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D. Hennig

Publications and source records attributed to D. Hennig.

At least 19 recordsLinked to original sources
arXiv2023

Existence, stability and spatio-temporal dynamics of time-quasiperiodic solutions on a finite background in discrete nonlinear Schr\"odinger models

In the present work we explore the potential of models of the discrete nonlinear Schr\"odinger (DNLS) type to support spatially localized and temporally quasiperiodic solutions on top of a finite background. Such solutions are rigorously shown to exist in the vicinity of the anti-continuum, vanishing coupling limit of the model. We then use numerical continuation to illustrate their persistence for finite coupling, as well as to explore their spectral stability. We obtain an intricate bifurcation diagram showing a progression of such solutions from simpler ones bearing single- and two-site excitations to more complex, multi-site ones with a direct connection of the branches of the self-focusing and self-defocusing nonlinear regime. We further probe the variation of the solutions obtained towards the limit of vanishing frequency for both signs of the nonlinearity. Our analysis is complemented by exploring the dynamics of the solutions via direct numerical simulations.

nlin.PS↗
arXiv2015

Cooperative surmounting of bottlenecks

The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers. In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case. The second part deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated high-dimensional phase space are the source for the directed long-range transport.

nlin.AO↗
arXiv2013

Nonlinear response of a linear chain to weak driving

We study the escape of a chain of coupled units over the barrier of a metastable potential. It is demonstrated that a very weak external driving field with suitably chosen frequency suffices to accomplish speedy escape. The latter requires the passage through a transition state the formation of which is triggered by permanent feeding of energy from a phonon background into humps of localised energy and elastic interaction of the arising breather solutions. In fact, cooperativity between the units of the chain entailing coordinated energy transfer is shown to be crucial for enhancing the rate of escape in an extremely effective and low-energy cost way where the effect of entropic localisation and breather coalescence conspire.

nlin.PS↗
arXiv2011

From collective periodic running states to completely chaotic synchronised states in coupled particle dynamics

We consider the damped and driven dynamics of two interacting particles evolving in a symmetric and spatially periodic potential. The latter is exerted to a time-periodic modulation of its inclination. Our interest is twofold: Firstly we deal with the issue of chaotic motion in the higher-dimensional phase space. To this end a homoclinic Melnikov analysis is utilised assuring the presence of transverse homoclinic orbits and homoclinic bifurcations for weak coupling allowing also for the emergence of hyperchaos. In contrast, we also prove that the time evolution of the two coupled particles attains a completely synchronised (chaotic) state for strong enough coupling between them. The resulting `freezing of dimensionality' rules out the occurrence of hyperchaos. Secondly we address coherent collective particle transport provided by regular periodic motion. A subharmonic Melnikov analysis is utilised to investigate persistence of periodic orbits. For directed particle transport mediated by rotating periodic motion we present exact results regarding the collective character of the running solutions entailing the emergence of a current. We show that coordinated energy exchange between the particles takes place in such a manner that they are enabled to overcome - one particle followed by the other - consecutive barriers of the periodic potential resulting in collective directed motion.

cond-mat.stat-mech↗
arXiv2010

Directed current in the Holstein system

We propose a mechanism to rectify charge transport in the semiclassical Holstein model. It is shown that localised initial conditions, associated with a polaron solution, in conjunction with a nonreversion symmetric static electron on-site potential constitute minimal prerequisites for the emergence of a directed current in the underlying periodic lattice system. In particular, we demonstrate that for unbiased spatially localised initial conditions, violation of parity prevents the existence of pairs of counter-propagating trajectories, thus allowing for a directed current despite the time-reversibility of the equations of motion. Occurrence of long-range coherent charge transport is demonstrated.

cond-mat.other↗
arXiv2010

Emergence of continual directed flow in Hamiltonian systems

We propose a minimal model for the emergence of a directed flow in autonomous Hamiltonian systems. It is shown that internal breaking of the spatio-temporal symmetries, via localised initial conditions, that are unbiased with respect to the transporting degree of freedom, and transient chaos conspire to form the physical mechanism for the occurrence of a current. Most importantly, after passage through the transient chaos, trajectories perform solely regular transporting motion so that the resulting current is of continual ballistic nature. This has to be distinguished from the features of transport reported previously for driven Hamiltonian systems with mixed phase space where transport is determined by intermittent behaviour exhibiting power-law decay statistics of the duration of regular ballistic periods.

cond-mat.stat-mech↗
arXiv2009

Directed transport of two interacting particles in a washboard potential

We study the conservative and deterministic dynamics of two nonlinearly interacting particles evolving in a one-dimensional spatially periodic washboard potential. A weak tilt of the washboard potential is applied biasing one direction for particle transport. However, the tilt vanishes asymptotically in the direction of bias. Moreover, the total energy content is not enough for both particles to be able to escape simultaneously from an initial potential well; to achieve transport the coupled particles need to interact cooperatively. For low coupling strength the two particles remain trapped inside the starting potential well permanently. For increased coupling strength there exists a regime in which one of the particles transfers the majority of its energy to the other one, as a consequence of which the latter escapes from the potential well and the bond between them breaks. Finally, for suitably large couplings, coordinated energy exchange between the particles allows them to achieve escapes -- one particle followed by the other -- from consecutive potential wells resulting in directed collective motion. The key mechanism of transport rectification is based on the asymptotically vanishing tilt causing a symmetry breaking of the non-chaotic fraction of the dynamics in the mixed phase space. That is, after a chaotic transient, only at one of the boundaries of the chaotic layer do resonance islands appear. The settling of trajectories in the ballistic channels associated with transporting islands provides long-range directed transport dynamics of the escaping dimer.

cond-mat.stat-mech↗
arXiv2009

Delayed feedback induced directed inertia particle transport in a washboard potential

We consider motion of an underdamped Brownian particle in a washboard potential that is subjected to an unbiased time-periodic external field. While in the limiting deterministic system in dependence of the strength and phase of the external field directed net motion can exist, for a finite temperature the net motion averages to zero. Strikingly, with the application of an additional time-delayed feedback term directed particle motion can be accomplished persisting up to fairly high levels of the thermal noise. In detail, there exist values of the feedback strength and delay time for which the feedback term performs oscillations that are phase locked to the time-periodic external field. This yields an effective biasing rocking force promoting periods of forward and backward motion of distinct duration, and thus directed motion. In terms of phase space dynamics we demonstrate that with applied feedback desymmetrization of coexisting attractors takes place leaving the ones supporting either positive or negative velocities as the only surviving ones. Moreover, we found parameter ranges for which in the presence of thermal noise the directed transport is enhanced compared to the noise-less case.

cond-mat.stat-mech↗
arXiv2008

Resonance-like phenomena of the mobility of a chain of nonlinear coupled oscillators in a two-dimensional periodic potential

We study the Langevin dynamics of a two-dimensional discrete oscillator chain absorbed on a periodic substrate and subjected to an external localized point force. Going beyond the commonly used harmonic bead-spring model, we consider a nonlinear Morse interaction between the next-nearest-neighbors. We focus interest on the activation of directed motion instigated by thermal fluctuations and the localized point force. In this context the local transition states are identified and the corresponding activation energies are calculated. As a novel feature it is found that the transport of the chain in point force direction is determined by stepwise escapes of a single unit or segments of the chain due to the existence of multiple locally stable attractors. The non-vanishing net current of the chain is quantitatively assessed by the value of the mobility of the center of mass. It turns out that the latter as a function of the ratio of the competing length scales of the system, that is the period of the substrate potential and the equilibrium distance between two chain units, shows a resonance behavior. More precisely there exist a set of optimal parameter values maximizing the mobility. Interestingly, the phenomenon of negative resistance is found, i.e. the mobility possesses a minimum at a finite value of the strength of the thermal fluctuations for a given overcritical external driving force.

nlin.AO↗
arXiv2008

Surmounting collectively oscillating bottlenecks

We study the collective escape dynamics of a chain of coupled, weakly damped nonlinear oscillators from a metastable state over a barrier when driven by a thermal heat bath in combination with a weak, globally acting periodic perturbation. Optimal parameter choices are identified that lead to a drastic enhancement of escape rates as compared to a pure noise-assisted situation. We elucidate the speed-up of escape in the driven Langevin dynamics by showing that the time-periodic external field in combination with the thermal fluctuations triggers an instability mechanism of the stationary homogeneous lattice state of the system. Perturbations of the latter provided by incoherent thermal fluctuations grow because of a parametric resonance, leading to the formation of spatially localized modes (LMs). Remarkably, the LMs persist in spite of continuously impacting thermal noise. The average escape time assumes a distinct minimum by either tuning the coupling strength and/or the driving frequency. This weak ac-driven assisted escape in turn implies a giant speed of the activation rate of such thermally driven coupled nonlinear oscillator chains.

cond-mat.stat-mech↗
arXiv2008

Slowly rocking symmetric, spatially periodic Hamiltonians: The role of escape and the emergence of giant transient directed transport

The nonintegrable Hamiltonian dynamics of particles placed in a symmetric, spatially periodic potential and subjected to a periodically varying field is explored. Such systems can exhibit a rich diversity of unusual transport features. In particular, depending on the setting of the initial phase of the drive, the possibility of a giant transient directed transport in a symmetric, space-periodic potential when driven with an adiabatically varying field arises. Here, we study the escape scenario and corresponding mean escape times of particles from a trapping region with the subsequent generation of a transient directed flow of an ensemble of particles. It is shown that for adiabatically slow inclination modulations the unidirectional flow proceeds over giant distances. The direction of escape and, hence, of the flow is entirely governed whether the periodic force, modulating the inclination of the potential, starts out initially positive or negative. In the phase space, this transient directed flow is associated with a long-lasting motion taking place within ballistic channels contained in the non-uniform chaotic layer. We demonstrate that for adiabatic modulations all escaping particles move ballistically into the same direction, leading to a giant directed current.

nlin.CD↗
arXiv2007

Self-organized escape of oscillator chains in nonlinear potentials

We present the noise free escape of a chain of linearly interacting units from a metastable state over a cubic on-site potential barrier. The underlying dynamics is conservative and purely deterministic. The mutual interplay between nonlinearity and harmonic interactions causes an initially uniform lattice state to become unstable, leading to an energy redistribution with strong localization. As a result a spontaneously emerging localized mode grows into a critical nucleus. By surpassing this transition state, the nonlinear chain manages a self-organized, deterministic barrier crossing. Most strikingly, these noise-free, collective nonlinear escape events proceed generally by far faster than transitions assisted by thermal noise when the ratio between the average energy supplied per unit in the chain and the potential barrier energy assumes small values.

cond-mat.stat-mech↗
arXiv2007

Quantum Diffusion in Polaron Model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers

We numerically investigate quantum diffusion of an electron in a model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers with fluctuation of the parameters due to the impact of colored noise. The randomness is introduced by fluctuations of distance between two consecutive bases along the stacked base pairs. We demonstrate that in the model the decay time of the correlation can control the spread of the electronic wavepacket. Furthermore it is shown that in a motional narrowing regime the averaging over fluctuation causes ballistic propagation of the wavepacket, and in the adiabatic regime the electronic states are affected by localization.

cond-mat.soft↗
arXiv2004

Modeling the thermal evolution of enzyme-created bubbles in DNA

The formation of bubbles in nucleic acids (NAs) are fundamental in many biological processes such as DNA replication, recombination, telomeres formation, nucleotide excision repair, as well as RNA transcription and splicing. These precesses are carried out by assembled complexes with enzymes that separate selected regions of NAs. Within the frame of a nonlinear dynamics approach we model the structure of the DNA duplex by a nonlinear network of coupled oscillators. We show that in fact from certain local structural distortions there originate oscillating localized patterns, that is radial and torsional breathers, which are associated with localized H-bond deformations, being reminiscent of the replication bubble. We further study the temperature dependence of these oscillating bubbles. To this aim the underlying nonlinear oscillator network of the DNA duplex is brought in contact with a heat bath using the Nos$\rm{\acute{e}}$-Hoover-method. Special attention is paid to the stability of the oscillating bubbles under the imposed thermal perturbations. It is demonstrated that the radial and torsional breathers, sustain the impact of thermal perturbations even at temperatures as high as room temperature. Generally, for nonzero temperature the H-bond breathers move coherently along the double chain whereas at T=0 standing radial and torsional breathers result.

q-bio.BM↗
arXiv2004

Moving breathers in bent DNA with realistic parameters

Recent papers have considered moving breathers (MBs) in DNA models including long range interaction due to the dipole moments of the hydrogen bonds. We have recalculated the value of the charge transfer when hydrogen bonds stretch using quantum chemical methods which takes into account the whole nucleoside pairs. We explore the consequences of this value on the properties of MBs, including the range of frequencies for which they exist and their effective masses. They are able to travel through bending points with fairly large curvatures provided that their kinetic energy is larger than a minimum energy which depends on the curvature. These energies and the corresponding velocities are also calculated in function of the curvature.

nlin.PS↗
arXiv2003

Effect of base-pair inhomogeneities on charge transport along DNA mediated by twist and radial polarons

Some recent results for a three--dimensional, semi--classical, tight--binding model for DNA show that there are two types of polarons, named radial and twist polarons, that can transport charge along the DNA molecule. However, the existence of two types of base pairs in real DNA, makes it crucial to find out if charge transport also exist in DNA chains with different base pairs. In this paper we address this problem in its simple case, an homogeneous chain except for a single different base pair, what we call a base-pair inhomogeneity, and its effect on charge transport. Radial polarons experience either reflection or trapping. However, twist polarons are good candidates for charge transport along real DNA. This transport is also very robust with respect to weak parametric and diagonal disorder.

nlin.PS↗
arXiv2003

Nonlinear charge transport in DNA mediated by twist modes

Recent works on localized charge transport along DNA, based on a three--dimensional, tight--binding model (Eur. Phys. J. B 30:211, 2002; Phys. D 180:256, 2003), suggest that charge transport is mediated by the coupling of the radial and electron variables. However, these works are based on a linear approximation of the distances among nucleotides, which forces for consistency the assumption that the parameter $α$, that describes the coupling between the transfer integral and the distance between nucleotides is fairly small. In the present letter we perform an improvement of the model which allows larger values of $α$, showing that there exist two very different regimes. Particulary, for large $α$, the conclusions of the previous works are reversed and charge transport can be produced only by the coupling with the twisting modes.

nlin.PS↗