Temperature effects in a nonlinear model of monolayer Scheibe aggregates

Bang, Ole; Christiansen, Peter Leth; If, F.; Rasmussen, Kim Ø.; Gaididei, Yuri

doi:10.1103/physreve.49.4627

Cited by 99 publications

(100 citation statements)

References 33 publications

Supporting

Mentioning

100

Contrasting

Order By: Relevance

“…Another example of NLS equation with noise is given in [1] and [2], where it describes energy transfer in monolayer molecular aggregates, and where the noise stands for thermal fluctuations. As explained in [2], this noise may be multiplicative if it describes process where excitation is not being created or destroyed and in this case the noise appears in the equation as a linear potential.…”

Section: Introductionmentioning

confidence: 99%

Finite-time blow-up in the additive supercritical stochastic nonlinear Schrödinger equation: the real noise case

Bouard¹,

Debussche²

2002

The Legacy of the Inverse Scattering Transform in Applied Mathematics

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Finite-time blow-up in the additive supercritical stochastic nonlinear Schrödinger equation: the real noise case

Bouard¹,

Debussche²

2002

The Legacy of the Inverse Scattering Transform in Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…This is to be expected, since those discrete systems are effectively discretizations of SNLS with noise of spatial correlation on length scale comparable to the mesh spacing of the discretization. The full 2D Stochastic NLS equation with spatially uncorrelated noise has been simulated by Bang, Christiansen, If, Rasmussen and Gaididei in [1], and the 1D quintic case of the Stochastic NLS equation by DeBussche and Di Menza in [9]. In each case it is observed that spatially uncorrelated noise above a certain threshold level prevents wave collapse.…”

Section: 7mentioning

confidence: 99%

“…An exciton-phonon system with phase noise and damping. Such thin films can be modeled as an exciton-phonon system with noise and damping acting on the internal modes as described by Bang, Christiansen, If, Rasmussen and Gaididei in [1], which adds damping to the purely quantum mechanical modeling of Bartnick and Tuszyński [2]:…”

Section: Introductionmentioning

confidence: 99%

Wave energy self-trapping by self-focusing in large molecular structures: A damped stochastic discrete nonlinear Schrödinger equation model

LeMesurier

Whitehead

2007

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

Abstract. Wave self-focusing in molecular systems subject to thermal effects, such as thin molecular films and long biomolecules, can be modeled by stochastic versions of the Discrete Self-Trapping equation of Eilbeck, Lomdahl and Scott, and this can be approximated by continuum limits in the form of stochastic nonlinear Schrödinger equations.Previous studies directed at the SNLS approximations have indicated that the selffocusing of wave energy to highly localized states can be inhibited by phase noise (modeling thermal effects) and can be restored by phase damping (modeling heat radiation).Here it is shown that the continuum limit is probably ill-posed in the presence of spatially uncorrelated noise, at least with little or no damping, so that discrete models need to be addressed directly. Also, as has been noted by other authors, omission of damping produces highly unphysical results.Numerical results are presented here for the first time for the discrete models including the highly nonlinear damping term, and new numerical methods are introduced for this purpose.Previous conjectures are in general confirmed, and the damping is shown to strongly stabilize the highly localized states of the discrete models. It appears that the previously noted inhibition of nonlinear wave phenomena by noise is an artifact of modeling that includes the effects of heat, but not of heat loss.Foreword. This is a revised version of the material presented in several talks, given at the

show abstract

“…14 Since the 2D DNLS equation also has been used to describe exciton dynamics in models for so-called Scheibe aggregates in molecular thin films, 15,16 the discrete breathers may be of importance also in this context.…”

Section: Introductionmentioning

confidence: 99%

Breatherlike excitations in discrete lattices with noise and nonlinear damping

Christiansen¹,

Gaididei²,

Johansson

et al. 1997

Phys. Rev. B

View full text Add to dashboard Cite

We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrödinger equation in the regime of high nonlinearity, where temperature effects are included as multiplicative white noise and nonlinear damping. Numerical analysis shows that the lifetime of the breather is always finite and, in a large parameter regime, inversely proportional to the noise variance for fixed damping and nonlinearity. We also find that the decay rate of the breather decreases with increasing nonlinearity and with increasing damping. Using a collective-coordinate approximation, we show how the qualitative features of the numerical results can be analytically understood. Finally, in the dimer case we show that the multiplicative noise can be transformed into additive noise, and an exact stationary solution to the Fokker-Planck equation is obtained. From this solution, the dimer system is found to exhibit a noise ͑temperature͒ induced phase transition. ͓S0163-1829͑97͒07409-2͔

show abstract

Temperature effects in a nonlinear model of monolayer Scheibe aggregates

Cited by 99 publications

References 33 publications

Finite-time blow-up in the additive supercritical stochastic nonlinear Schrödinger equation: the real noise case

Finite-time blow-up in the additive supercritical stochastic nonlinear Schrödinger equation: the real noise case

Wave energy self-trapping by self-focusing in large molecular structures: A damped stochastic discrete nonlinear Schrödinger equation model

Breatherlike excitations in discrete lattices with noise and nonlinear damping

Contact Info

Product

Resources

About