The <Emphasis Type="Bold">±</Emphasis><Emphasis Type="Bold">J</Emphasis> spin glass in Migdal-Kadanoff approximation

We study the low-temperature phase of the three-dimensional ± J Ising spin glass in Migdal-Kadanoff approximation. At zero temperature, T = 0, the properties of the spin glass result from the ground-state degeneracy and can be elucidated using scaling arguments based on entropy. The approach to the asymptotic scaling regime is very slow, and the correct exponents are only visible beyond system sizes around 64. At T > 0, a crossover from the zero-temperature behaviour to the behaviour expected from the droplet picture occurs at length scales proportional to T ^-2/ds where d_s is the fractal dimension of a domain wall. Canonical droplet behaviour is not visible at any temperature for systems whose linear dimension is smaller than 16 lattice spacings, because the data are either affected by the zero-temperature behaviour or the critical point behaviour. Received 18 February 2001     

Ground-state landscape of J Ising spin glasses

Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40². A combination of a genetic algorithm and Cluster-Exact Approximation is used. For each quenched realization of the bonds up to 40 independent ground states are obtained. For the infinite system a ground-state energy of e =-1.4015(3) is extrapolated. The ground-state landscape is investigated using a finite-size scaling analysis of the distribution of overlaps. The mean-field picture assuming a complex landscape describes the situation better than the droplet-scaling model, where for the infinite system mainly two ground states exist. Strong evidence is found that the ground states are not organized in an ultrametric fashion in contrast to previous results for three-dimensional spin glasses. Received 12 October 1998     

Performance limitations of flat-histogram methods

We determine the optimal scaling of local-update flat-histogram methods with system size by using a perfect flat-histogram scheme based upon the exact density of states of 2D Ising models. The typical tunneling time needed to sample the entire bandwidth does not scale with the number of spins N as the minimal N2 of an unbiased random walk in energy space. While the scaling is power law for the ferromagnetic and fully frustrated Ising model, for the +/-J nearest-neighbor spin glass the distribution of tunneling times is governed by a fat-tailed Fréchet extremal value distribution that obeys exponential scaling. Furthermore, the shape parameters of these distributions indicate that statistical sample means become ill defined already for moderate system sizes within these complex energy landscapes.     

Some exact results on the ultrametric overlap distribution in mean field spin glass models (I)

The mean field spin glass model is analyzed by a combination of exact methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural networks.It is well known that the probability measure of overlaps among replicas carries the whole physical content of these models. A functional order parameter of Parisi type is introduced by rigorous methods, according to previous works by F. Guerra. By the Ansatz that the functional order parameter is the correct order parameter of the model, we explicitly find the full overlap distribution. The physical interpretation of the functional order parameter is obtained, and ultrametricity of overlaps is derived as a natural consequence of a branching diffusion process.It is shown by explicit construction that ultrametricity of the 3-replicas overlap distribution together with the Ghirlanda-Guerra relations determines the distribution of overlaps among s replicas, for any s, in terms of the one-overlap distribution.     

Triplet interactions in star polymer solutions

We analyze the effective triplet interactions between the centers of star polymers in a good solvent. Using an analytical short-distance expansion inspired by scaling theory, we deduce that the triplet part of the three-star force is attractive but only 11% of the pairwise part even for a close approach of three star polymers. We have also performed extensive computer simulations for different arm numbers f to extract the effective triplet force. The simulation data show good correspondence with the theoretical predictions. Our results justify the effective pair potential picture even beyond the star polymer overlap concentration. Received 1 September 1999 and Received in final form 18 January 2000     

Some exact results on the ultrametric overlap distribution in mean field spin glass models (I)

The mean field spin glass model is analyzed by a combination of exact methods and a simple Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural networks. It is well known that the probability measure of overlaps among replicas carries the whole physical content of these models. A functional order parameter of Parisi type is introduced by rigorous methods, according to previous works by F. Guerra. By the Ansatz that the functional order parameter is the correct order parameter of the model, we explicitly find the full overlap distribution. The physical interpretation of the functional order parameter is obtained, and ultrametricity of overlaps is derived as a natural consequence of a branching diffusion process. It is shown by explicit construction that ultrametricity of the 3-replicas overlap distribution together with the Ghirlanda-Guerra relations determines the distribution of overlaps among s replicas, for any s, in terms of the one-overlap distribution. Received 14 February 2000     

Overlap distribution in random and designed heteropolymers

We study the overlap between low-energy states in lattice models of heteropolymers with contact interactions. The overlap distribution gives information on the degree of correlation in the energy landscape. Designed sequences have rather correlated energy landscapes, which favor fast folding kinetics. Chains with random interactions have much less correlated energy landscapes. It is indeed believed that the mean-field theory for this model coincides with the Random Energy Model, whose different low-energy states are completely unrelated. This picture has been supported by numerical studies of maximally compact configurations. Without applying this constraint, we find that the overlap distribution is indeed bimodal as expected, but it has a broad peak at large overlap, indicating a non-vanishing width for the valleys of low-energy states. This feature probably plays an important role in the kinetics of the model. It is not evident that the range of such correlations shrinks to zero for large systems. The range of the correlations seems to be influenced by the number of contacts per residue in the ground state: the smaller this quantity, the larger the correlations. Received 16 August 2000     

Spin and link overlaps in three-dimensional spin glasses

Excitations of three-dimensional spin glasses are computed numerically. We find that one can flip a finite fraction of an LxLxL lattice with an O(1) energy cost, confirming the mean-field picture of a nontrivial spin overlap distribution P(q). These low energy excitations are not domain-wall-like, rather they are topologically nontrivial and they reach out to the boundaries of the lattice. Their surface to volume ratios decrease as L increases and may asymptotically go to zero. If so, link and window overlaps between the ground state and these excited states become "trivial."     

Transport between multiple users in complex networks

We study the transport properties of model networks such as scale-free and Erd?s-Rényi networks as well as a real network. We consider few possibilities for the trnasport problem. We start by studying the conductance G between two arbitrarily chosen nodes where each link has the same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G, with a power-law tail distribution $\Phi_{\rm SF}(G)\sim G^{-g_G}$ , where g_G=2λ-1, and λ is the decay exponent for the scale-free network degree distribution. The power-law tail in Φ_SF(G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erd?s-Rényi networks where the tail of the conductivity distribution decays exponentially. We develop a simple physical picture of the transport to account for the results. The other model for transport is the max-flow model, where conductance is defined as the number of link-independent paths between the two nodes, and find that a similar picture holds. The effects of distance on the value of conductance are considered for both models, and some differences emerge. We then extend our study to the case of multiple sources ans sinks, where the transport is defined between two groups of nodes. We find a fundamental difference between the two forms of flow when considering the quality of the transport with respect to the number of sources, and find an optimal number of sources, or users, for the max-flow case. A qualitative (and partially quantitative) explanation is also given.     

Electro-optical phase shift in polymer dispersed liquid crystals

An anisotropic version of the Maxwell Garnett approximation is applied for studying the electro-optical phase modulation by polymer dispersed liquid crystals (PDLC). The PDLC contain bipolar liquid crystal droplets that can be reoriented by an external field causing a change in the optical birefringence. This approach provides an explicit link between the droplet orientation distribution and the electro-optical phase shift. For aligned droplets we find that the sharpness of the change in the birefringence may be controlled by selecting the initial orientation. For a planar distribution we find sharp transitions with a hysteresis loop whose width depends on the droplet concentration. For a random distribution, the droplet orientation and the optical phase shift change more gradually with the applied field. These results demonstrate that PDLC may be suitable for a wide range of electro-optic applications based on their field-induced phase modulation properties. In addition, it is apparent that the optical phase shift is quite sensitive to changes in droplet orientation. It should therefore be useful for studying reorientation phenomena in PDLC, overcoming the problems due to light scattering in these materials. Received 25 November 1999 and Received in final form 20 January 2000     

Interpersonal interactions and human dynamics in a large social network

We study a large social network consisting of over 10⁶ individuals, who form an Internet community and organize themselves in groups of different sizes. On the basis of the users’ list of friends and other data registered in the database we investigate the structure and time development of the network. The structure of this friendship network is very similar to the structure of different social networks. However, here a degree distribution exhibiting two scaling regimes, power-law for low connectivity and exponential for large connectivity, was found. The groups size distribution and distribution of number of groups of an individual have power-law form. We found very interesting scaling laws concerning human dynamics. Our research has shown how long people are interested in a single task.     

Direct measurement of the spatial Wigner function with area-integrated detection

We demonstrate experimentally a novel technique for characterizing transverse spatial coherence by using the Wigner distribution function. The method is based on the measurement of interference between a pair of rotated and displaced replicas of the input beam with an area-integrating detector, and it provides an optimal signal-to-noise ratio in regimes when array detectors are not available. We analyze the quantum-optical picture of the presented measurement for single-photon signals and discuss possible applications in quantum information processing.     

Probing particle-particle interactions in flocculated oil-in-water emulsions using ultrasonic attenuation spectrometry

The flocculation of silicone oil-in-water emulsions ( φ = 0.1) containing quasi-monodisperse droplets was studied by ultrasound. The ultrasonic attenuation spectra of emulsions with different particle sizes (200-1600 nm) were measured between 0.5 and 10 MHz using an interferometer. Flocculation was induced by adding excess sodium dodecyl sulphate micelles to the emulsions to increase the attractive forces between the droplets. Droplet flocculation decreased the ultrasonic attenuation at low frequencies because of overlap of the thermal waves caused by the close proximity of the droplets within the flocs. A mean-field model which takes into account this effect was used to determine the droplet volume fraction within the flocs and thus to estimate the distance between the droplets. Received 17 July 2000     

Rayleigh instability of charged droplets in the presence of counterions

The classical instability of a charged spherical droplet is reconsidered in the presence of counterions. An ensemble of such droplets is studied within a simplified cell model. Screening of the electric field by the counterions is found to increase the equilibrium droplet size. Furthermore, if the ions can enter the droplet, a first-order phase transition occurs upon increasing Bjerrum length, surface tension or droplet density, leading to a phase separation. Simple scaling properties of the free energy give the shape of the phase boundary and show the system to be scale-invariant there. Pearl-necklace structures of hydrophobic polyelectrolytes are discussed as an application. Received 30 August 2001     

Quantum fidelity in the thermodynamic limit

We study quantum fidelity, the overlap between two ground states of a many-body system, focusing on the thermodynamic regime. We show how a drop in fidelity near a critical point encodes universal information about a quantum phase transition. Our general scaling results are illustrated in the quantum Ising chain for which a remarkably simple expression for fidelity is found.     

Correlations and aggregate statistics in granular packs

We study how the aggregate statistical properties for density fluctuations in granular aggregates scale with the sample size and how such a scaling is associated with the correlations between grains. Correlations are studied both between grain positions and between Vorono? cell volumes, showing distinct behaviors and properties. A non-linear scaling in the aggregate volume fluctuations as function of the sample size is discovered and the connection between such anomalous scaling and correlations is explained. It emerges that volume fluctuations might be described by means of a single universal equation for all samples at all cluster sizes.     

Difference in the dynamic scaling behavior of droplet size distribution for coalescence under pulsed and continuous vapor delivery

Dynamic scaling behavior of the droplet size distribution in the coalescence regime for growth by pulsed laser deposition is studied experimentally and by computer simulation, and the same is compared with that for continuous vapor deposition. The scaling exponent for pulsed deposition is found to be (1.2 +/- 0.1), which is significantly lower as compared to that for continuous deposition (1.6 +/- 0.1). Simulations reveal that this dramatic difference can be traced to the large fraction of multiple droplet coalescence under pulsed vapor delivery. A possible role of the differing diffusion fields in the two cases is also suggested.     

Single-shot measurement of a carrier-envelope phase by use of a time-dependent polarization pulse

We propose a method for single-shot measurement of the carrier-envelope phase of high-intensity laser pulses. The method is based on observation of the electrons' spatial distribution ionized by a time-dependent polarization pulse generated by a combination of replicas of the measuring pulse. The dependence of the electrons' angular distribution on carrier-envelope phase, pulse width, delay between two combining components, and a peak intensity is calculated. Important experimental issues such as broadening of the angular distribution, Gouy phase, difference between the two replicas, and asymmetric pulse shape are also discussed.     

Aging of the zero-field-cooled magnetization in Ising spin glasses: experiment and numerical simulation

Growth of the zero-field-cooled magnetization (ZFCM) under continuous heating with and without an intermittent stop(s) is studied on Ising spin glasses both experimentally and numerically. Despite the large difference between time scales of the experiment and the simulation, the ZFCM behavior observed in the two systems can be quantitatively interpreted by means of a common set of the scaling expressions based on the droplet picture. The results strongly suggest that the spin-glass coherence length reached by the laboratory time scales is about a hundred lattice spacings or less. Within this length scale no signature of the chaos effect (rejuvenation) has been found in the ZFCM measured.