Ginzburg-Landau theory of the cluster glass phase

On the basis of a recent field theory for site-disordered spin glasses a Ginzburg-Landau free energy is proposed to describe the low temperatures glassy phase(s) of site-disordered magnets. The prefactors of the cubic and dominant quartic terms change gradually along the transition line in the concentration-temperature phase diagram. Either of them may vanish at certain points $(c_*, T_*)$, where new transition lines originate. The new phases are classifiedComment: 6 pages Revtex, 5 figures. To appear in J. Phys. A. Let

Theory of semi-ballistic wave propagation

Wave propagation through waveguides, quantum wires or films with a modest amount of disorder is in the semi-ballistic regime when in the transversal direction(s) almost no scattering occurs, while in the long direction(s) there is so much scattering that the transport is diffusive. For such systems randomness is modelled by an inhomogeneous density of point-like scatterers. These are first considered in the second order Born approximation and then beyond that approximation. In the latter case it is found that attractive point scatterers in a cavity always have geometric resonances, even for Schr\"odinger wave scattering. In the long sample limit the transport equation is solved analytically. Various geometries are considered: waveguides, films, and tunneling geometries such as Fabry-P\'erot interferometers and double barrier quantum wells. The predictions are compared with new and existing numerical data and with experiment. The agreement is quite satisfactory.Comment: 24 pages Revtex; 10 figure

Theory of site-disordered magnets

In realistic spinglasses, such as CuMn, AuFe and EuSrS, magnetic atoms are located at random positions. Their couplings are determined by their relative positions. For such systems a field theory is formulated. In certain limits it reduces to the Hopfield model, the Sherrington-Kirkpatrick model, and the Viana-Bray model. The model has a percolation transition, while for RKKY couplings the ``concentration scaling'' T_g proportional to c occurs. Within the Gaussian approximation the Ginzburg-Landau expansion is considered in the clusterglass phase, that is to say, for not too small concentrations. Near special points, the prefactor of the cubic term, or the one of the replica-symmetry- breaking quartic term, may go through zero. Around such points new spin glass phases are found.Comment: 26 pages Revtex, 6 figure

Multiple scattering of classical waves: from microscopy to mesoscopy and diffusion

A tutorial discussion of the propagation of waves in random media is presented. In first approximation the transport of the multiple scattered waves is given by diffusion theory, but important corrections are present. These corrections are calculated with the radiative transfer or Schwarzschild-Milne equation, which describes intensity transport at the ``mesoscopic'' level and is derived from the ``microscopic'' wave equation. A precise treatment of the diffuse intensity is derived which automatically includes the effects of boundary layers. Effects such as the enhanced backscatter cone and imaging of objects in opaque media are also discussed within this framework. In the second part the approach is extended to mesoscopic correlations between multiple scattered intensities which arise when scattering is strong. These correlations arise from the underlying wave character. The derivation of correlation functions and intensity distribution functions is given and experimental data are discussed. Although the focus is on light scattering, the theory is also applicable to micro waves, sound waves and non-interacting electrons.Comment: Review. 86 pages Latex, 32 eps-figures included. To appear in Rev. Mod. Phy

Thermodynamics of the glassy state: effective temperature as an additional system parameter

A system is glassy when the observation time is much smaller than the equilibration time. A unifying thermodynamic picture of the glassy state is presented. Slow configurational modes are in quasi-equilibrium at an effective temperature. It enters thermodynamic relations with the configurational entropy as conjugate variable. Slow fluctuations contribute to susceptibilities via quasi-equilibrium relations, while there is also a configurational term. Fluctuation-dissipation relations also involve the effective temperature. Fluctuations in the energy are non-universal, however. The picture is supported by analytically solving the dynamics of a toy model.Comment: 5 pages, REVTEX. Phys. Rev. Lett, to appea

Thermodynamics of black holes: an analogy with glasses

The present equilibrium formulation of thermodynamics for black holes has several drawbacks, such as assuming the same temperature for black hole and heat bath. Recently the author formulated non-equilibrium thermodynamics for glassy systems. This approach is applied to black holes, with the cosmic background temperature being the bath temperature, and the Hawking temperature the internal temperature. Both Hawking evaporation and absorption of background radiation are taken into account. It is argued that black holes did not form in the very early universe.Comment: 4 pages revtex; submitted to Phys. Rev. Let

Third Cumulant of the total Transmission of diffuse Waves

The probability distribution of the total transmission is studied for waves multiple scattered from a random, static configuration of scatterers. A theoretical study of the second and third cumulant of this distribution is presented. Within a diagrammatic approach a theory is developed which relates the third cumulant normalized to the average, $\langle \langle T_a^3 \rangle \rangle$, to the normalized second cumulant $\langle \langle T_a^2 \rangle \rangle$. For a broad Gaussian beam profile it is found that $\langle \langle T_a^3 \rangle \rangle= \frac{16}{5} \langle \langle T_a^2 \rangle \rangle^2$. This is in good agreement with data of optical experiments.Comment: 16 pages revtex, 8 separate postscript figure