Breather Modes Research Articles

Nano breathers and molecular dynamics simulations in hydrogen-bonded chains.

Non-linear localization phenomena in biological lattices have attracted a steadily growing interest and their existence has been predicted in a wide range of physical settings. We investigate the non-linear proton dynamics of a hydrogen-bonded chain in a semi-classical limit using the coherent state method combined with a Holstein-Primakoff bosonic representation. We demonstrate that even a weak inherent discreteness in the hydrogen-bonded (HB) chain may drastically modify the dynamics of the non-linear system, leading to instabilities that have no analog in the continuum limit. We suggest a possible localization mechanism of polarization oscillations of protons in a hydrogen-bonded chain through modulational instability analysis. This mechanism arises due to the neighboring proton-proton interaction and coherent tunneling of protons along hydrogen bonds and/or around heavy atoms. We present a detailed analysis of modulational instability, and highlight the role of the interaction strength of neighboring protons in the process of bioenergy localization. We perform molecular dynamics simulations and demonstrate the existence of nanoscale discrete breather (DB) modes in the hydrogen-bonded chain. These highly localized and long-lived non-linear breather modes may play a functional role in targeted energy transfer in biological systems.

On the nonlinear stability of mKdV breathers

Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under a class of small perturbations. Our proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.

Collective dynamics of the electron gas in an anharmonic quantum well

Within a quantum hydrodynamic model and using a variational method, the collective dynamics of the electron gas with the exchange-correlation effect in an anharmonic quantum well are studied both analytically and numerically. The two collective excitation modes, i.e. the dipole mode and the breather mode, are obtained analytically. The frequency shift induced by the exchange correlation, and the periodic collapse revival of the collective dynamics of the electron gas originating from nonlinear coupling between the two modes, are discussed. We found that the anharmonicity and the exchange-correlation effect are coupled, and the frequency shift and the collapse revival of the collective excitations depend strongly on the number of particles, the anharmonicity, and the quantum and exchange-correlation effects.

Klein-Gordon equation approach to nonlinear split-ring resonator based metamaterials: One-dimensional systems

The electrodynamics of a one-dimensional split-ring resonator (SRR) based nonlinear metamaterial is studied. The metamaterial is a one-dimensional periodic array of weakly coupled SRRs, with each SRR represented by a nonlinear resistor-inductor-capacitor (RLC) equivalent resonator circuit. Nonlinearity is introduced into the system by the addition of Kerr-type dielectric medium within the SRRs or by the introduction into the system of certain other nonlinear elements (e.g. diodes). In the continuum limit of the system, variations of the charge stored within the capacitive slits of the SRRs in both time and space are shown to be described along the array by a nonlinear Klein-Gordon equation. Analytical solutions of the nonlinear Klein-Gordon equation for various dark and bright envelope, breather, and pulse soliton solutions are obtained and studied. A discussion is given of the relationship between the Klein-Gordon solutions and the solutions of the nonlinear Schr\odinger equation approximation to the nonlinear Klein-Gordon equation. A comparison is made of the Klein-Gordon solutions with intrinsic localized mode (discrete breather) solutions of the discrete system and their continuum limits. An additional continuum limit differential equation for the breather modes of the system is obtained which is not bound by a weak coupling assumption, and its relation to the Klein-Gordon equation is studied. Analytic forms are given for the effects of dissipation in the system on the various bright and dark envelope, breather, and pulse solitons. Discussions are given of the effects of further than first neighbor couplings in the SRR system.

Quantized Hamilton dynamics describes quantum discrete breathers in a simple way

We study the localization of energy in a nonlinear coupled system, exhibiting so-called breather modes, using quantized Hamilton dynamics (QHD). Already at the lowest order, which is only twice as complex as classical mechanics, this simple semiclassical method incorporates quantum-mechanical effects. The transition between the localized and delocalized regimes is instantaneous in classical mechanics, while it is gradual due to tunneling in both quantum mechanics and QHD. In contrast to classical mechanics, which predicts an abrupt appearance of breathers, quantum mechanics and QHD show an alternation of localized and delocalized behavior in the transient region. QHD includes zero-point energy that is reflected in a shifted energy asymptote for the localized states, providing another improvement on the classical perspective. By detailed analysis of the distribution and transfer of energy within classical mechanics, QHD, and quantum dynamics, we conclude that QHD is an efficient approach that accounts for moderate quantum effects and can be used to identify quantum breathers in large nonlinear systems.

Modeling DNA response to terahertz radiation

Collective response of DNA to terahertz electric fields is studied in a simple pair bond model. We confirm, with some caveats, a previous observation of destabilizing DNA breather modes and explore the parameter dependence of these modes. It is shown that breather modes are eliminated under reasonable physical conditions and that thermal effects are significant.

Structure and Stability of Nonlinear Vibration Mode in Graphene Sheet

Energy localization due to nonlinearity of atomic interactions in a graphene sheet is investigated. In nonlinear lattices, localized vibrational modes called discrete breather (DB) or intrinsic localized mode (ILM) exist. We search the DB in a graphene sheet as aperiodic solution with larger frequency than phonon modes by a procedure combining the Newton-Raphson method and molecular dynamics (MD) method. We obtain long-alive vibrational modes. Some characteristics of the localized mode such as spatial structure, amplitude and vibrational frequency are discussed. Adding to this, we investigate the linear stability of the DB solutions by numerical analysis based on Floquet theory of periodic solutions. Dynamical instability of the vibrational mode is observed by MD simulations, which may lead to change of the structure of DB.

Breathing Modes of Long Josephson Junctions with Phase-Shifts

We consider a spatially inhomogeneous sine-Gordon equation with a time-periodic drive, modeling a microwave driven long Josephson junction with phase-shifts. Under appropriate conditions, Josephson junctions with phase-shifts can have a spatially nonuniform ground state. In recent reports [K. Buckenmaier et al., Phys. Rev. Lett., 98 (2007), 117006], [J. Pfeiffer et al., http://arxiv.org/abs/0903.1046 (2009)], it is experimentally shown that a microwave drive can be used to measure the eigenfrequency of a junction's ground state. Such a microwave spectroscopy is based on the observation that when the frequency of the applied microwave is in the vicinity of the natural frequency of the ground state, the junction can switch to a resistive state, characterized by a nonzero junction voltage. It was conjectured that the process is analogous to the resonant phenomenon in a simple pendulum motion driven by a time-periodic external force. In the case of long junctions with phase-shifts, it would be a resonance between the internal breathing mode of the ground state and the microwave field. Nonetheless, it was also reported that the microwave power needed to switch the junction into a resistive state depends on the magnitude of the eigenfrequency to be measured. Using multiple scale expansions, we show here that an infinitely long Josephson junction with phase-shifts cannot be switched to a resistive state by microwave field with frequency close to the system's eigenfrequency, provided that the applied microwave amplitude is small enough, which confirms the experimental observations. The reason for this inability to switch is that higher harmonics with frequencies in the continuous spectrum are excited, in the form of continuous wave radiation. The breathing mode thus experiences radiative damping. In the absence of driving, the breathing mode decays at rates of at most $\mathcal{O}(t^{-1/4})$ and $\mathcal{O}(t^{-1/2})$ for junctions with a uniform and nonuniform ground state, respectively. The presence of applied microwaves balances the nonlinear damping, creating a stable breather mode oscillation. As a particular example, we consider the so-called $0-\pi-0$ and $0-\kappa$ Josephson junctions, respectively, representing the two cases. We confirm our analytical results numerically. Using our numerical computations, we also show that there is a critical microwave amplitude at which the junction switches to the resistive state. Yet, it appears that the switching process is not necessarily caused by the breathing mode. We show a case where a junction switches to a resistive state due to the continuous wave background becoming modulationally unstable.

Breathers and kinks in a simulated crystal experiment

We develop a simple 1D model for the scattering of an incoming particle hitting the surface of mica crystal, the transmission of energy through the crystal by a localized mode, and the ejection of atom(s) at the incident or distant face. This is the first attempt to model the experiment described by Russell and Eilbeck in 2007 (EPL, <strong>78</strong>, 10004). Although very basic, the model shows many interesting features, for example a complicated energy dependent transition between breather modes and a kink mode, and multiple ejections at both incoming and distant surfaces. In addition, the effect of a heavier surface layer is modelled, which can lead to internal reflections of breathers or kinks at the crystal surface.

Theory of the Optical Conductivity of Spin Liquid States in One-Dimensional Mott Insulators

The low-energy dynamical optical response of dimerized and undimerized spin liquid states in a one-dimensional charge transfer Mott insulator is theoretically studied. An exact analysis is given for the low-energy asymptotic behavior using conformal field theory for the undimerized state. In the dimerized state, the infrared absorption due to the bound state of two solitons, i.e., the breather mode, is predicted with an accurate estimate for its oscillator strength, offering a way to detect experimentally the excited singlet state. The effects of external magnetic fields are also discussed.

Breather mode in the many-electron dynamics of semiconductor quantum wells

We demonstrate the existence of a breather mode in the self-consistent electron dynamics of a semiconductor quantum well. A nonperturbative variational method based on quantum hydrodynamics is used to determine the salient features of the electron breather mode. Numerical simulations of the time-dependent Wigner-Poisson or Hartree equations are shown to be in excellent agreement with our analytical results. For asymmetric quantum wells, a signature of the breather mode is observed in the dipole response, which can be detected by standard optical means.

Ultrafast real-time vibronic coupling dynamics of a breather soliton in trans-polyacetylene with a few-optical-cycle-pulse laser

The dynamics preceding the spatial separation of a charged soliton pair after photoexcitation in trans-polyacetylene was successfully investigated by using ultrafast spectroscopy with a 6.2fs pulse laser. It was directly verified that after photoexcitation, the electron–hole pair relaxes with a breather mode (i.e. multi-quanta vibronic states), as theory predicts, with an electron–hole pair lifetime of 33–50fs. By applying spectrogram analysis to the time trace of the absorbance change, the ultrafast amplitude and frequency modulations of CC and CC stretching modes, induced by breathers and lasting no longer than 100fs, can be observed simultaneously for the first time. The frequency shifts of both modes were in good agreement with a simulation based on the Su–Schrieffer–Heeger model. It was found that the intensities of transition dipoles changed due to breathers, whereas transition energies were dominantly modulated by CC stretching modes as recent theoretical work predicted.

The observation of strong dynamic electron‐phonon couplings due to a breather state in trans ‐polyacetylene

AbstractThe dynamics preceding the separation process of a charged soliton pair after photoexcitation in trans ‐polyacetylene was successfully time‐resolved using ultrafast spectroscopy with a few‐optical‐cycle laser. It was directly verified that after photoexcitation, the electron‐hole pair relaxes with a breather mode as theory predicts with an electron‐hole pair lifetime of 33–50 fs, which is in agreement with the electronic dephasing time. By applying the spectrogram analysis to the time trace of the absorbance change, the ultrafast amplitude and frequency modulations of C–C and C=C stretching modes lasting only shorter than 100 fs induced by breather modes can be observed simultaneously for the first time. The frequency shift of C–C and C=C stretching modes caused by the breather mode are observed in good agreement with the SSH Hamiltonian. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Nonlinear dynamics and resistive transition in intrinsic Josephson junctions

We study the dynamics of phase differences in intrinsic Josephson junctions by using numerical simulations. We especially pay attention to the dynamics of junctions with weak dissipation under an externally applied electric current, where nonlinear character of the system appears most significant. It is found that, when an electric current is applied, the spatially localized oscillations appear. These oscillations are similar to the so-called “breather modes”, which are well known in the dynamics of the sine-Gordon systems. We show that the development of these modes depends on the number of junctions, and the dynamics significantly differs between even and odd numbers. As a result, the critical current of the system also undergoes this even–odd effect.

Mixed-symmetry localized modes and breathers in binary mixtures of Bose-Einstein condensates in optical lattices

We study localized modes in binary mixtures of Bose-Einstein condensates embedded in one-dimensional optical lattices. We report a diversity of asymmetric modes and investigate their dynamics. We concentrate on the cases where one of the components is dominant, i.e. has much larger number of atoms than the other one, and where both components have the numbers of atoms of the same order but different symmetries. In the first case we propose a method of systematic obtaining the modes, considering the "small" component as bifurcating from the continuum spectrum. A generalization of this approach combined with the use of the symmetry of the coupled Gross-Pitaevskii equations allows obtaining breather modes, which are also presented.

Nonlinear dynamics of intrinsic Josephson junctions under an applied current

Nonlinear dynamics of Josephson plasma oscillations in intrinsic Josephson junctions formed in high Tc superconductors is studied based on numerical simulations. The dynamics is described by a differential equation similar to sine-Gordon equation. We discuss within classical dynamics that the eigenmodes, well defined in linearized equation, are modified by the nonlinear effects. Especially we concentrate on the formation of the so-called “breather modes”, which gives rise to the mixing of eigenmodes.

One-dimensional and two-dimensional arrays of nanoholes generated by laser in the semiconfined configuration

We have shown that nanoporosity can be generated on metal surfaces by nanosecond laser-matter interactions in the semiconfined configuration. The scanning electron microscope analysis has shown that nanoholes of ∼25–50nm in diameter, arranged in one-dimensional (1D) and two-dimensional (2D) irregular and regular arrays, have been formed. The interpretation is based on the generation of a dispersive, dissipative system of nonlinear solitary plasma waves (humps) that leave temperature/pressure fingerprints on the metal surface. It has been shown that the 1D irregular array of nanoholes can be interpreted as a result of the irregular string of solitary humps obtained by numerical simulation based on the Benney pd equation with the Gaussian perturbation. The 2D random array of nanoholes can be interpreted as a result of random solitary humps that can be obtained by numerical simulation from the Benney equation with the periodic perturbation. The regular string of nanoholes has been shown to appear as a result of breather modes (bound state of solitons), the numerical simulation of which has been based on the Boussinesq equation. The regular 2D array of nanoholes has been interpreted as fingerprints of breather modes, in agreement with the result of the numerical simulation of Tajiri and Murakami, [J. Math. Phys. 34, 2400 (1993)], based on the Kadomtsev-Petviashvili equation.

Can low‐power electromagnetic radiation disrupt hydrogen bonds in dsDNA?

AbstractMicrowave radiation resonant with the natural phonon frequencies of double‐stranded DNA (dsDNA) is shown to couple strongly to the breather modes of dsDNA under certain conditions. The excitation of the disruptive breather modes is controlled to a great extent by energy dissipation to its aqueous environment. For sufficiently high power—much higher than expected under ambient conditions—the breather solutions become unstable. Our analysis discounts the disruptive effect of low frequency, low power radiation on dsDNA. The authors hope to stimulate experiments via their analysis. The resulting data will dictate the future evolution of their models. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2740–2747, 2006

Confined breather-type excitation in a quinoidal thiophene after sub-5fs pulse excitation

A quinoidal thiophene molecule which is a prototype of the repeated unit of s-trans-cis-polyacetylene was studied by sub-5 fs spectroscopy. A breatherlike mode modulation of both the amplitude and frequency of the C[Double Bond]C stretching was observed for the first time. It generates two sidebands of 2238 and 700 cm(-1) with a separation of 769 cm(-1) corresponding to the modulation frequency. The latter mode is very close to the C-S-C ring deformation, which indicate that this mode mediates coupling between the breather mode and the C(beta)-C(beta) stretching mode. It was also found that the breather-type excitation has a longer lifetime (2-3 ps) than in all-trans-polyacetylene (50 fs) due to its confinement.

Tricritical wedge filling transitions with short-ranged forces

We show that the 3D wedge filling transition in the presence of short-ranged interactionscan be first order or second order depending on the strength of the line tension associatedwith the wedge bottom. This fact implies the existence of a tricritical point characterizedby a short-distance expansion which differs from the usual continuous filling transition. Ouranalysis is based on an effective one-dimensional model for the 3D wedge filling, whicharises from the identification of the breather modes as the only relevant interfacialfluctuations. From such analysis we find a correspondence between continuous 3Dfilling at bulk coexistence and 2D wetting transitions with random-bond disorder.