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Vacuum expectation values (VEVs) of the current densities for charged scalar and Dirac spinor fields are investigated in (D+1)-dimensional de Sitter (dS) spacetime with toroidally compactified spatial dimensions. Along compact dimensions we impose quasiperiodicity conditions with arbitrary phases. In addition, the presence of a classical constant gauge field is assumed. The VEVs of the charge density and of the components for the current density along noncompact dimensions vanish. The gauge field leads to Aharonov-Bohm-like oscillations of the components along compact dimensions as functions of the magnetic flux. For small values of the comoving length of a compact dimension, compared with the dS curvature scale, the current density is related to the corresponding current in the Minkowski spacetime by a conformal relation. For large values of the comoving length and for a scalar field, depending on the mass of the field, two different regimes are realized with the monotonic and oscillatory damping of the current density. For a massive spinor field, the decay of the current density is always oscillatory. In supersymmetric models on the background of Minkowski spacetime with equal number of scalar and fermionic degrees of freedom and with the same phases in the periodicity conditions, the total current density vanishes due to the cancellation between the scalar and fermionic parts. The background gravitational field modifies the current densities for scalar and fermionic fields in different ways and for massive fields there is no cancellation in the dS spacetime., Comment: 19 pages, 4 figures, discussion and references added

We analyze the exact perturbative solution of N=2 Born-Infeld theory which is believed to be defined by Ketov's equation. This equation can be considered as a truncation of an infinite system of coupled differential equations defining Born-Infeld action with one manifest N=2 and one hidden N=2 supersymmetries. We explicitly demonstrate that infinitely many new structures appear in the higher orders of the perturbative solution to Ketov's equation. Thus, the full solution cannot be represented as a function depending on {\it a finite number} of its arguments. We propose a mechanism for generating the new structures in the solution and show how it works up to 18-th order. Finally, we discuss two new superfield actions containing an infinite number of terms and sharing some common features with N=2 supersymmetric Born-Infeld action., Comment: 8 pages, PACS: 11.30.Pb, 12.60.Jv

We investigate combined effects of topology and boundaries on the vacuum expectation value (VEV) of the fermionic current in the space with an arbitrary number of toroidally compactified dimensions. As a geometry of boundaries we consider two parallel plates on which the fermion field obeys bag boundary conditions. Along the compact dimensions, periodicity conditions are imposed with arbitrary phases. In addition, the presence of a constant gauge field is assumed. The nontrivial topology gives rise to an Aharonov-Bohm effect for the fermionic current induced by the gauge field. It is shown that the VEV of the charge density vanishes and the current density has nonzero expectation values for the components along compact dimensions only. The latter are periodic odd functions of the magnetic flux with the period equal to the flux quantum. In the region between the plates, the VEV of the fermionic current is decomposed into pure topological, single plate and interference parts. For a massless field the single plate part vanishes and the interference part is distributed uniformly. The corresponding results are generalized for conformally-flat spacetimes. Applications of the general formulas to finite-length carbon nanotubes are given within the framework of the Dirac model for quasiparticles in graphene. In the absence of the magnetic flux, two sublattices of the honeycomb graphene lattice yield opposite contributions and the fermionic current vanishes. A magnetic flux through the cross section of the nanotube breaks the symmetry allowing the current to flow along the compact dimension., Comment: 22 pages, 5 figures

We explicitly constructed the generators of $SU(n+1)$ group which commute with the supercharges of N=4 supersymmetric $\mathbb{CP}^n$ mechanics in the background U(n) gauge fields. The corresponding Hamiltonian can be represented as a direct sum of two Casimir operators: one Casimir operator on $SU(n+1)$ group contains our bosonic and fermionic coordinates and momenta, while the second one, on the SU(1,n) group, is constructed from isospin degrees of freedom only., Comment: 10 pages, PACS numbers: 11.30.Pb, 03.65.-w; minor changes in Introduction, references added

The string corrections to the Riemann Curvature tensor are found to first order in the string slope parameter, here proportional to $\g$. This is done for D=10 supergravity, the presumed low energy limit of string theory. We follow the perturbative approach. We also simplify a crucial result in our previous solution., Comment: 7 pages, LaTeX file, PACS number: 04.65.+e, a few typos in the Conclusion were corrected

New crystal technique - array of bent strips and a fan-type reflector, based on thin straight plates - have been used for research of extraction and collimation a circulating beam in the U-70 accelerator at the energy 50 GeV and 1.3 GeV. It is shown, that new devices can effectively steer a beam in a wide energy range. For protons with energy 50 GeV efficiency of extraction and collimation about 90 % has been achieved which is record for this method. Reduction of particle losses in 2-3 times was observed also in accelerator at application of different crystals in comparison with the usual one-stage collimation scheme of beam with a steel absorber., Comment: 14 pages, 12 figures

The fermionic condensate is investigated in a (2+1)-dimensional conical spacetime in the presence of a circular boundary and a magnetic flux. It is assumed that on the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, we consider a special case of boundary conditions at the cone apex, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The fermionic condensate is a periodic function of the magnetic flux with the period equal to the flux quantum. For both exterior and interior regions, the fermionic condensate is decomposed into boundary-free and boundary-induced parts. Two integral representations are given for the boundary-free part for arbitrary values of the opening angle of the cone and magnetic flux. At distances from the boundary larger than the Compton wavelength of the fermion particle, the condensate decays exponentially with the decay rate depending on the opening angle of the cone. If the ratio of the magnetic flux to the flux quantum is not a half-integer number, for a massless field the boundary-free part in the fermionic condensate vanishes, whereas the boundary-induced part is negative. For half-integer values of the ratio of the magnetic flux to the flux quantum, the irregular mode gives non-zero contribution to the fermionic condensate in the boundary-free conical space., Comment: 23 pages, 6 figures

This paper presents the intrinsic geometric model for the solution of power system planning and its operation. This problem is large-scale and nonlinear, in general. Thus, we have developed the intrinsic geometric model for the network reliability and voltage stability, and examined it for the IEEE 5 bus system. The robustness of the proposed model is illustrated by introducing variations of the network parameters. Exact analytical results show the accuracy as well as the efficiency of the proposed solution technique., Comment: 8 pages, 4 figures, 2 tables, Index Terms -- Circuit modeling, geometric modeling, parameter space method, power system reliability, power system stability, transmission planning, nonlinear methods, geometric controls, components optimization

Under the fluctuation of the electric charge and atomic mass, this paper considers the theory of the thin film depletion layer formation of an ensemble of finitely excited, non-empty $d/f$-orbital heavy materials, from the thermodynamic geometric perspective. At each state of the local adiabatic evolutions, we examine the nature of the thermodynamic parameters, \textit{viz.}, electric charge and mass, changing at each respective embeddings. The definition of the intrinsic Riemannian geometry and differential topology offers the properties of (i) local heat capacities, (ii) global stability criterion and (iv) global correlation length. Under the Gaussian fluctuations, such an intrinsic geometric consideration is anticipated to be useful in the statistical coating of the thin film layer of a desired quality-fine high cost material on a low cost durable coatant. From the perspective of the daily-life applications, the thermodynamic geometry is thus intrinsically self-consistent with the theory of the local and global economic optimizations. Following the above procedure, the quality of the thin layer depletion could self-consistently be examined to produce an economic, quality products at a desired economic value., Comment: 22 pages, 5 figures, Keywords: Thermodynamic Geometry, Metal Depletion, Nano-science, Thin Film Technology, Quality Economic Characterization; added 1 figure and 1 section (n.10), and edited bibliography

The attractor mechanism in five dimensional Einstein-Maxwell Chern-Simons theory is studied. The expression of the five dimensional rotating black object potential depending on Taub-NUT, electric and magnetic charges as well as on all the scalar and gauge fields, is investigated. The first order formalism in d=5 is constructed and analyzed. We derive a general expression defining the fake superpotential which is valid for all charge configurations. An explicit expression for the fake superpotential is constructed, for all very special geometries, in the case of vanishing Taub-NUT charge. We carry out an analogous construction in the very special geometries corresponding to $t^3$ and $stu$ models, for the most general charge configurations. The attractor flows and horizon values of all fields are given., Comment: 33 pages, PACS numbers: 04.65.+e, 04.50.Gh, 04.70.Bw, 04.70.Dy, keywords: five dimensional supergravity, black objects, entropy, attractor flows, first order formalism, fake superpotential. Several typos corrected; one reference added; section 6 (conclusions) expanded

This work explores the role of thermodynamic fluctuations in the two parameter Hawking radiating black hole configurations. The system is characterized by an ensemble of arbitrary mass and radiation frequency of the black holes. In the due course of the Hawking radiations, we find that the intrinsic geometric description exhibits an intriguing set of exact pair correction functions and global correlation lengths. We investigate the nature of the constant amplitude radiation and find that it's not stable under fluctuations of the mass and frequency. Subsequently, the consideration of the York model decreasing amplitude radiation demonstrates that thermodynamic fluctuations are globally stable in the small frequency region. In connection with quantum gravity refinements, we take an account of the logarithmic correction into the constant amplitude and York amplitude over the Hawking radiation. In both considerations, we notice that the nature of the possible parametric fluctuations may precisely be ascertained without any approximation. In the frequency domain $w \in (0, \infty)$, we observe that both the local and the global thermodynamic fluctuations of the radiation energy flux are stable in the s-channel. The intrinsic geometry exemplifies a definite stability character to the thermodynamic fluctuations, and up to finitely many topological defects on the parametric surface, the notion remains almost the same for both the constant amplitude and the York model. The Gaussian fluctuations over equilibrium radiation energy flux and fluctuating horizon configurations accomplish a well-defined, non-degenerate, curved and regular intrinsic Riemannian manifolds, for all the physically admissible domains of the radiation parameters. PACS numbers: 04.70.-s: Physics of black holes; 04.70.-Bw: Classical black holes; 04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics; 04.60.Cf Gravitational aspects of string theory. Keywords: Quantum Gravity, Hawking Radiation; Horizon Perturbations; Vaidya Geometry; York Model; Statistical Fluctuations; Thermodynamic Configurations, Comment: 38 pages, 12 figures

The vacuum expectation value of the fermionic current is evaluated for a massive spinor field in spacetimes with an arbitrary number of toroidally compactified spatial dimensions in presence of a constant gauge field. By using the Abel-Plana type summation formula and the zeta function technique we present the fermionic current in two different forms. Non-trivial topology of the background spacetime leads to the Aharonov-Bohm effect on the fermionic current induced by the gauge field. The current is a periodic function of the magnetic flux with the period equal to the flux quantum. In the absence of the gauge field it vanishes for special cases of untwisted and twisted fields. Applications of the general formulae to Kaluz-Klein type models and to cylindrical and toroidal carbon nanotubes are given. In the absence of magnetic flux the total fermionic current in carbon nanotubes vanishes, due to the cancellation of contributions from two different sublattices of the graphene hexagonal lattice., Comment: 18 pages, 5 figures, explicit regularization procedure added

We compute the effective black hole potential V of the most general N=2, d=4 (local) special Kaehler geometry with quantum perturbative corrections, consistent with axion-shift Peccei-Quinn symmetry and with cubic leading order behavior. We determine the charge configurations supporting axion-free attractors, and explain the differences among various configurations in relations to the presence of ``flat'' directions of V at its critical points. Furthermore, we elucidate the role of the sectional curvature at the non-supersymmetric critical points of V, and compute the Riemann tensor (and related quantities), as well as the so-called E-tensor. The latter expresses the non-symmetricity of the considered quantum perturbative special Kaehler geometry., Comment: 1+43 pages; v2: typo corrected in the curvature of Jordan symmetric sequence at page 29

We evaluate the Casimir energy and force for a massive fermionic field in the geometry of two parallel plates on background of Minkowski spacetime with an arbitrary number of toroidally compactified spatial dimensions. The bag boundary conditions are imposed on the plates and periodicity conditions with arbitrary phases are considered along the compact dimensions. The Casimir energy is decomposed into purely topological, single plate and interaction parts. With independence of the lengths of the compact dimensions and the phases in the periodicity conditions, the interaction part of the Casimir energy is always negative. In order to obtain the resulting force, the contributions from both sides of the plates must be taken into account. Then, the forces coming from the topological parts of the vacuum energy cancel out and only the interaction term contributes to the Casimir force. Applications of the general formulae to Kaluza-Klein type models and carbon nanotubes are given. In particular, we show that for finite length metallic nanotubes the Casimir forces acting on the tube edges are always attractive, whereas for semiconducting-type ones they are attractive for small lengths of the nanotube and repulsive for large lengths., Comment: 20 pages, 3 figures

Higher order derivative corrections to the Einstein--Maxwell action are considered and an explicit form is found for the corrections to the entropy of extremal black holes. We speculate on the properties of these corrections from the point of view of small black holes and in the case when the classical black hole potential exhibits flat directions. A particular attention is paid to the issue of stability of several solutions, including large and small black holes by using properties of the Hessian matrix of the effective black hole potential. This is done by using a model independent expression for such matrix derived within the entropy function formalism., Comment: 21 pages, PACS numbers: 04.50.Gh, 04.70.Dy, 04.65.+e

We report on recent results in the study of extremal black hole attractors in N=2, d=4 ungauged Maxwell-Einstein supergravities. For homogeneous symmetric scalar manifolds, the three general classes of attractor solutions with non-vanishing Bekenstein-Hawking entropy are discussed. They correspond to three (inequivalent) classes of orbits of the charge vector, which sits in the relevant symplectic representation R_{V} of the U-duality group. Other than the 1/2-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge. The complete classification of the U-duality orbits, as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon), is also reviewed. Finally, we consider the analogous classification for N>2-extended, d=4 ungauged supergravities, in which also the 1/N-BPS attractors yield a related moduli space., Comment: 1+29 pages, 8 Tables. Contribution to the Proceedings of the School on Attractor Mechanism 2007 (SAM2007), June 18--22 2007, INFN--LNF, Frascati, Italy

Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for a massive spinor fields in higher-dimensional spacetimes with an arbitrary number of toroidally compactified spatial dimensions. By using the Abel-Plana summation formula and the zeta function technique we present the vacuum expectation values in two different forms. Applications of the general formulae to cylindrical and toroidal carbon nanotubes are given. We show that the topological Casimir energy is positive for metallic cylindrical nanotubes and is negative for semiconducting ones. The toroidal compactification of a cylindrical nanotube along its axis increases the Casimir energy for metallic-type (periodic) boundary conditions along its axis and decreases the Casimir energy for the semiconducting-type compactifications., Comment: 17 pages, 3 figures

Alternative theories of gravity predict the presence of massive scalar, vector, and tensor gravitational wave modes in addition to the standard massless spin~2 graviton of general relativity. The deflection and frequency shift effects on light from distant sources propagating through a stochastic background of gravitational waves, containing such modes, differ from their counterparts in general relativity. Such effects are considered as a possible signature for alternative gravity in attempts to detect deviations from Einstein's gravity by astrophysical means., Comment: 9 pages, 1 figure

We study N=2, d=4 attractor equations for the quantum corrected two-moduli prepotential $\mathcal{F}=st^2+i\lambda$, with $\lambda$ real, which is the only correction which preserves the axion shift symmetry and modifies the geometry. In the classical case the black hole effective potential is known to have a flat direction. We found that in the presence of D0-D6 branes the black hole potential exhibits a flat direction in the quantum case as well. It corresponds to non-BPS $Z\neq 0$ solutions to the attractor equations. Unlike the classical case, the solutions acquire non-zero values of the axion field. For the cases of D0-D4 and D2-D6 branes the classical flat direction reduces to separate critical points which turn out to have a vanishing axion field., Comment: 11 pages, 5 figures

The general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing central charge Z and for Z=0, are obtained for the so-called stu model, the minimal rank-3 N=2 symmetric supergravity in d=4 space-time dimensions. Comparisons with previous results, as well as the fake supergravity (first order) formalism and an analysis of the BPS bound all along the non-BPS attractor flows and of the marginal stability of corresponding D-brane configurations, are given., Comment: 1+40 pages; v2: various typos fixed; v3: improved version, with the BPS bound for ADM mass obtained for all non-BPS configurations, both with non-vanishing and vanishing central charge

We consistently incorporate Yang Mills matter fields into string corrected (deformed), D=10, N=1 Supergravity. We solve the Bianchi identities within the framework of the modified beta function favored constraints to second order in the string slope parameter $\g$ also including the Yang Mills fields. In the torsion, curvature and H sectors we find that a consistent solution is readily obtained with a Yang Mills modified supercurrent $A_{abc}$. We find a solution in the F sector following our previously developed method., Comment: 11 pages, LaTeX file, PACS number: 04.65.+e

The motion of a particle near the Reissner-Nordstrom black hole horizon is described by conformal mechanics. In this paper we present an extended one-dimensional analysis of the N=4 superconformal mechanics coupled to n copies of N=8, d=1 vector supermultiplets. The constructed system possesses a special Kahler geometry in the scalar sector of the vector multiplets as well as an N=4 superconformal symmetry which is provided by a proper coupling to a dilaton superfield. The superconformal symmetry completely fixes the resulting action. We explicitly demonstrate that the electric and magnetic charges, presenting in the "effective black hole" action, appear as a result of resolving constraints on the auxiliary components of the vector supermultiplets. We present the component action, supercharges and Hamiltonian with all fermionic terms included. One of the possible ways to generalize the black hole potential is to consider a modified version of the N=4 superconformal multiplet where its auxiliary components acquire non-zero constant values. We explicitly write down the corresponding modified black hole potential., Comment: 1+11 pages, no figures. v2: two references added, minor modifications in conclusion

We give a complete and consistent solution to string corrected (deformed), D=10, N=1 supergravity as the non-minimal low energy limit of string theory. We solve the Bianchi identities with suitable constraints to second order in the string slope parameter. In so doing we pave the way for continuing the study of the many applications of these results. We also modify, reaffirm and correct a previously given incomplete solution, and we introduce an important adjustment to the known first order results., Comment: 11 pages, PACS number: 04.65.+e, to be published in: Problems of Modern Theoretical Physics. Tomsk State Pedagogical University Press, Tomsk, 2008

We constructed the most general N=4 superconformal 3-particles systems with translation invariance. In the basis with decoupled center of mass the supercharges and Hamiltonian possess one arbitrary function which defines all potential terms. We have shown that with the proper choice of this function one may describe the standard, $A_2$ Calogero model as well as $BC_2, B_2,C_2$ and $D_2$ Calogero models with N=4 superconformal symmetry. The main property of all these systems is that even with the coupling constant equal to zero they still contain nontrivial interactions in the fermionic sector. In other words, there are infinitely many non equivalent N=4 supersymmetric extensions of the free action depending on one arbitrary function. We also considered quantization and explicitly showed how the supercharges and Hamiltonian are modified., Comment: 13 pages, LaTeX file, PACS: 11.30.Pb, 03.65.-w

We review recent results in the study of attractor horizon geometries (with non-vanishing Bekenstein-Hawking entropy) of dyonic extremal d=4 black holes in supergravity. We focus on N=2, d=4 ungauged supergravity coupled to a number n_{V} of Abelian vector multiplets, outlining the fundamentals of the special Kaehler geometry of the vector multiplets' scalar manifold (of complex dimension n_{V}), and studying the 1/2-BPS attractors, as well as the non-BPS (non-supersymmetric) ones with non-vanishing central charge. For symmetric special Kaehler geometries, we present the complete classification of the orbits in the symplectic representation of the classical U-duality group (spanned by the black hole charge configuration supporting the attractors), as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon). Finally, we report on an analogous classification for N>2-extended, d=4 ungauged supergravities, in which also the 1/N-BPS attractors yield a related moduli space., Comment: 1+31 pages, 5 tables. Contribution to the Proceedings of the 3rd RTN Workshop ``Constituents, Fundamental Forces and Symmetries of the Universe'', 1-5 October 2007, Valencia, Spain

We investigate the Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor for a scalar field with general curvature coupling parameter in $(D+1)$-dimensional de Sitter spacetime with an arbitrary number of compactified spatial dimensions. Both cases of periodicity and antiperiodicity conditions along the compactified dimensions are considered. Recurrence formulae are derived which express the vacuum expectation values for the dS spacetime of topology $\mathrm{R}^{p}\times (\mathrm{S}^{1})^{q}$ in the form of the sum of the vacuum expectation values in the topology $\mathrm{R}^{p+1}\times (\mathrm{S}^{1})^{q-1}$ and the part induced by the compactness of the $(p+1)$th spatial dimension. The behavior of the topological parts is investigated in various asymptotic regions of the parameters. In the early stages of the cosmological evolution the topological parts dominate the contribution in the expectation values due to the uncompactified dS part. In this limit the behavior of the topological parts does not depend on the curvature coupling parameter and coincides with that for a conformally coupled massless field. At late stages of the cosmological expansion the expectation values are dominated by the part corresponding to uncompactified dS spacetime. The vanishing of the topological parts is monotonic or oscillatory in dependence of the mass and the curvature coupling parameter of the field., Comment: 17 pages, 4 figures

We generalize the description of the d=4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and they can be extended to d>4, as well. Thence, we work out the example of the stu model of N=2 supergravity in the presence of Fayet-Iliopoulos terms, for the supergravity analogues of the magnetic and D0-D6 BH charge configurations, and in three different symplectic frames: the SO(1,1)^{2}, SO(2,2) covariant and SO(8)-truncated ones. The attractive nature of the critical points, related to the semi-positive definiteness of the Hessian matrix, is also studied., Comment: 1+33 pages

These lectures provide a pedagogical, introductory review of the so-called Attractor Mechanism (AM) at work in two different 4-dimensional frameworks: extremal black holes in N=2 supergravity and N=1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and magnetic charges, whereas in the second context the AM is responsible for the stabilization of the universal axion-dilaton and of the (complex structure) moduli purely in terms of the RR and NSNS fluxes. Two equivalent approaches to AM, namely the so-called ``criticality conditions'' and ``New Attractor'' ones, are analyzed in detail in both frameworks, whose analogies and differences are discussed. Also a stringy analysis of both frameworks (relying on Hodge-decomposition techniques) is performed, respectively considering Type IIB compactified on $CY_{3}$ and its orientifolded version, associated with $\frac{CY_{3}\times T^{2}}{\mathbb{Z}_{2}}$. Finally, recent results on the U-duality orbits and moduli spaces of non-BPS extremal black hole attractors in $3\leqslant N\leqslant 8$, d=4 supergravities are reported., Comment: 1+74 pages, 2 Tables. Contribution to the Proceedings of the Winter School on Attractor Mechanism 2006 (SAM2006), 20-24 March 2006, INFN-LNF, Frascati, Italy

We propose a unified superfield formulation of N=4 off-shell supermultiplets in one spacetime dimension using the standard N=4 superspace. The main idea of our approach is a "gluing" together of two linear supermultiplets along their fermions. The functions defining such a gluing obey a system of equations. Each solution of this system provides a new supermultiplet, linear or nonlinear, modulo equivalence transformations. In such a way we reproduce all known linear and nonlinear N=4, d=1 supermultiplets and propose some new ones. Particularly interesting is an explicit construction of nonlinear N=4 hypermultiplets., Comment: 16 pages, no figures

We study the attractor equations for a quantum corrected prepotential F=t^3+i\lambda, with \lambda \in R,which is the only correction which preserves the axion shift symmetry and modifies the geometry. By performing computations in the ``magnetic'' charge configuration, we find evidence for interesting phenomena (absent in the classical limit of vanishing \lambda). For a certain range of the quantum parameter \lambda we find a ``separation'' of attractors, i.e. the existence of multiple solutions to the Attractor Equations for fixed supporting charge configuration. Furthermore, we find that, away from the classical limit, a ``transmutation'' of the supersymmetry-preserving features of the attractors takes place when \lambda reaches a particular critical value., Comment: 1+24 pages, 11 figures; v2: new section added; v3: change in title, minor updates, published version

Quantum interference effects in rings provide suitable means for controlling spin at mesoscopic scales. Here we apply such a control mechanism to the spin-dependent transport in a ballistic quasi one dimensional ring patterned in two dimensional electron gases (2DEGs). The study is essentially based on the {\it natural} spin-orbit (SO) interactions, one arising from the laterally confining electric field {($\beta$ term) and the other due to to the quantum-well potential that confines electrons in the 2DEG (conventional Rashba SO interaction or $\alpha$ term).} We focus on single-channel transport and solve analytically the spin polarization of the current. As an important consequence of the presence of spin splitting, we find the occurrence of spin dependent current oscillations. We analyze %the effects of disorder by discussing the transport in the presence of one non-magnetic obstacle in the ring. We demonstrate that a spin polarized current can be induced when an unpolarized charge current is injected in the ring, by focusing on the central role that the presence of the obstacle plays., Comment: 9 pages, 7 figures, PACS numbers: 72.25.-b, 72.20.My, 73.50.Jt, accepted for publication in J. Phys. - Cond. Mat

We propose a new scheme of spin filtering employing ballistic nanostructures in two dimensional electron gases (2DEGs). The proposal is essentially based on the spin-orbit (SO) interaction arising from the lateral confining electric field. This sets the basic difference with other works employing ballistic crosses and T junctions with the conventional SO term arising from 2DEG confinement. We discuss the consequences of this different approach on magnetotransport properties of the device, showing that the filter can in principle be used not only to generate a spin polarized current but also to perform an electric measurement of the spin polarization of a charge current. We focus on single-channel transport and investigate numerically the spin polarization of the current., Comment: 6 pages, 5 figures, PACS numbers: 72.25.-b, 72.20.My, 73.50.Jt, accepted for publication in J. Phys. - Cond. Mat

We propose a new scheme of spin filtering based on nanometric crossjunctions in the presence of Spin Orbit interaction, employing ballistic nanojunctions patterned in a two-dimensional electron gas. We demonstrate that the flow of a longitudinal unpolarized current through a ballistic X junction patterned in a two-dimensional electron gas with Spin Orbit coupling (SOC) induces a spin accumulation which has opposite signs for the two lateral probes. This spin accumulation, corresponding to a transverse pure spin current flowing in the junction, is the main observable signature of the spin Hall effect in such nanostructures. We benchmark the effects of two different kinds of Spin Orbit interactions. The first one ($\alpha$-SOC) is due to the interface electric field that confines electrons to a two-dimensional layer, whereas the second one ($\beta$-SOC) corresponds to the interaction generated by a lateral confining potential., Comment: 6 pages, 3 figures

We discuss the Luttinger Liquid behaviour of Large Radius Carbon Nanotube e.g. the Multi Wall ones (MWNT), under the action of a transverse magnetic field $B$. Our results imply a reduction with $B$ in the value of the $bulk$ critical exponent, $\alpha_{bulk}$, for the tunneling density of states, which is in agreement with that observed in transport experiments. Then, the problem of the transport through a Quantum Dot formed by two intramolecular tunneling barriers along the MWNT, weakly coupled to Tomonaga-Luttinger liquids is studied, including the action of a strong transverse magnetic field $B$. {We predict the presence of some peaks in the conductance G versus $B$, related to the magnetic flux quantization in the ballistic regime (at a very low temperature, $T$) and also at higher $T$, where the Luttinger behaviour dominates}. The temperature dependence of the maximum $G_{max}$ of the conductance peak according to the Sequential Tunneling follows a power law, $G\propto T^{\gamma_e-1}$ with $\gamma_e$ linearly dependent on the critical exponent, $\alpha_{end}$, strongly reduced by $B$., Comment: 8 pages, 3 figures, PACS numbers: 05.60.Gg, 71.10.Pm, 73.63.-b, 71.20.Tx, 72.80.Rj

We develop a long wavelength approximation in order to describe the low-energy states of carbon nanotubes in a transverse magnetic field. We show that, in the limit where the square of the magnetic length $l = \sqrt{\hbar c /e B}$ is much larger than the $C$-$C$ distance times the nanotube radius $R$, the low-energy theory is given by the linear coupling of a two-component Dirac spinor to the corresponding vector potential. We investigate in this regime the evolution of the band structure of zig-zag nanotubes for values of $R/l > 1$, showing that for radius $R \approx 20$ nm a clear pattern of Landau levels start to develop for magnetic field strength $B \gtrsim 10$ T. The levels tend to be four-fold degenerate, and we clarify the transition to the typical two-fold degeneracy of graphene as the nanotube is unrolled to form a curved strip. We show that the dynamics of the Dirac fermions leads to states which are localized at the flanks of the nanotube and that carry chiral currents in the longitudinal direction. We discuss the possibility to observe the quantization of the Hall conductivity in thick carbon nanotubes, which should display steps at even multiples of $2 e^2/h$, with values doubled with respect to those in the odd-integer quantization of graphene., Comment: To appear in Phys. Rev. B

We consider the Attractor Equations of particular $\mathcal{N}=2$, d=4 supergravity models whose vector multiplets' scalar manifold is endowed with homogeneous symmetric cubic special K\"{a}hler geometry, namely of the so-called $st^{2}$ and $stu$ models. In this framework, we derive explicit expressions for the critical moduli corresponding to non-BPS attractors with vanishing $\mathcal{N}=2$ central charge. Such formul\ae hold for a generic black hole charge configuration, and they are obtained without formulating any \textit{ad hoc} simplifying assumption. We find that such attractors are related to the 1/2-BPS ones by complex conjugation of some moduli. By uplifting to $\mathcal{N}=8$, d=4 supergravity, we give an interpretation of such a relation as an exchange of two of the four eigenvalues of the $\mathcal{N}=8$ central charge matrix $Z_{AB}$. We also consider non-BPS attractors with non-vanishing $\mathcal{Z}$; for peculiar charge configurations, we derive solutions violating the Ansatz usually formulated in literature. Finally, by group-theoretical considerations we relate Cayley's hyperdeterminant (the invariant of the stu model) to the invariants of the st^{2} and of the so-called t^{3} model., Comment: 17 pages, LaTeX file

Starting from quaternionic N=8 supersymmetric mechanics we perform a reduction over a bosonic radial variable, ending up with a nonlinear off-shell supermultiplet with three bosonic end eight fermionic physical degrees of freedom. The geometry of the bosonic sector of the most general sigma-model type action is described by an arbitrary function obeying the three dimensional Laplace equation on the sphere S^3. Among the bosonic components of this new supermultiplet there is a constant which gives rise to potential terms. After dualization of this constant one may come back to the supermultiplet with four physical bosons. However, this new supermultiplet is highly nonlinear. The geometry of the corresponding sigma-model action is briefly discussed., Comment: 9 pages, LaTeX file, PACS: 11.30.Pb, 03.65.-w

Proceeding from the superfield action for $N=4, d=1$ nonlinear supermultiplet, equipped with the most general potential term, we find the action describing a charged particle on the sphere $S^3$ in the field of $n$ fixed Dirac dyons. We construct the supercharges and Hamiltonian and analyze some particulary interesting potentials corresponding to the N=4 supersymmetric extension of the integrable one- and two-center McIntosh--Cisneros--Zwanziger--Kepler (MICZ-Kepler) systems on $S^3$., Comment: 8 pages, PACS: 11.30.Pb, 03.65.-w; corrected a misprint in (3.12), added the last sentence on page 3, added the paragraph after (3.7), added the sentence after (4.5)

We investigate the electronic instabilities in carbon nanotubes (CNs), looking for the break-down of the one dimensional Luttinger liquid regime due to the strong screening of the long-range part of the Coulomb repulsion. We show that such a breakdown is realized both in ultra-small single wall CNs and multi wall CNs, while a purely electronic mechanism could explain the superconductivity (SC) observed recently in ultra-small (diameter $ \sim 0.4 nm$) single wall CNs ($T_c\sim 15 ^{o}K$) and entirely end-bonded multi-walled ones ($T_c\sim 12 ^{o}K$). We show that both the doping and the screening of long-range part of the electron-electron repulsion, needed to allow the SC phase, are related to the intrinsically 3D nature of the environment where the CNs operate., Comment: 5 pages, 3 figures, PACS: 71.10.Pm,74.50.+r,71.20.Tx, to appear in J. Phys. Cond. Mat

A theoretical analysis of the superconductivity observed recently in Carbon nanotubes is proposed. We argue that ultra-small (diameter $ \sim 0.4 nm$) single wall carbon nanotubes (with transition temperature $T_c\sim 15 ^{o}K$) and entirely end-bonded multi-walled ones ($T_c\sim 12 ^{o}K$) can superconduct by an electronic mechanism, basically the same in both cases. By a Luttinger liquid -like approach, one finds enhanced superconducting correlations due to the strong screening of the long-range part of the Coulomb repulsion. Based on this finding, we perform a detailed analysis on the resulting Hubbard-like model, and calculate transition temperatures of the same order of magnitude as the measured ones., Comment: 6 pages, 1 figure, PACS: 71.10.Pm,74.50.+r,71.20.Tx, to appear in Phys. Rev. B

We show that a nanometric four-probe ballistic junction can be used to check the presence of a transverse spin Hall current in a system with a Spin Orbit coupling not of the Rashba type, but rather due to the in-plane electric field. Indeed, the spin Hall effect is due to the presence of an effective small transverse magnetic field corresponding to the Spin Orbit coupling generated by the confining potential. The strength of the field and the junction shape characterize the quenching Hall regime, usually studied by applying semi-classical approaches. We discuss how a quantum mechanical relativistic effect, such as the Spin Orbit one, can be observed in a low energy system and explained by using classical mechanics techniques., Comment: 5 pages, 4 figures, PACS: 72.25.-b, 72.20.My, 73.50.Jt, to appear in Phys. Rev. B

We analyse the geometry of four-dimensional bosonic manifolds arising within the context of $N=4, D=1$ supersymmetry. We demonstrate that both cases of general hyper-K\"ahler manifolds, i.e. those with translation or rotational isometries, may be supersymmetrized in the same way. We start from a generic N=4 supersymmetric three-dimensional action and perform dualization of the coupling constant, initially present in the action. As a result, we end up with explicit component actions for $N=4, D=1$ nonlinear sigma-models with hyper-K\"ahler geometry (with both types of isometries) in the target space. In the case of hyper-K\"ahler geometry with translational isometry we find that the action possesses an additional hidden N=4 supersymmetry, and therefore it is N=8 supersymmetric one., Comment: 8 pages, PACS: 11.30.Pb, 03.65.-w

We construct the general action for $N=4, d=1$ nonlinear supermultiplet including the most general interaction terms which depend on the arbitrary function $h$ obeying the Laplace equation on $S^3$. We find the bosonic field $B$ which depends on the components of nonlinear supermultiplet and transforms as a full time derivative under N=4 supersymmetry. The most general interaction is generated just by a Fayet-Iliopoulos term built from this auxiliary component. Being transformed through a full time derivative under $N=4, d=1$ supersymmetry, this auxiliary component $B$ may be dualized into a fourth scalar field giving rise to a four dimensional $N=4, d=1$ sigma-model. We analyzed the geometry in the bosonic sector and find that it is not a hyper-K\"ahler one. With a particular choice of the target space metric $g$ the geometry in the bosonic sector coincides with the one which appears in heterotic $(4,0)$ sigma-model in $d=2$., Comment: 9 pages, LaTeX file, PACS: 11.30.Pb, 03.65.-w