Series Expansion of the Off-Equilibrium Mode Coupling Equations

We show that computing the coefficients of the Taylor expansion of the solution of the off-equilibrium dynamical equations characterizing models with quenched disorder is a very effective way to understand the long time asymptotic behavior. We study the $p=3$ spherical spin glass model, and we compute the asymptotic energy (in the critical region and down to $T=0$) and the coefficients of the time decay of the energy.Comment: 9 pages, LaTeX, 3 uuencoded figure

The response of glassy systems to random perturbations: A bridge between equilibrium and off-equilibrium

We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free energy. By exploiting this fact, we define a new order parameter function, and we relate it to the ratio between response and fluctuation, which is in principle measurable in an aging experiment. For a class of systems possessing stochastic stability, we show that this new order parameter function is intimately related to the static order parameter function, describing the distribution of overlaps between clustering states. The same method is applied to investigate the geometrical organization of pure states. We show that the ultrametric organization in the dynamics implies static ultrametricity, and we relate these properties to static separability, i.e., the property that the measure of the overlap between pure states is essentially unique. Our results, especially relevant for spin glasses, pave the way to an experimental determination of the order parameter function.Comment: 17 page

The convolution theorem for nonlinear optics

We have expressed the nonlinear optical absorption of a semiconductor in terms of its linear spectrum. We determined that the two-photon absorption coefficient in a strong DC-electric field of a direct gap semiconductor can be expressed as the product of a differential operator times the convolution integral of the linear absorption without a DC-electric field and an Airy function. We have applied this formalism to calculate the two-photon absorption coefficient and nonlinear refraction for GaAs and ZnSe using their linear absorption and have found excellent agreement with available experimental data.Comment: 8 pages, 2 figures (6 sub fugures

Structure and dynamics in glass-formers: predictability at large length scales

Dynamic heterogeneity in glass-formers has been related to their static structure using the concept of dynamic propensity. We re-examine this relationship by analyzing dynamical fluctuations in two atomistic glass-formers and two theoretical models. We introduce quantitative statistical indicators which show that the dynamics of individual particles cannot be predicted on the basis of the propensity, nor by any structural indicator. However, the spatial structure of the propensity field does have predictive power for the spatial correlations associated with dynamic heterogeneity. Our results suggest that the quest for a connection between static and dynamic properties of glass-formers at the particle level is vain, but they demonstrate that such connection does exist on larger length scales.Comment: 7 pages; 4 figs - Extended, clarified versio

Infrared light extinction by charged dielectric core-coat particles

We study the effect of surplus electrons on the infrared extinction of dielectric particles with a core-coat structure and propose to use it for an optical measurement of the particle charge in a dusty plasma. The particles consist of an inner core with negative and an outer coat with positive electron affinity. Both the core and the coat give rise to strong transverse optical phonon resonances, leading to anomalous light scattering in the infrared. Due to the radial profile of the electron affinity electrons accumulate in the coat region making the infrared extinction of this type of particles very charge-sensitive, in particular, the extinction due to a resonance arising solely due to the core-coat structure. The maximum of this resonance is in the far-infrared and responds to particle charges realizable in ordinary dusty laboratory plasmas.Comment: 12 pages, 8 figure

Convexity and potential sums for Salpeter-like Hamiltonians

The semirelativistic Hamiltonian H = \beta\sqrt{m^2 + p^2} + V(r), where V(r) is a central potential in R^3, is concave in p^2 and convex in p. This fact enables us to obtain complementary energy bounds for the discrete spectrum of H. By extending the notion of 'kinetic potential' we are able to find general energy bounds on the ground-state energy E corresponding to potentials with the form V = sum_{i}a_{i}f^{(i)}(r). In the case of sums of powers and the log potential, where V(r) = sum_{q\ne 0} a(q) sgn(q)r^q + a(0)ln(r), the bounds can all be expressed in the semi-classical form E \approx \min_{r}{\beta\sqrt{m^2 + 1/r^2} + sum_{q\ne 0} a(q)sgn(q)(rP(q))^q + a(0)ln(rP(0))}. 'Upper' and 'lower' P-numbers are provided for q = -1,1,2, and for the log potential q = 0. Some specific examples are discussed, to show the quality of the bounds.Comment: 21 pages, 4 figure

Relaxation processes and entropic traps in the Backgammon model

We examine the density-density correlation function in a model recently proposed to study the effect of entropy barriers in glassy dynamics. We find that the relaxation proceeds in two steps with a fast beta process followed by alpha relaxation. The results are physically interpreted in the context of an adiabatic approximation which allows to separate the two processes, and to define an effective temperature in the off-equilibrium dynamics of the model. We investigate the behavior of the response function associated to the density, and find violations of the fluctuation dissipation theorem.Comment: 4 Pages including 3 Figures, Revte

Metastable States, Relaxation Times and Free-energy Barriers in Finite Dimensional Glassy Systems

In this note we discuss metastability in a long-but-finite range disordered model for the glass transition. We show that relaxation is dominated by configuration belonging to metastable states and associate an in principle computable free-energy barrier to the equilibrium relaxation time. Adam-Gibbs like relaxation times appear naturally in this approach.Comment: 4 pages, 2 figures. Typos correcte

Posttraumatic Stress and Parenting Behaviors: The Mediating Role of Emotion Regulation

Maternal trauma has been linked with problematic parenting, including both harsh and permissive behaviors. However, little is known about mechanisms accounting for this association. The current study examined the potential impact of posttraumatic stress disorder (PTSD) and emotion regulation on dysfunctional parenting behaviors in a sample of community mothers. We hypothesized a mediation model wherein PTSD would be associated with dysfunctional parenting (i.e., lax and overreactive behaviors) indirectly through deficits in maternal emotion regulation. Seventy-eight community mothers of 18- to 36-month-old children were administered the Clinician Administered PTSD Scale for DSM-5 (CAPS-5) and 19 mothers met criteria for PTSD. Mothers also completed self-report measures of difficulties with emotion regulation and maternal laxness and overreactivity in parenting. Results revealed that emotion dysregulation fully mediated relations between PTSD status and lax (but not overreactive) parenting behaviors. Compared to mothers without PTSD, those with PTSD reported greater lax parenting behaviors indirectly through greater emotion dysregulation. Mothers with PTSD may struggle to parent assertively when trauma symptoms interfere with emotion regulation abilities. The current study highlights the need to design interventions focused on helping trauma-exposed mothers manage distress, ultimately aiming to enhance parenting effectiveness and improve child outcomes