Propagation and stability of kinks in driven and damped nonlinear Klein-Gordon chains

Büttiker, Μ.; Thomas, H.

doi:10.1103/physreva.37.235

Cited by 32 publications

(18 citation statements)

References 26 publications

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“…͑4.5͒, which describes the motion of the kinks, is basically equivalent to the reaction-diffusion equation, based on which the constant motion of the kinks is concluded. 3 We here present the estimation of the velocity of the kinks in this discretized model.…”

Section: Motion Of the Kinksmentioning

confidence: 99%

“…1 In one-dimensional systems, the critical droplet has the form of a kink-antikink pair, and its physical properties are investigated based on the models such as the kinetic Ising model, the reaction-diffusion equation, and so on. 2,3 In these works, the trigger for nucleation is attributed to the thermal fluctuations, and nucleation of a critical droplet occurs when a large enough fluctuating force to get over the activation energy is applied to the system.…”

Section: Introductionmentioning

confidence: 99%

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Photoinduced nucleation theory in one-dimensional systems

Koshino

Ogawa

1998

Phys. Rev. B

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Photoinduced nucleation of a kink-antikink pair in a one-dimensional system is investigated theoretically, using a model composed of localized two-level electrons and classical lattices, which has two structural phases. We treat the case of the finite-ranged intersite interaction, in order to discuss the crossover from short-ranged to long-ranged interaction. In particular, we focused on the structural change induced by a one-site photoexcitation. When a single site is excited, a local structural change is created around the excited site at first. After the emission of a photon from the excited site, this local structural change ͑a͒ remains local, ͑b͒ grows into a kink-antikink pair, or ͑c͒ disappears and the system returns to the initial phase. Nucleation of a kink-antikink pair occurs only when the intersite interaction is short ranged and moderately strong. The motion of the kinks is also examined. ͓S0163-1829͑98͒03046-X͔

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Section: Motion Of the Kinksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Photoinduced nucleation theory in one-dimensional systems

Koshino

Ogawa

1998

Phys. Rev. B

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“…Obviously, the ansatz in Eq. (26) is very restrictive and we may consider ourselves fortunate that we have been led to the solution y' ' which is the only existing domain-wall front.…”

Section: B Subsonic Relaxation Modesmentioning

confidence: 99%

“…Biittiker and Thomas [26] analyze qualitatively the propagation of subsonic kinks of domain-wall type in a sine-Gordon chain with damping and perform a linear stability analysis for a restrictive form of perturbation and some other restrictive assumptions. Technical complexity of the stability analysis performed by previous authors and other related problems seem to have resulted from the lack of knowledge of velocity values for traveling kinks.…”

Section: Introductionmentioning

confidence: 99%

Propagation and stability of relaxation modes and transition regions in the Landau-Ginzburg model with dissipation

1992

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Exact traveling-wave solutions of the nonlinear Klein-Gordon equation with dissipation are found. The solutions are discussed in the context of propagating nonlinear mechanical waves as well as domain walls (solutions interpolating between two local minima in the potential) and relaxation modes (solutions interpolating between a local minimum and a local maximum in the potential) in systems undergoing second-order phase transitions. Using the Lyapunov method the stability of traveling waves is analyzed.Explicit solutions for domain walls are found and shown to be asymptotically stable. While domain walls propagate with a velocity uniquely determined by the parameters of the model, relaxation modes can move with arbitrary velocities. Among those solutions only one solution propagating with a characteristic velocity u, is asymptotically stable. Other solutions are demonstrated to be Lyapunov unstable.It is found that relative values of the mass density and the damping coeScient are crucial for the dynamic critical behavior, which changes from U, -(T, -T)' for small densities to v. that is temperature independent for large densities.

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“…X sinh (±(IX, I -+ ;k 2 /4)(1 -Jo)) + 2ff (14) with p = ((161X,1 2 _ jXA 2 )/64XA analytical solution of the DSGE is given by (14). cal analog solutions shown in figs.…”

Section: Mmentioning

confidence: 99%

Coherence and Chaos Phenomena in Josephson Oscillators for Superconducting Electronics.

Christiansen¹,

Paramentier²,

Skovgaard³

1989

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REp Oate Jun30, 1986 la REPORT SECURITY CLASSIFICATION lb RESTRICTIVE MARKINGS Unclassified 2a SECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTION /AVAILABILITY OF REPORT Approved for public release; distribution 2b DECLASSIFICATIONIDOWNGRADING SCHEDULE unlimited 4 PERFORMING ORGANIZATION REPORT NUMBER(S) S MONITORING ORGANIZATION REPORT NUMBER(S) R&D 4943-PH-01 6a NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION

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Propagation and stability of kinks in driven and damped nonlinear Klein-Gordon chains

Cited by 32 publications

References 26 publications

Photoinduced nucleation theory in one-dimensional systems

Photoinduced nucleation theory in one-dimensional systems

Propagation and stability of relaxation modes and transition regions in the Landau-Ginzburg model with dissipation

Coherence and Chaos Phenomena in Josephson Oscillators for Superconducting Electronics.

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