disappear through energy loss with dissipation, because it is topologically equivalent to a vacuum. This feature makes it difficult to prepare the initial |0 state needed for quantum computing.Here we propose a new type of mobile qubit that utilizes a bound pair of half fluxons in a long superconductor-ferromagnet-superconductor (SFS) Josephson junction. Transitions between usual (0) and π junction states have been demonstrated in SFS junctions as a function of temperature [3] and barrier thickness [4]. The π junction state is characterized by a ground state at a phase difference of π. In the vicinity of the crossover between the 0 and π states, the second harmonic term in the current-phase relation is expected to dominate [5,6,7,8]. This term would modify the electrodynamics of long SFS junctions, and the propagation of fluxons would be governed by the double sine-Gordon equation (DSGE) instead of the sine-Gordon equation that governs usual long junctions. Since a 2π kink in the double sine-Gordon system splits into two π kinks (half fluxons) and forms a bound pair with nonlinear internal oscillation modes (called π-π kink oscillation), the bound-half-fluxon pair in long SFS junctions can carry

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Soliton excitations in the classical one‐dimensional antiferromagnet in a staggered field

Cassino

Pires

1992

Physica Status Solidi (b)

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Soliton excitations in an easy-plane classical one-dimensional antiferromagnet in the presence of a staggered magnetic field transverse to the chain direction are studied. The out-of-plane soliton solution is found to have an instability similar to the one found before by Magyari-Thomas-Kumar for the easy-plane ferromagnetic chain in an external magnetic field. Also studied are the soliton stability and the phase shift of spin waves in the presence of the soliton.Soliton-Anregungen in einem klassischen eindimensionalen Antiferromagneten mit leichter Ebene in einem gezackten Magnetfeld senkrecht zur Kettenrichtung werden untersucht. Die nichtebene SolitonLosung weist eine Instabilitat auf, ahnlich der von Magyar-Thomas-Kumar fur eine ferromagnetische Kette mit leichter Ebene im Magnetfeld gefundene. Weiterhin werden die Solitonenstabilitat und die Phasenverschiebung der Spinwellen in Anwensenheit des Soliton betrachtet.

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Hamiltonian dynamics of the double sine-Gordon kink

Cited by 31 publications

References 18 publications

Hamiltonian dynamics of the general double sine-Gordon kinks

Hamiltonian dynamics of the general double sine-Gordon kinks

Mobile fluxon qubits in a long superconductor-ferromagnet-superconductor Josephson junction

Soliton excitations in the classical one‐dimensional antiferromagnet in a staggered field

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