Intersubband excitations at finite temperatures and their roles in different quasi-one-dimensional systems

We theoretically study many-body excitations in three different quasi-one-dimensional (Q1D) electron systems: (i) those formed on the surface of liquid Helium; (ii) in two coupled semiconductor quantum wires; and (iii) Q1D electrons embedded in polar semiconductor-based quantum wires. Our results show intersubband coupling between higher subbands and the two lowest subbands affecting even the lower energy intersubband plasmons on the liquid Helium surface. Concerning the second system, we show a pronounced extra peak appearing in the intersubband impurity spectral function for temperatures as high as 20 K. We finally show coupled intersubband plasmon-phonon modes surviving for temperatures up to 300 K.

Entanglement Entropies in One-Dimensional Systems

In the thesis, we discuss some aspects of 1D quantum systems related to entanglement entropies; in particular, we develop a new numerical method for the detection of crossovers in Luttinger liquids, and we discuss the behaviour of Rényi entropies in open conformal systems, when the boundary conditions preserve their conformal invariance.

Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems

Consider N sites randomly and uniformly distributed in a d-dimensional hypercube. A walker explores this disordered medium going to the nearest site, which has not been visited in the last mu (memory) steps. The walker trajectory is composed of a transient part and a periodic part (cycle). For one-dimensional systems, travelers can or cannot explore all available space, giving rise to a crossover between localized and extended regimes at the critical memory mu(1) = log(2) N. The deterministic rule can be softened to consider more realistic situations with the inclusion of a stochastic parameter T (temperature). In this case, the walker movement is driven by a probability density function parameterized by T and a cost function. The cost function increases as the distance between two sites and favors hops to closer sites. As the temperature increases, the walker can escape from cycles that are reminiscent of the deterministic nature and extend the exploration. Here, we report an analytical model and numerical studies of the influence of the temperature and the critical memory in the exploration of one-dimensional disordered systems.

Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Continuous structural transitions in quasi-one-dimensional classical Wigner crystals

We study the structural phase transitions in confined systems of strongly interacting particles. We consider infinite quasi-one-dimensional systems with different pairwise repulsive interactions in the presence of an external confinement following a power law. Within the framework of Landau's theory, we find the necessary conditions to observe continuous transitions and demonstrate that the only allowed continuous transition is between the single-and the double-chain configurations and that it only takes place when the confinement is parabolic. We determine analytically the behavior of the system at the transition point and calculate the critical exponents. Furthermore, we perform Monte Carlo simulations and find a perfect agreement between theory and numerics.

Conservation laws, integrability, and transport in one-dimensional quantum systems

In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where a conserved spin current exists.

Magnetic relaxation of a one-dimensional model for small particle systems with dipolar interactions: Monte Carlo simulation

Atribution as a function of the time are analyzed and this study leads to a deeper knowledge of the microscopic processes involved in the magnetic relaxation

Transport properties of one-dimensional, disordered two-band systems

We have studied the transport properties of disordered one-dimensional two-band systems. The model includes a narrow d band hybridised with an s band. The Landauer formula was used in the case of a very narrow d band or in the case of short chains. The results were compared with the localisation length of the wavefunctions calculated by the transfer matrix method, which allows the use of very lang chains, and an excellent agreement was obtained.

Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

Unfolding of plasmon-polariton modes in one-dimensional layered systems containing anisotropic left-handed materials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Innovative Homogeneous and Heterogeneous Systems for Electrochemically Generated Luminescence Investigations: Towards One-Dimensional ECL

My research PhD work is focused on the Electrochemically Generated Luminescence (ECL) investigation of several different homogeneous and heterogeneous systems. ECL is a redox induced emission, a process whereby species, generated at electrodes, undergo a high-energy electron transfer reaction to form excited states that emit light. Since its first application, the ECL technique has become a very powerful analytical tool and has widely been used in biosensor transduction. ECL presents an intrinsically low noise and high sensitivity; moreover, the electrochemical generation of the excited state prevents scattering of the light source: for all these characteristics, it is an elective technique for ultrasensitive immunoassay detection. The majority of ECL systems involve species in solution where the emission occurs in the diffusion layer near to the electrode surface. However, over the past few years, an intense research has been focused on the ECL generated from species constrained on the electrode surface. The aim of my work is to study the behavior of ECL-generating molecular systems upon the progressive increase of their spatial constraints, that is, passing from isolated species in solution, to fluorophores embedded within a polymeric film and, finally, to patterned surfaces bearing “one-dimensional” emitting spots. In order to describe these trends, I use different “dimensions” to indicate the different classes of compounds. My thesis was mostly developed in the electrochemistry group of Bologna with the supervision of Prof Francesco Paolucci and Dr Massimo Marcaccio. With their help and also thanks to their long experience in the molecular and supramolecular ECL fields and in the surface investigations using scanning probe microscopy techniques, I was able to obtain the results herein described. Moreover, during my research work, I have established a new collaboration with the group of Nanobiotechnology of Prof. Robert Forster (Dublin City University) where I spent a research period. Prof. Forster has a broad experience in the biomedical field, especially he focuses his research on film surfaces biosensor based on the ECL transduction. This thesis can be divided into three sections described as follows: (i) in the fist section, homogeneous molecular and supramolecular ECL-active systems, either organic or inorganic species (i.e., corannulene, dendrimers and iridium metal complex), are described. Driving force for this kind of studies includes the search for new luminophores that display on one hand higher ECL efficiencies and on the other simple mechanisms for modulating intensity and energy of their emission in view of their effective use in bioconjugation applications. (ii) in the second section, the investigation of some heterogeneous ECL systems is reported. Redox polymers comprising inorganic luminophores were described. In such a context, a new conducting platform, based on carbon nanotubes, was developed aimed to accomplish both the binding of a biological molecule and its electronic wiring to the electrode. This is an essential step for the ECL application in the field of biosensors. (iii) in the third section, different patterns were produced on the electrode surface using a Scanning Electrochemical Microscopy. I developed a new methods for locally functionalizing an inert surface and reacting this surface with a luminescent probe. In this way, I successfully obtained a locally ECL active platform for multi-array application.

Defect-induced effects on carrier migration through one-dimensional poly(para-phenylenevinylene) chains

Defects in one-dimensional (1D) systems can be intrinsically distinct from its three-dimensional counterparts, and polymer films are good candidates for showing both extremes that are difficult to individuate in the experimental data. We study theoretically the impact of simple hydrogen and oxygen defects on the electron transport properties of one-dimensional poly(para-phenylenevinylene) chains through a multiscale technique, starting from classical structural simulations for crystalline films to extensive ab initio calculations within density functional theory for the defects in single crystalline-constrained chains. The most disruptive effect on carrier transport comes from conjugation breaking imposed by the overcoordination of a carbon atom in the vinyl group independently from the chemical nature of the defect. The particular case of the [C=O] (keto-defect) shows in addition unexpected electron-hole separation, suggesting that the experimentally detected photoluminescence bleaching and photoconductivity enhancement could be due to exciton dissociation caused by the 1D characteristics of the defect.

Orbital multicriticality in spin-gapped quasi-one-dimensional antiferromagnets

Motivated by the quasi-one-dimensional antiferromagnet CaV(2)O(4), we explore spin-orbital systems in which the spin modes are gapped but orbitals are near a macroscopically degenerate classical transition. Within a simplified model we show that gapless orbital liquid phases possessing power-law correlations may occur without the strict condition of a continuous orbital symmetry. For the model proposed for CaV(2)O(4), we find that an orbital phase with coexisting order parameters emerges from a multicritical point. The effective orbital model consists of zigzag-coupled transverse field Ising chains. The corresponding global phase diagram is constructed using field theory methods and analyzed near the multicritical point with the aid of an exact solution of a zigzag XXZ model.

Ladder operator for the one-dimensional Hubbard model

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.

Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t-J model

An integrable Kondo problem in the one-dimensional supersymmetric t-J model is studied by means of the boundary supersymmetric quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained. (C) 1999 Elsevier Science B.V.