Amplitude Of Random Field Research Articles

Dynamics of a self‐trapped quasiparticle in a one‐dimensional molecular lattice with two phonon modes

AbstractIn this work we study numerically the dynamics of a self‐trapped quasiparticle (electron, hole or excitation) in a one‐dimensional molecular chain with two phonon modes, one acoustical and one optical. This model generalizes the model of Davydov solitons and Holstein polaron model: Davydov solitons are formed by a quasiparticle interacting with acoustical phonons, and Holstein polarons are formed due the interaction with optical phonons. Our model describes soliton‐like (large polaron) states in soft quasi‐one‐dimensional systems, such as conducting polymers, alpha‐helical polypeptide macromolecules, DNA etc. For the purpose of modelling self‐trapping of quasiparticles without any influence of chain boundaries, we consider a molecular chain with periodic boundary conditions. Then, to study the dynamics of quasiparticles in such states, we use the adiabatic acceleration method. We show that soliton velocity is an oscillating function of time. These oscillations are caused by the presence of optical vibrations and by the Peierls–Nabarro barrier formed by discrete lattice. We also show that self‐trapping of a quasiparticle takes place at random dynamical lattice potential induced by some random initial conditions for acoustical and optical phonons, provided the random range constant, i.e., the amplitude of random field, is not too big. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

THE EFFECT OF THE INITIAL BED PERTURBTION TO THE SAND BAR FORMATION AND EVOLUTION PROCESS

This paper presents investigations, performed to assess the effect of the initial bed perturbation on the sand bar formation and evolution process. Computations were conducted with two different kind of initial bed perturbations. In the series of first computations, the influence of the amplitude of random field of perturbations was tested. The time to reach an equilibrium state was found to be depending on the amplitude of the initial random bed perturbation. It was found that the larger the amplitude, the shorter the time to reach an equilibrium state. The second test was conducted with the initial bed perturbation in the form of a double row bar. During the first stage of the computation, double row bar type bed configurations were formed, however the modes of bed configurations appeared to be reduced and finally turned into single mode type bed configurations. Since the hydraulic condition of the numerical experiment is single-bar regime, this experiment corresponds to the transformation of bar conditions from the doublemodes to the single-mode during the flood in the natural rivers.

Chaotic versus random ionization.

We use Kepler maps to study the classical ionization of the hydrogen atom driven by electric fields; we compare the ionization rate (IR) due to chaotic motion (constant field amplitude) with the IR due to randomness (random field amplitude). We find that for weak fields the ionization due to random amplitude is more effective, while for strong fields the ionization due to chaos is more effective; so, there is a cross of such ionization curves. A physical explanation of this phenomenon, based on the trajectory behavior, is given.

Exact zero-temperature critical behaviour of the ferromagnet in the uniaxial random field

The zero-temperature critical behaviours of the classical Heisenberg and XY ferromagnets in the uniaxial random field are studied in the arbitrary spatial dimension. Exact results are obtained for the magnetization, transversal to the random field direction, at the Gaussian and bimodal distributions of the random field. For the Gaussian distribution the critical behaviour in strong random fields is independent of the spatial dimension. The transversal magnetization, , where is the distribution width. For the bimodal distribution of the random field, the transversal magnetization obeys the law , where is a critical field, and H is the random field amplitude. The same critical behaviour is expected for related systems, for example random antiferromagnets in the uniform field.

Quantum Ising model in a transverse random field: A density-matrix renormalization-group analysis

The spin-1/2 quantum Ising chain in a transverse random magnetic field is studied by means of the density-matrix renormalization group. The system evolves from an ordered to a paramagnetic state as the amplitude of the random field is increased. The dependence of the magnetization on a uniform magnetic field in the z direction and the spontaneous magnetization as a function of the amplitude of the transverse random magnetic field are determined. The behavior of the spin-spin correlation function both above and at criticality is studied. The scaling laws for magnetization and correlation functions are tested against previous numerical and renormalization-group results.

Metastability and Depinning Threshold in the Random Field Ising Model

AbstractA unified description of the depinning threshold Ec for domain walls in the random field Ising model is given. The coherence length Rc ∼ E of the metastable state is proportional to h−vh, where h is the random field amplitude. For broad walls, the results interpolate between recent findings of Bruinsma and Aeppli (vH = 4/(5 – d)) valid at temperatures T ≪ Th(t) and those of Villain (vH = 2) for Th(t) < T ≪ Tco. Tco is the transition temperature of the pure system and Th(t) ∼ h2(3 – d)/(5 – d)/In t, t denotes the time. For narrow walls vH = 2/(3 – d) is found for T < Th(t), vH = 2 for T > Th(t), Th(t) ∼ h2(2 – d)/(3 – d)/In t and d ≦ 3. For d → 3 an exponential dependence is expected of Rc on h−2. Vacancies are found to be decisive for wall pinning in diluted antiferromagnets in small external fields.

Nonequilibrium "Critical" Exponents in the Random-Field Ising Model

The lower critical dimension for a random-field Ising model cooled from the paramagnetic region is found to be 4, although it is 2 at equilibrium. The coherence length $R$ is proportional to ${H}^{{\ensuremath{-}\ensuremath{\nu}}_{H}}f(t)$, where $H$ is the random-field amplitude and $t$ is the time. At low temperature, ${\ensuremath{\nu}}_{H}=2$ and $f(t)=\mathrm{ln}(\frac{t}{\ensuremath{\tau}})$. At the transition temperature ${T}_{c0}$ of the pure system, ${\ensuremath{\nu}}_{H}\ensuremath{\simeq}1$ and $f(t)=1$. The agreement with experiment is acceptable.