Soliton Lifetime Research Articles

Thermal stability of solitons in protein [formula omitted]-helices

Protein α-helices provide an ordered biological environment that is conducive to soliton-assisted energy transport. The nonlinear interaction between amide I excitons and phonon deformations induced in the hydrogen-bonded lattice of peptide groups leads to self-trapping of the amide I energy, thereby creating a localized quasiparticle (soliton) that persists at zero temperature. The presence of thermal noise, however, could destabilize the protein soliton and dissipate its energy within a finite lifetime. In this work, we have computationally solved the system of stochastic differential equations that govern the quantum dynamics of protein solitons at physiological temperature, T=310 K, for either a single isolated α-helix spine of hydrogen bonded peptide groups or the full protein α-helix comprised of three parallel α-helix spines. The simulated stochastic dynamics revealed that although the thermal noise is detrimental for the single isolated α-helix spine, the cooperative action of three amide I exciton quanta in the full protein α-helix ensures soliton lifetime of over 30 ps, during which the amide I energy could be transported along the entire extent of an 18-nm-long α-helix. Thus, macromolecular protein complexes, which are built up of protein α-helices could harness soliton-assisted energy transport at physiological temperature. Because the hydrolysis of a single adenosine triphosphate molecule is able to initiate three amide I exciton quanta, it is feasible that multiquantal protein solitons subserve a variety of specialized physiological functions in living systems.

The nonlinear Dirac equation in Bose–Einstein condensates: II. Relativistic soliton stability analysis

The nonlinear Dirac equation for Bose–Einstein condensates (BECs) in honeycomb optical lattices gives rise to relativistic multi-component bright and dark soliton solutions. Using the relativistic linear stability equations, the relativistic generalization of the Boguliubov-de Gennes equations, we compute soliton lifetimes against quantum fluctuations and classify the different excitation types. For a BEC of atoms, we find that our soliton solutions are stable on time scales relevant to experiments. Excitations in the bulk region far from the core of a soliton and bound states in the core are classified as either spin waves or as a Nambu–Goldstone mode. Thus, solitons are topologically distinct pseudospin- domain walls between polarized regions of . Numerical analysis in the presence of a harmonic trap potential reveals a discrete spectrum reflecting the number of bright soliton peaks or dark soliton notches in the condensate background. For each quantized mode the chemical potential versus nonlinearity exhibits two distinct power law regimes corresponding to the free-particle (weakly nonlinear) and soliton (strongly nonlinear) limits.

Dynamics of the soliton-sound interaction in the quasi-one-dimensional Munoz-Mateo–Delgado equation

In this paper we study the effects of the transverse confinement strength on the dark solitons dynamics in quasi-one-dimensional Bose–Einstein condensates (BECs). The theoretical model is based on the Muoz-Mateo & Delgado (MMD) equation that describes cigar-shaped BECs with repulsive interatomic interactions. Since the MMD equation presents a nonpolynomial form, the soliton-sound recombination may not display the same pattern presented in the cubic model. We perform numerical simulations for harmonic and anharmonic (Gaussian) external potentials to compare both cases. All results via the MMD equation are in perfect agreement with the 3D simulations. Also, we noticed some differences between MMD and cubic models and changes in the soliton lifetime due to the values of the transverse confinement.

Constructing a class of topological solitons in magnetohydrodynamics.

We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, nt and np, respectively. The special case of nt=1 and np=1 corresponds to the Kamchatnov-Hopf soliton, a magnetic field configuration everywhere tangent to the fibers of a Hopf fibration so that the field lines are circular, linked exactly once, and form the surfaces of nested tori. We show that for nt∈Z+ and np=1, these configurations represent stable, localized solutions to the magnetohydrodynamic equations for an ideal incompressible fluid with infinite conductivity. Furthermore, we extend our stability analysis by considering a plasma with finite conductivity, and we estimate the soliton lifetime in such a medium as a function of the toroidal winding number.

THREE-BODY INTERACTIONS BEYOND THE GROSS–PITAEVSKII EQUATION AND MODULATIONAL INSTABILITY OF BOSE–EINSTEIN CONDENSATES

Beyond the mean-field theory, a new model of the Gross–Pitaevskii equation (GPE) that describes the dynamics of Bose–Einstein condensates (BECs) is derived using an appropriate phase-imprint on the old wavefunction. This modified version of the GPE in addition to the two-body interactions term, also takes into account effects of the three-body interactions. The three-body interactions consist of a quintic term and the delayed nonlinear response of the condensate system term. Then, the modulational instability (MI) of the new GPE confined in an attractive harmonic potential is investigated. The analytical study shows that the three-body interactions destabilize more the condensate system while the external potential alleviates the instability. Numerical results confirm the theoretical predictions. Further numerical investigations of the behavior of solitons reveal that the three-body interactions enhance the appearance of solitons, increase the number of solitons generated and deeply change the lifetime of solitons. Moreover, the external potential delays the appearance of solitons. Besides, a new initial condition is introduced which enables to increase the number of solitons created and deeply affects the trail of chains of solitons generated. Moreover, the MI of a condensate without the external potential, and in a repulsive potential is also investigated.

Effect of hydrogen bond anharmonicity on supersonic discrete Davydov soliton propagation

We consider the propagation of energy along a protein chain in the Davydov approximation. We study the fully discrete Davydov equations including the anharmonic corrections in the hydrogen bond potential and find approximate variational solutions. We show analytically that for the harmonic interaction of the hydrogen bonds of the Davydov model the waves travel with velocities less than half the sound velocity for the relevant biological parameters. We find, for weak nonlinearity of the hydrogen bonds, two branches of soliton solutions. The first one gives a new type of strongly stable cusped discrete supersonic soliton. The second branch captures the main component of a more complicated breather solution compared to the one studied by Gaididei et al. and reproduces the Davydov soliton of the continuum limit. These results show the possibility of coherent protein chain deformation due to the anharmonicity of the hydrogen bond interactions. These supersonic waves are shown to provide a viable mechanism for energy transport in spite of the temperature influence in the soliton lifetime.

Fluctuating and dissipative dynamics of dark solitons in quasicondensates

The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark-soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long-lived soliton trajectories within each ensemble of numerical realizations [S. P. Cockburn et al., Phys. Rev. Lett. 104, 174101 (2010)]. Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based upon the dissipative Gross-Pitaevskii model (with the same ab initio damping). Probing the regime for which 0.8 ${k}_{B}T<\ensuremath{\mu}<1.6$ ${k}_{B}T$, we find average soliton lifetimes to scale with temperature as $\ensuremath{\tau}\ensuremath{\sim}{T}^{\ensuremath{-}4}$, in agreement with predictions previously made for the low-temperature regime ${k}_{B}T\ensuremath{\ll}\ensuremath{\mu}$. The model is also shown to capture the experimentally relevant decrease in the visibility of an oscillating soliton due to the presence of background fluctuations.

Динамика плоской солитонной волны сжатия в наноленте графена

It is demonstrated that planar solitary waves of the <br /> longitudinal compression can propagate in a graphene <br /> sheet with supersonic velocities from a narrow range. In <br /> an infinite sheet, such a solitary wave does not change its <br /> shape, and interaction between two solitary waves is elastic <br /> with no energy loss for radiation. However, in a graphene <br /> nanoribbon the solitary waves are affected by the nanoribbon <br /> edges which stipulate the phonon emission. As a result, the <br /> soliton lifetime becomes finite, and it is roughly equal to the <br /> double width of the nanoribbon.

Quantum Decay of Dark Solitons

Unless protected by the exact integrability, solitons are subject to dissipative forces, originating from a thermally fluctuating background. At low enough temperatures T background fluctuations should be considered as being quantized which enables us to calculate finite lifetime of the solitons τ∼T(-4). We also find that the coherent nature of the quantum fluctuations leads to long-range interactions between the solitons mediated by the superradiation. Our results are of relevance to current experiments with ultracold atoms, while the approach may be extended to solitons in other media.

Nonlinear Schrödinger equation with spatiotemporal perturbations

We investigate the dynamics of solitons of the cubic nonlinear Schrödinger equation (NLSE) with the following perturbations: nonparametric spatiotemporal driving of the form f(x,t)=a exp[iK(t)x], damping, and a linear term which serves to stabilize the driven soliton. Using the time evolution of norm, momentum and energy, or, alternatively, a Lagrangian approach, we develop a collective-coordinate-theory which yields a set of ordinary differential equations (ODEs) for our four collective coordinates. These ODEs are solved analytically and numerically for the case of a constant, spatially periodic force f(x). The soliton position exhibits oscillations around a mean trajectory with constant velocity. This means that the soliton performs, on the average, a unidirectional motion although the spatial average of the force vanishes. The amplitude of the oscillations is much smaller than the period of f(x). In order to find out for which regions the above solutions are stable, we calculate the time evolution of the soliton momentum P(t) and the soliton velocity V(t): This is a parameter representation of a curve P(V) which is visited by the soliton while time evolves. Our conjecture is that the soliton becomes unstable, if this curve has a branch with negative slope. This conjecture is fully confirmed by our simulations for the perturbed NLSE. Moreover, this curve also yields a good estimate for the soliton lifetime: the soliton lives longer, the shorter the branch with negative slope is.

Subdiffractive solitons of Bose-Einstein condensates in time-dependent optical lattices

We study Bose-Einstein condensates trapped in periodically shaken shallow optical lattices, and demonstrate the existence of subdiffractive solitons, analogous to those encountered in periodically blinking lattices [K. Staliunas, R. Herrero, and G. J. de Valcarcel, Phys. Rev. E 73, 065603(R) (2006)]. We also show that solitons in periodically shaken optical lattices radiate weakly into the near-to-resonance modes. For typical experimental conditions, however, the soliton lifetime turns out to be much longer than the typical lifetime of the condensate, therefore the subdiffractive solitons are expected to be observable in periodically shaken shallow optical lattices.

Spatiotemporal intermittency and scaling laws in the coupled sine circle map lattice

We study spatiotemporal intermittency (STI) in a system of coupled sine circle maps. The phase diagram of the system shows parameter regimes with STI of both the directed percolation (DP) and non-DP class. STI with synchronized laminar behavior belongs to the DP class. The regimes of non-DP behavior show spatial intermittency (SI), where the temporal behavior of both the laminar and burst regions is regular, and the distribution of laminar lengths scales as a power law. The regular temporal behavior for the bursts seen in these regimes of spatial intermittency can be periodic or quasiperiodic, but the laminar length distributions scale with the same power law, which is distinct from the DP case. STI with traveling wave laminar states also appears in the phase diagram. Solitonlike structures appear in this regime. These are responsible for crossovers with accompanying nonuniversal exponents. The soliton lifetime distributions show power-law scaling in regimes of long average soliton lifetimes, but peak at characteristic scales with a power-law tail in regimes of short average soliton lifetimes. The signatures of each type of intermittent behavior can be found in the dynamical characterizers of the system viz. the eigenvalues of the stability matrix. We discuss the implications of our results for behavior seen in other systems which exhibit spatiotemporal intermittency.

Parametric Driving of Dark Solitons in Atomic Bose-Einstein Condensates

A dark soliton oscillating in an elongated harmonically confined atomic Bose-Einstein condensate continuously exchanges energy with the sound field. Periodic optical paddles are employed to controllably enhance the sound density and transfer energy to the soliton, analogous to parametric driving. In the absence of damping, the amplitude of the soliton oscillations can be dramatically reduced, whereas with damping, a driven soliton equilibrates as a stable soliton with lower energy, thereby extending the soliton lifetime up to the lifetime of the condensate.

Soliton analysis of the electro-optical response of blue bronze

In recent measurements on the charge-density-wave (CDW) conductor blue bronze (K 0.3MoO 3), the electro-transmittance and electro-reflectance spectra were searched for intragap states that could be associated with solitons created by injection of electrons into the CDW at the current contacts [Eur. Phys. J. B16 (2000), 295; Eur. Phys. J. B35 (2003) 233]. In this work, we adapt the model of soliton absorption in dimerized polyacetylene to the blue bronze results, to obtain the (order of magnitude) estimate that current induced solitons occur on less than ∼10% of the conducting chains. We discuss the implications of these results on models of soliton lifetimes and motion of CDW phase dislocations.

Influence of solitons on the transition to spatiotemporal chaos in coupled map lattices.

We study the transition from laminar to chaotic behavior in deterministic chaotic coupled map lattices and in an extension of the stochastic Domany-Kinzel cellular automaton [E. Domany and W. Kinzel, Phys. Rev. Lett. 53, 311 (1984)]. For the deterministic coupled map lattices, we find evidence that "solitons" can change the nature of the transition: for short soliton lifetimes it is of second order, while for longer but finite lifetimes, it is more reminiscent of a first-order transition. In the second-order regime, the deterministic model behaves like directed percolation with infinitely many absorbing states; we present evidence obtained from the study of bulk properties and the spreading of chaotic seeds in a laminar background. To study the influence of the solitons more specifically, we introduce a soliton including variant of the stochastic Domany-Kinzel cellular automaton. Similar to the deterministic model, we find a transition from second- to first-order behavior due to the solitons, both in a mean-field analysis and in a numerical study of the statistical properties of this stochastic model. Our study illustrates that under the appropriate mapping some deterministic chaotic systems behave like stochastic models; but it is hard to know precisely which degrees of freedom need to be included in such description.

Atomic “needles” and “bullets” in Bose-Einstein condensate and the formation of nanosized structures

The Gross-Pitaevski equation modified through the inclusion of a term accounting for the nonlocality of interatomic interaction was used to demonstrate the occurrence of extremely narrow two-and three-dimensional solitonic states in atomic Bose-Einstein condensates. The estimates of the sizes of these states gave a value of ∼ 20–60 nm (atomic “needles” and “bullets”) for lithium atoms. The soliton lifetimes caused by two-and three-particle collisions were estimated. The limiting possibilities of the formation of nanostructures using needles and bullets were compared with the possibilities of other nanolithographic methods.

The lifetime of the soliton in the improved Davydov model at the biological temperature 300 K for protein molecules

We study the effects of quantum fluctuations and thermal perturbations on the lifetime of the soliton in the improved Davydov model proposed by us with two-quanta and with an added interaction. By using quantum perturbation theory, we compute the soliton lifetime for a wide ranges of parameter values relevant for protein molecules. The lifetime of the new soliton at the biological temperature 300 K is of the order of 10(-10) second or tau/tau (0) greater than or equal to 500 for parameters appropriate to alpha -helical protein molecules. This shows clearly that the new soliton in the improved model is a viable mechanism for the bio-energy transport in the alpha -helix region of proteins.

Relaxation of Bloch oscillations of a magnetic soliton in a nonuniform magnetic field

The influence of damping on the Bloch oscillations arising in the motion of a magnetic soliton in an easy-axis one-dimensional ferromagnet in the presence of a small magnetic field gradient is investigated. The most interesting case, that of solitons with low frequencies and low velocities, is considered. In this case there are two soliton damping regimes. When the magnetic field gradient is greater than a critical value set by the damping, the soliton lifetime is considerably greater than the period of the Bloch oscillations. However, together with these oscillations there arises a translational motion of the soliton due to dissipation. If the magnetic field gradient is smaller than the critical value, then the Bloch oscillations vanish, and the soliton undergoes only translational motion.

Decay and slowing down of the multiquanta Davydov-like solitons in molecular chains.

Dynamics and the stability of the multivibron solitons in molecular chains have been examined by means of the perturbation method based upon the inverse scattering transform. We demonstrate that due to the coupling with phonons the soliton radiates energy which causes its slowing down and gradual decay of its amplitude. It was shown that the soliton lifetime depends strongly on temperature and the values of the basic physical parameters of the system. On the basis of these results the possible role of the multivibron solitons in the intramolecular vibrational energy transfer has been critically assessed.

Complexity in biological systems

We describe some aspects of complex behaviour that can be present in biopolymers. The study is based on a nonlinear thermodynamics of non-equilibrium, dissipative systems. Such complexity consists of a Frohlich- Bose- Einstein-like condensation and propagation of Schrodinger- Davydov soliton-wave-like excitations, which are of relevance in Bioenergetics. The question of the soliton lifetime under physiological conditions is discussed, and comparison made with experiments performed in the case of an organic molecular polymer. Further complex behaviour apparently present in ultrasonic medical imaging, dubbed the Frohlich- Cherenkov effect, is briefly discussed.