Spin relaxation in a complex environment

We report the study of a model of a two-level system interacting in a non-diagonal way with a complex environment described by Gaussian orthogonal random matrices (GORM). The effect of the interaction on the total spectrum and its consequences on the dynamics of the two-level system are analyzed. We show the existence of a critical value of the interaction, depending on the mean level spacing of the environment, above which the dynamics is self-averaging and closely obey a master equation for the time evolution of the observables of the two-level system. Analytic results are also obtained in the strong coupling regimes. We finally study the equilibrium values of the two-level system population and show under which condition it thermalizes to the environment temperature.Comment: 45 pages, 49 figure

Quantum master equation for a system influencing its environment

A perturbative quantum master equation is derived for a system interacting with its environment, which is more general than the ones derived before. Our master equation takes into account the effect of the energy exchanges between the system and the environment and the conservation of energy in a finite total system. This master quantum describes relaxation mechanisms in isolated nanoscopic quantum systems. In its most general form, this equation is non-Markovian and a Markovian version of it rules the long-time relaxation. We show that our equation reduces to the Redfield equation in the limit where the energy of the system does not affect the density of state of its environment. This master equation and the Redfield one are applied to a spin-environment model defined in terms of random matrices and compared with the solutions of the exact von Neumann equation. The comparison proves the necessity to allow energy exchange between the subsystem and the environment in order to correctly describe the relaxation in isolated nanoscopic total system.Comment: 39 pages, 10 figure

Effect of FET geometry on charge ordering of transition metal oxides

We examine the effect of an FET geometry on the charge ordering phase diagram of transition metal oxides using numerical simulations of a semiclassical model including long-range Coulomb fields, resulting in nanoscale pattern formation. We find that the phase diagram is unchanged for insulating layers thicker than approximately twice the magnetic correlation length. For very thin insulating layers, the onset of a charge clump phase is shifted to lower values of the strength of the magnetic dipolar interaction, and intermediate diagonal stripe and geometric phases can be suppressed. Our results indicate that, for sufficiently thick insulating layers, charge injection in an FET geometry can be used to experimentally probe the intrinsic charge ordering phases in these materials.Comment: 4 pages, 4 postscript figure

Interactions between proteins bound to biomembranes

We study a physical model for the interaction between general inclusions bound to fluid membranes that possess finite tension, as well as the usual bending rigidity. We are motivated by an interest in proteins bound to cell membranes that apply forces to these membranes, due to either entropic or direct chemical interactions. We find an exact analytic solution for the repulsive interaction between two similar circularly symmetric inclusions. This repulsion extends over length scales of order tens of nanometers, and contrasts with the membrane-mediated contact attraction for similar inclusions on tensionless membranes. For non circularly symmetric inclusions we study the small, algebraically long-ranged, attractive contribution to the force that arises. We discuss the relevance of our results to biological phenomena, such as the budding of caveolae from cell membranes and the striations that are observed on their coats.Comment: 22 pages, 2 figure

Counterion Condensation and Fluctuation-Induced Attraction

We consider an overall neutral system consisting of two similarly charged plates and their oppositely charged counterions and analyze the electrostatic interaction between the two surfaces beyond the mean-field Poisson-Boltzmann approximation. Our physical picture is based on the fluctuation-driven counterion condensation model, in which a fraction of the counterions is allowed to ``condense'' onto the charged plates. In addition, an expression for the pressure is derived, which includes fluctuation contributions of the whole system. We find that for sufficiently high surface charges, the distance at which the attraction, arising from charge fluctuations, starts to dominate can be large compared to the Gouy-Chapmann length. We also demonstrate that depending on the valency, the system may exhibit a novel first-order binding transition at short distances.Comment: 15 pages, 8 figures, to appear in PR

Partially Annealed Disorder and Collapse of Like-Charged Macroions

Charged systems with partially annealed charge disorder are investigated using field-theoretic and replica methods. Charge disorder is assumed to be confined to macroion surfaces surrounded by a cloud of mobile neutralizing counterions in an aqueous solvent. A general formalism is developed by assuming that the disorder is partially annealed (with purely annealed and purely quenched disorder included as special cases), i.e., we assume in general that the disorder undergoes a slow dynamics relative to fast-relaxing counterions making it possible thus to study the stationary-state properties of the system using methods similar to those available in equilibrium statistical mechanics. By focusing on the specific case of two planar surfaces of equal mean surface charge and disorder variance, it is shown that partial annealing of the quenched disorder leads to renormalization of the mean surface charge density and thus a reduction of the inter-plate repulsion on the mean-field or weak-coupling level. In the strong-coupling limit, charge disorder induces a long-range attraction resulting in a continuous disorder-driven collapse transition for the two surfaces as the disorder variance exceeds a threshold value. Disorder annealing further enhances the attraction and, in the limit of low screening, leads to a global attractive instability in the system.Comment: 21 pages, 2 figure

Nematic stability and the alignment-induced growth of anisotropic micelles

In this paper we treat for the first time a phenomenon in micellized soap solutions which arises uniquely from their being colloidal suspensions whose « particles » do not maintain their integrity. In particular we focus on the growth of anisotropic aggregates which is attendant upon their long-range orientational ordering. We consider a simple analytical form for the free energy per molecule and compare explicitly the sizes of rod-like micelles in coexisting isotropic (I) and nematic (N) phases. The coupling between growth and alignment is shown to limit the stability of finite-size, partially-ordered aggregates : the nematic phase is confined to a highly restricted concentration range, because its micelles can only survive (i.e. remain finite) if they are small. The roles of translational and rotational degrees of freedom, and of cosurfactant effects, are also considered : both are shown to enhance the stability range of the nematic. Within Onsager's theory for the long-range alignment of rod-like particles, we conclude further that : (i) the growth of micelles at the I → N transition is driven largely by the orientational « entropy of mixing » — bigger rods allow this entropy loss to be minimized; and (ii) the nematic order parameter and the ratio of coexisting sizes are essentially universal, with the average volume fraction at the transition scaling as the reciprocal of the average aggregation number.Dans cet article, nous examinons pour la première fois un phénomène qui se produit dans les solutions micellaires de savon, uniquement en raison de leur nature de suspensions colloidales formées de particules qui ne conservent pas leur intégrité. En particulier, nous nous intéressons à la croissance d'agrégats en relation avec leur ordre à grande distance. Nous considérons une forme analytique simple pour l'énergie libre par molécule et nous comparons explicitement la taille des micelles en bâtonnets dans des systèmes où coexistent des phases isotropes (I) et nématiques (N). Nous montrons que le couplage entre croissance et alignement limite la stabilité des agrégats partiellement ordonnés et de taille finie. La phase nématique est limitée à une gamme de concentrations très restreinte car ses micelles ne peuvent survivre (c'est-à-dire rester finies) que si elles sont petites. Le rôle des degrés de liberté de translation et de rotation ainsi que les effets de cosurfactant sont également pris en considération : tous deux augmentent le domaine de stabilité de la phase nématique. Dans le cadre de la théorie d'Onsager de l'alignement à longue portée de particules en bâtonnets, nous en arrivons à la conclusion (1) que la croissance des micelles à la transition I → N est contrôlée par l'« entropie de melange » orientationnel, (2) que le paramètre d'ordre nématique et le rapport entre tailles qui coexistent est essentiellement universel, la fraction moyenne en volume à la transition se mesurant en termes de l'inverse du nombre d'agrégation moyen