H. Haken

A theoretical model of phase transitions in human hand movements

Earlier experimental studies by one of us (Kelso, 1981a, 1984) have shown that abrupt phase transitions occur in human hand movements under the influence of scalar changes in cycling frequency. Beyond a critical frequency the originally prepared out-of-phase, antisymmetric mode is replaced by a symmetrical, in-phase mode involving simultaneous activation of homologous muscle groups. Qualitavely, these phase transitions are analogous to gait shifts in animal locomotion as well as phenomena common to other physical and biological systems in which new “modes” or spatiotemporal patterns arise when the system is parametrically scaled beyond its equilibrium state (Haken, 1983). In this paper a theoretical model, using concepts central to the interdisciplinary field of synergetics and nonlinear oscillator theory, is developed, which reproduces (among other features) the dramatic change in coordinative pattern observed between the hands.

A stochastic theory of phase transitions in human hand movement

The order parameter equation for the relative phase of correlated hand movements, derived in a previous paper by Haken et al. (1985), is extended to a time-dependent stochastic differential equation. Its solutions are determined close to stationary points and for the transition region. Remarkably good agreement between this theory and recent experiments done by Kelso and Scholz (1985) is found, and new predictions are offered.

Information and Self-Organization

The process of “self-organization” takes place in open and complex systems that acquire spatio-temporal or functional structures without specific ordering instructions from the outside. [...]

Analogy between higher instabilities in fluids and lasers

Abstract The Lorenz model of instabilities in fluids is shown to be identical with that of the single mode laser and applicable to undamped laser spikes. Further instabilities connected with small-band excitations are also discussed.

An exactly solvable model for coherent and incoherent exciton motion

We treat the motion of a Frenkel exciton using a Hamiltonian which comprises a completely coherent part and a fluctuating part which describes both fluctuations of the energy of a localized exciton and fluctuations of the transition matrix elements between different lattice sites. Under the assumption that the fluctuating forces are Markoffian and Gaussian we derive exactly a density matrix equation which can be solved by a Greens function method.

Quantum theory of light propagation in a fluctuating laser-active medium

The basic equations are derived which describe the propagation of an electromagnetic field in a fluctuating laser-active medium. The well-known methods of Langevinequations and master-equation for a few discrete modes are generalized to meet also the case of a radiation field with continuous spectrum. The medium is described by two-level atoms which are embedded in a merely passive solid matrix and homogeneously distributed over space. They have an inversion which is kept constant by an externally applied pump. The atomic line may be homogeneously or inhomogeneously broadened. We obtain a complete set of partial differential equations for the field operators with damping terms and fluctuating forces homogeneously distributed over the material. The telegraph equation with a fluctuating force occurs as a special case. After the exact elimination of the atomic variables we obtain a nonlinear field equation for the radiation field alone. By means of a pseudo-Hamiltonian and by a simple one-dimensional example we show that in a certain sense there exists a close formal analogy between the present theory and the theory of an interacting Bose gas. The characteristic differences between the two theories are also discussed. We find, that there occurs a phase transition of the radiation field because above a certain threshold of the pump the photons condense into a single mode and establish an “offdiagonal-long-range order”. The amplitude fluctuations and the phase fluctuations, which restore the broken phase symmetry, are calculated in detail. A new condition for the occurrence of undamped spiking (pulse formation) for a continuum of modes is derived.

The coupled coherent and incoherent motion of excitons and its influence on the line shape of optical absorption

AbstractWe treat the coupled coherent and incoherent motion of Frenkel excitons by a model calculation. The model contains the four parametersa (distance of neighbouring atoms),J (exchange interaction integral), γo (describing the strength of the local energy fluctuations) and γ1 (a measure of the fluctuations of the exchange interaction integral, i.e. nonlocal fluctuations). Calculation of the optical absorption of systems with two differently oriented molecules/unit cells results in the Davydov-splitting given by Δ=8J and the linewidth given by Γ=γo+γ1. From the equation of motion of the density matrix we derive a diffusion equation. The diffusion constant is given by

Phase-Locked Modes, Phase Transitions and Component Oscillators in Biological Motion

D = \frac{{a^2 }}{\hbar }\left( {2\gamma _1 + \frac{{J^2 }}{{\gamma _1 + \Gamma }}} \right)