Quantum Hall Effect on the Flag Manifold F_2

The Landau problem on the flag manifold ${\bf F}_2 = SU(3)/U(1)\times U(1)$ is analyzed from an algebraic point of view. The involved magnetic background is induced by two U(1) abelian connections. In quantizing the theory, we show that the wavefunctions, of a non-relativistic particle living on ${\bf F}_2$, are the SU(3) Wigner ${\cal D}$-functions satisfying two constraints. Using the ${\bf F}_2$ algebraic and geometrical structures, we derive the Landau Hamiltonian as well as its energy levels. The Lowest Landau level (LLL) wavefunctions coincide with the coherent states for the mixed SU(3) representations. We discuss the quantum Hall effect for a filling factor $\nu =1$. where the obtained particle density is constant and finite for a strong magnetic field. In this limit, we also show that the system behaves like an incompressible fluid. We study the semi-classical properties of the system confined in LLL. These will be used to discuss the edge excitations and construct the corresponding Wess-Zumino-Witten action.Comment: 23 pages, two sections and references added, misprints corrected, version to appear in IJMP

A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schr\"odinger cat states

A recursive approach to determine the Hilbert-Schmidt measure of pairwise quantum discord in a special class of symmetric states of $k$ qubits is presented. We especially focus on the reduced states of $k$ qubits obtained from a balanced superposition of symmetric $n$-qubit states (multiqubit Schr\"odinger cat states) by tracing out $n-k$ particles $(k=2,3, \cdots ,n-1)$. Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the party grouping $(k-1)$ qubits is explicitly derived. This uses recursive relations between the Fano-Bloch correlation matrices associated with subsystems comprising $k$, $k-1$, $\cdots$ and $2$ particles. A detailed analysis is given for two, three and four qubit systems. In the second scheme, the subsystem comprising the $(k-1)$ qubits is mapped into a system of two logical qubits. We show that these two bipartition schemes are equivalents in evaluating the pairwise correlation in multi-qubits systems. The explicit expressions of classical states presenting zero discord are derived.Comment: 26 page

Scaling theory of DNA confined in nanochannels and nanoslits

A scaling analysis is presented of the statistics of long DNA confined in nanochannels and nanoslits. It is argued that there are several regimes in between the de Gennes and Odijk limits introduced long ago. The DNA chain folds back on itself giving rise to a global persistence length which may be very large owing to entropic deflection. Moreover, there is an orientational excluded-volume effect between the DNA segments imposed solely by the nanoconfinement. These two effects cause the chain statistics to be intricate leading to nontrivial power laws for the chain extension in the intermediate regimes. It is stressed that DNA confinement within nanochannels differs from that in nanoslits because the respective orientational excluded-volume effects are not the same.Comment: 5 pages, 1 figure Several corrections, some minor changes in the text and replacement of one referenc

Aggregation number distributions and mesoglobules in dilute solutions of diblock and triblock copolymers

We investigate the aggregation number and size distributions for inter-molecular clusters of amphiphilic diblock and triblock copolymers in poor solvent at very low concentrations. Diblocks and triblocks with hydrophilic ends are shown to possess narrow distributions corresponding to formation of monodispersed mesoglobules. Diblocks with hydrophobic ends are found to produce inter-cluster multimers due to bridging by the hydrophilic middle blocks, resulting in polydisperse distributions. Implications of these observations for preparation of monodispersed nanoparticles and, potentially, understanding of the quaternary structure of proteins are discussed.Comment: 4 pages, 4 PS figures. Accepted for publication in EP

Structure of bottle-brush brushes under good solvent conditions. A molecular dynamics study

We report a simulation study for bottle-brush polymers grafted on a rigid backbone. Using a standard coarse-grained bead-spring model extensive molecular dynamics simulations for such macromolecules under good solvent conditions are performed. We consider a broad range of parameters and present numerical results for the monomer density profile, density of the untethered ends of the grafted flexible backbones and the correlation function describing the range that neighboring grafted bottle-brushes are affected by the presence of the others due to the excluded volume interactions. The end beads of the flexible backbones of the grafted bottle-brushes do not access the region close to the rigid backbone due to the presence of the side chains of the grafted bottle-brush polymers, which stretch further the chains in the radial directions. Although a number of different correlation lengths exist as a result of the complex structure of these macromolecules, their properties can be tuned with high accuracy in good solvents. Moreover, qualitative differences with "typical" bottle-brushes are discussed. Our results provide a first approach to characterizing such complex macromolecules with a standard bead spring model.Comment: To appear in Journal of Physics Condensed Matter (2011

On supersymmetric quantum mechanics

This paper constitutes a review on N=2 fractional supersymmetric Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl-Heisenberg algebra W_k. It is shown how a general Hamiltonian can be associated with the algebra W_k. This general Hamiltonian covers various supersymmetrical versions of dynamical systems (Morse system, Poschl-Teller system, fractional supersymmetric oscillator of order k, etc.). The case of ordinary supersymmetric Quantum Mechanics corresponds to k=2. A connection between fractional supersymmetric Quantum Mechanics and ordinary supersymmetric Quantum Mechanics is briefly described. A realization of the algebra W_k, of the N=2 supercharges and of the corresponding Hamiltonian is given in terms of deformed-bosons and k-fermions as well as in terms of differential operators.Comment: Review paper (31 pages) to be published in: Fundamental World of Quantum Chemistry, A Tribute to the Memory of Per-Olov Lowdin, Volume 3, E. Brandas and E.S. Kryachko (Eds.), Springer-Verlag, Berlin, 200

Magnetism of Two Coupled Harmonic Oscillators

The thermodynamical properties of a system of two coupled harmonic oscillators in the presence of an uniform magnetic field B are investigated. Using an unitary transformation, we show that the system can be diagonalized in simple way and then obtain the energy spectrum solutions. These will be used to determine the thermodynamical potential in terms of different physical parameters like the coupling parameter \alpha. This allows us to give a generalization of already significant published work and obtain different results, those could be used to discuss the magnetism of the system. Different limiting cases, in terms of \alpha and B, have been discussed. In fact, quantum corrections to the Landau diamagnetism and orbital paramagnetism are found.Comment: 25 page