Thomas Nattermann

Hysteretic dynamics of domain walls at finite temperatures.

Theory of domain wall motion in a random medium is extended to the case when the driving field is below the zero-temperature depinning threshold and the creep of the domain wall is induced by thermal fluctuations. Subject to an ac drive, the domain wall starts to move when the driving force exceeds an effective threshold which is temperature and frequency dependent. Similar to the case of zero temperature, the hysteresis loop displays three dynamical phase transitions at increasing ac field amplitude h(0). The phase diagram in the 3D phase space of temperature, driving force amplitude, and frequency is investigated.

Driven interface depinning in a disordered medium

The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity v, which increases as v ∼(FFc)θ for driving forces F close to its threshold value Fc. We consider a Langevin-type Eq. which is expected to be valid close to the depinning transition of an interface in a statistically isotropic medium. By a functional renormalization group scheme the critical exponents characterizing the depinning transition are obtained to the first order in ϵ = 4 — D > 0, where D is the interface dimension. The main results were published earlier [T. Nattermann et al., J. Phys. II France 2 (1992) 1483]. Here, we present details of the perturbative calculation and of the derivation of the functional flow Eq. for the random-force correlator. The fixed point function of the correlator has a cusp singularity which is related to a finite value of the threshold Fc, similar to the mean field theory. We also present extensive numerical simulations and compare them with our analytical results for the critical exponents. For ϵ = 1 the numerical and analytical results deviate from each other by only a few percent. The deviations in lower dimensions ϵ = 2, 3 are larger and suggest that the roughness exponent is somewhat larger than the value ξ = e/3 of an interface in thermal equilibrium.

Topological order in the vortex-glass phase of high-temperature superconductors

The stability of a vortex glass phase with quasi-long-range positional order is examined for a disordered layered superconductor. The role of topological defects is investigated using a scaling argument supplemented by a variational calculation. The results indicate that topological order is preserved for some range of parameters in the vortex glass phase. The stability regime is given in terms of a simple Lindemann-like criterion and is consistent with recent experiments. {copyright} {ital 1997} {ital The American Physical Society}

Theory of the hysteresis loop in ferromagnets

We consider three mechanisms of hysteresis phenomena in alternating magnetic field: the domain-wall motion in a random medium, the nucleation, and the retardation of magnetization due to slow (critical) fluctuations. We construct a quantitative theory for all these processes. The hysteresis is characterized by two dynamic threshold fields, a coercive field and the so-called reversal field. Their ratios to the static threshold field is shown to be a function of two dimensionless variables constituted from the frequency and amplitude of the ac field as well as from some characteristics of the magnet. The area and the shape of the hysteresis loop are found. We consider different limiting cases in which power dependencies are valid. Numerical simulations show the domain-wall formation and propagation and confirm the main theoretical predictions. Theory is compared with available experimental data. {copyright} {ital 1999} {ital The American Physical Society}

Weakly interacting Bose gas in a random environment

The localization-disorder paradigm is analyzed for a specific system of weakly repulsive Bose gas at zero temperature placed into a quenched random potential. We show that at low average density or weak enough interaction the particles fill deep potential wells of the random potential whose radius and depth depend on the characteristics of the random potential and the interacting gas. The localized state is the random singlet with no long-range phase correlation. At a critical density the quantum phase transition to the coherent superfluid state proceeds. We calculate the critical density in terms of the geometrical characteristics of the noise and the gas. In a finite system the ground state becomes nonergodic at very low density. For atoms in traps four different regimes are found; only one of it is superfluid. The theory is extended to lower (one and two) dimensions. Its quantitative predictions can be checked in experiments with ultracold atomic gases and other Bose systems.

Criterion for crack formation in disordered materials

Crack formation is conventionally described as a nucleation phenomenon despite the fact that the temperatures necessary to overcome the nucleation barrier are far too high. In this paper we consider the possibility that cracks are created due to the presence of frozen disorder (e.g. heterogeneities or frozen dislocations). In particular we calculate the probability for the occurrence of a critical crack in a quasi two-dimensional disordered elastic system. It turns out that this probability takes the form of an Arrhenius law (as for thermal nucleation) but with the temperature T replaced by an effective disorder temperature T_eff which depends on the strength of the disorder. The extension of these results to d=3 dimensions is briefly discussed.

Variable-range hopping and quantum creep in one dimension.

We study the quantum nonlinear response to an applied electric field E of a one-dimensional pinned charge-density wave or Luttinger liquid in the presence of disorder. From an explicit construction of low-lying metastable states and of bounce instanton solutions between them, we demonstrate quantum creep v=e(-c/E(1/2)) as well as a sharp crossover at E=E(*) towards a linear response form consistent with variable-range hopping arguments, but dependent only on electronic degrees of freedom.

Domain Wall Depinning in Random Media by AC Fields

The viscous motion of an interface driven by an ac external field of frequency omega(0) in a random medium is considered here in the nonadiabatic regime. The velocity exhibits a smeared depinning transition showing a double hysteresis which is absent in the adiabatic case omega(0)-->0. Using scaling arguments and an approximate renormalization group calculation we explain the main characteristics of the hysteresis loop. In the low frequency limit these can be expressed in terms of the depinning threshold and the critical exponents of the adiabatic case.

Disorder-induced depinning transition

The competition in the pinning of a directed polymer by a columnar pin and a background of random point impurities is investigated systematically using the renormalization-group method. With the aid of the mapping to the noisy-Burgers equation and the use of the mode-coupling method, the directed polymer is shown to be marginally localized to an arbitrary weak columnar pin in 1+1 dimensions. This weak-localization effect is attributed to the existence of large scale, nearly degenerate optimal paths of the randomly pinned directed polymer. The critical behavior of the depinning transition above 1+1 dimensions is obtained via an [epsilon] expansion.

Bose-Einstein Condensates in Strongly Disordered Traps

A Bose-Einstein condensate in an external potential consisting of a superposition of a harmonic and a random potential is considered theoretically. From a semiquantitative analysis we find the size, shape, and excitation energy as a function of the disorder strength. For positive scattering length and sufficiently strong disorder the condensate decays into fragments each of the size of the Larkin length L. This state is stable over a large range of particle numbers. The frequency of the breathing mode scales as 1/L(2). For negative scattering length a condensate of size L may exist as a metastable state. These findings are generalized to anisotropic traps.