Exchange-correlation effects on quantum wires with spin-orbit interactions under the influence of in-plane magnetic fields.

Within the noncollinear local spin-density approximation, we have studied the ground state structure of a parabolically confined quantum wire submitted to an in-plane magnetic field, including both Rashba and Dresselhaus spin-orbit interactions. We have explored a wide range of linear electronic densities in the weak (strong) coupling regimes that appear when the ratio of spin-orbit to confining energy is small (large). These results are used to obtain the conductance of the wire. In the strong coupling limit, the interplay between the applied magnetic field¿irrespective of the in-plane direction, the exchange-correlation energy, and the spin-orbit energy-produces anomalous plateaus in the conductance vs linear density plots that are otherwise absent, or washes out plateaus that appear when the exchange-correlation energy is not taken into account.

Spin-orbit effects in GaAs quantum wells: Interplay between Rashba, Dresselhaus, and Zeeman interactions

The interplay between Rashba, Dresselhaus, and Zeeman interactions in a quantum well submitted to an external magnetic field is studied by means of an accurate analytical solution of the Hamiltonian, including electron-electron interactions in a sum-rule approach. This solution allows us to discuss the influence of the spin-orbit coupling on some relevant quantities that have been measured in inelastic light scattering and electron-spin resonance experiments on quantum wells. In particular, we have evaluated the spin-orbit contribution to the spin splitting of the Landau levels and to the splitting of charge- and spin-density excitations. We also discuss how the spin-orbit effects change if the applied magnetic field is tilted with respect to the direction perpendicular to the quantum well.

Effective mass and dielectric constant mismatch effects in spherical multishell quantum dots

The role of effective mass and dielectric mismatches on chemical potentials and addition energies of many-electron multishell quantum dots (QDs) is explored within the framework of a recent extension of the spin density functional theory. It is shown that although the gross electronic density is located in the wells of these multishell QDs, taking position-dependent effective mass and dielectric constant into account can lead to the appearance of relevant differences in chemical potential and addition energies as compared to standard calculations in which the effective mass and the dielectric constant of the well is assumed for the whole multishell structure.

Large scale assessment of regulatory evolution and transcriptome complexity in mammals

AbstractIn addition to genetic changes affecting the function of gene products, changes in gene expression have been suggested to underlie many or even most of the phenotypic differences among mammals. However, detailed gene expression comparisons were, until recently, restricted to closely related species, owing to technological limitations. Thus, we took advantage of the latest technologies (RNA-Seq) to generate extensive qualitative and quantitative transcriptome data for a unique collection of somatic and germline tissues from representatives of all major mammalian lineages (placental mammals, marsupials and monotremes) and birds, the evolutionary outgroup.In the first major project of my thesis, we performed global comparative analyses of gene expression levels based on these data. Our analyses provided fundamental insights into the dynamics of transcriptome change during mammalian evolution (e.g., the rate of expression change across species, tissues and chromosomes) and allowed the exploration of the functional relevance and phenotypic implications of transcription changes at a genome-wide scale (e.g., we identified numerous potentially selectively driven expression switches).In a second project of my thesis, which was also based on the unique transcriptome data generated in the context of the first project we focused on the evolution of alternative splicing in mammals. Alternative splicing contributes to transcriptome complexity by generating several transcript isoforms from a single gene, which can, thus, perform various functions. To complete the global comparative analysis of gene expression changes, we explored patterns of alternative splicing evolution. This work uncovered several general and unexpected patterns of alternative splicing evolution (e.g., we found that alternative splicing evolves extremely rapidly) as well as a large number of conserved alternative isoforms that may be crucial for the functioning of mammalian organs.Finally, the third and final project of my PhD consisted in analyzing in detail the unique functional and evolutionary properties of the testis by exploring the extent of its transcriptome complexity. This organ was previously shown to evolve rapidly both at the phenotypic and molecular level, apparently because of the specific pressures that act on this organ and are associated with its reproductive function. Moreover, my analyses of the amniote tissue transcriptome data described above, revealed strikingly widespread transcriptional activity of both functional and nonfunctional genomic elements in the testis compared to the other organs. To elucidate the cellular source and mechanisms underlying this promiscuous transcription in the testis, we generated deep coverage RNA-Seq data for all major testis cell types as well as epigenetic data (DNA and histone methylation) using the mouse as model system. The integration of these complete dataset revealed that meiotic and especially post-meiotic germ cells are the major contributors to the widespread functional and nonfunctional transcriptome complexity of the testis, and that this "promiscuous" spermatogenic transcription is resulting, at least partially, from an overall transcriptionally permissive chromatin state. We hypothesize that this particular open state of the chromatin results from the extensive chromatin remodeling that occurs during spermatogenesis which ultimately leads to the replacement of histones by protamines in the mature spermatozoa. Our results have important functional and evolutionary implications (e.g., regarding new gene birth and testicular gene expression evolution).Generally, these three large-scale projects of my thesis provide complete and massive datasets that constitute valuables resources for further functional and evolutionary analyses of mammalian genomes.

Quantum metric spaces as a model for pregeometry

A new arena for the dynamics of spacetime is proposed, in which the basic quantum variable is the two-point distance on a metric space. The scaling dimension (that is, the Kolmogorov capacity) in the neighborhood of each point then defines in a natural way a local concept of dimension. We study our model in the region of parameter space in which the resulting spacetime is not too different from a smooth manifold.

Quantum nonlocality in two three-level systems

Recently a new Bell inequality has been introduced by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)], which is strongly resistant to noise for maximally entangled states of two d-dimensional quantum systems. We prove that a larger violation, or equivalently a stronger resistance to noise, is found for a nonmaximally entangled state. It is shown that the resistance to noise is not a good measure of nonlocality and we introduce some other possible measures. The nonmaximally entangled state turns out to be more robust also for these alternative measures. From these results it follows that two von Neumann measurements per party may be not optimal for detecting nonlocality. For d=3,4, we point out some connections between this inequality and distillability. Indeed, we demonstrate that any state violating it, with the optimal von Neumann settings, is distillable.

Minimal optimal generalized quantum measurements

Optimal and finite positive operator valued measurements on a finite number N of identically prepared systems have recently been presented. With physical realization in mind, we propose here optimal and minimal generalized quantum measurements for two-level systems. We explicitly construct them up to N = 7 and verify that they are minimal up to N = 5.

Majorization arrow in quantum-algorithm design

We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step by step until the optimal target state is found. Extensions of this situation are also found in algorithms based in quantum adiabatic evolution and the family of quantum phase-estimation algorithms, including Shor's algorithm. We state that in quantum algorithms the time arrow is a majorization arrow.

Separability and distillability of multiparticle quantum systems

We present a family of 3-qubit states to which any arbitrary state can be depolarized. We fully classify those states with respect to their separability and distillability properties. This provides a sufficient condition for nonseparability and distillability for arbitrary states. We generalize our results to N-particle states.

Generalized Schmidt decomposition and classification of three-quantum-bit states

We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.

Optimal strategies for sending information through a quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of N spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.

Exotic dynamically generated baryons with negative charm quantum number

Following a model based on the SU(8) symmetry that treats heavy pseudoscalars and heavy vector mesons on an equal footing, as required by heavy quark symmetry, we study the interaction of baryons and mesons in coupled channels within an unitary approach that generates dynamically poles in the scattering T-matrix. We concentrate in the exotic channels with negative charm quantum number for which there is the experimental claim of one state.