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Stefano Bellucci

Publications and source records attributed to Stefano Bellucci.

At least 73 records · Page 4Linked to original sources
arXiv2006

Hamiltonian reduction and supersymmetric mechanics with Dirac monopole

We apply the technique of Hamiltonian reduction for the construction of three-dimensional ${\cal N}=4$ supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional ${\cal N}=4$ supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparison with previous work is also carried out.

hep-th↗
arXiv2006

Correlated Nanoscopic Josephson Junctions

We discuss correlated lattice models with a time-dependent potential across a barrier and show how to implement a Josephson-junction-like behavior. The pairing occurs by a correlation effect enhanced by the symmetry of the system. In order to produce the effect we need a mild distortion which causes avoided crossings in the many-body spectrum. The Josephson-like response involves a quasi-adiabatic evolution in the time-dependent field. Besides, we observe an inverse-Josephson (Shapiro) current by applying an AC bias; a supercurrent in the absence of electromotive force can also be excited. The qualitative arguments are supported by explicit exact solutions in prototype 5-atom clusters with on-site repulsion. These basic units are then combined in ring-shaped systems, where one of the units sits at a higher potential and works as a barrier. In this case the solution is found by mapping the low-energy Hamiltonian into an effective anisotropic Heisenberg chain. Once again, we present evidence for a superconducting flux quantization, i.e. a Josephson-junction-like behavior suggesting the build-up of an effective order parameter already in few-electron systems. Some general implications for the quantum theory of transport are also briefly discussed, stressing the nontrivial occurrence of asymptotic current oscillations for long times in the presence of bound states.

cond-mat.supr-con↗
arXiv2006

On some properties of the Attractor Equations

We discuss the Attractor Equations of N=2, $d=4$ supergravity in an extremal black hole background with arbitrary electric and magnetic fluxes (charges) for field-strength two-forms. The effective one-dimensional Lagrangian in the radial (evolution) variable exhibits features of a spontaneously broken supergravity theory. Indeed, non-BPS Attractor solutions correspond to the vanishing determinant of a (fermionic) gaugino mass matrix. The stability of these solutions is controlled by the data of the underlying Special Kähler Geometry of the vector multiplets' moduli space. Finally, after analyzing the 1-modulus case more in detail, we briefly comment on the choice of the Kähler gauge and its relevance for the recently discussed entropic functional.

hep-th↗
arXiv2006

A Journey Through Garden Algebras

The main purpose of these lectures is to give a pedagogical overview on the possibility to classify and relate off-shell linear supermultiplets in the context of supersymmetric mechanics. A special emphasis is given to a recent graphical technique that turns out to be particularly effective for describing many aspects of supersymmetric mechanics in a direct and simplifying way.

hep-th↗
arXiv2006

Hyperboloid, instanton, oscillator

We suggest the exactly solvable model of the oscillator on a four-dimensional hyperboloid which interacts with a SU(2) instanton. We calculate its wavefunctions and spectrum.

hep-th↗
arXiv2005

A surprise in mechanics with nonlinear chiral supermultiplet

We show that the nonlinear chiral supermultiplet allows one to construct, over given two-dimensional bosonic mechanics, the family of two-dimensional ${\cal N}=4$ supersymmetric mechanics parameterized with the holomorphic function $λ(z)$. We show, that this family includes, as a particular case, the ${\cal N}=4$ superextensions of two-dimensional mechanics with magnetic fields, which have factorizable Schroedinger equations.

hep-th↗
arXiv2005

Noncommutative Coulombic Monopole

We have constructed the appropriate Hamiltonian of the noncommutative coulombic monopole (i.e. the noncommutative hydrogen atom with a monopole). The energy levels of this system have been calculated, discussed and compared with the noncommutative hydrogen atom ones. The main emphasis is put on the ground state. In addition, the Stark effect for the noncommutative coulombic monopole has been studied.

hep-th↗
arXiv2005

On matrix models for anomalous dimensions of super Yang-Mills theory

We consider the matrix model approach to the anomalous dimension matrix in $\mathcal{N}=4$ super Yang--Mills theory. We construct the path integral representation for the anomalous dimension density matrix and analyze the resulting action. In particular, we consider the large $N$ limit, which results in a classical field theory. Since the same limit leads to spin chains, we propose to consider the former as an alternative description of the latter. We consider also the limit of small $N$, which corresponds to the restriction to the diagrams of maximal topological genus.

hep-th↗
arXiv2005

(Super)Oscillator on CP(N) and Constant Magnetic Field

We define the "maximally integrable" isotropic oscillator on CP(N) and discuss its various properties, in particular, the behaviour of the system with respect to a constant magnetic field. We show that the properties of the oscillator on CP(N) qualitatively differ in the N>1 and N=1 cases. In the former case we construct the ``axially symmetric'' system which is locally equivalent to the oscillator. We perform the Kustaanheimo-Stiefel transformation of the oscillator on CP(2) and construct some generalized MIC-Kepler problem. We also define a N=2 superextension of the oscillator on CP(N) and show that for N>1 the inclusion of a constant magnetic field preserves the supersymmetry of the system.

hep-th↗
arXiv2004

Noncommutative Quantum Scattering in a Central Field

In this paper the problem of noncommutative elastic scattering in a central field is considered. General formulas for the differential cross-section for two cases are obtained. For the case of high energy of an incident wave it is shown that the differential cross-section coincides with that on the commutative space. For the case in which noncommutativity yields only a small correction to the central potential it is shown that the noncommutativity leads to the redistribution of particles along the azimuthal angle, although the whole cross-section coincides with the commutative case.

hep-th↗
arXiv2004

Quantum Oscillator on $\DC P^n$ in a constant magnetic field

We construct the quantum oscillator interacting with a constant magnetic field on complex projective spaces $\DC P^N$, as well as on their non-compact counterparts, i. e. the $N-$dimensional Lobachewski spaces ${\cal L}_N$. We find the spectrum of this system and the complete basis of wavefunctions. Surprisingly, the inclusion of a magnetic field does not yield any qualitative change in the energy spectrum. For $N>1$ the magnetic field does not break the superintegrability of the system, whereas for N=1 it preserves the exact solvability of the system. We extend this results to the cones constructed over $\DC P^N$ and ${\cal L}_N$, and perform the (Kustaanheimo-Stiefel) transformation of these systems to the three-dimensional Coulomb-like systems.

hep-th↗
arXiv2004

Quantum Mechanics Model on Kähler conifold

We propose an exactly-solvable model of the quantum oscillator on the class of Kähler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has non-constant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction and quantization procedures, the Hamiltonian of the reduced system gets non-trivial quantum corrections. We transform the reduced system into a MIC-Kepler-like one and find that quantum corrections arise only in its energy and coupling constant. We present the exact spectrum of the generalized MIC-Kepler system. The one-(complex) dimensional analog of the suggested model is formulated on the Riemann surface over the complex projective plane and could be interpreted as a system with fractional spin.

hep-th↗
arXiv2003

Can string bits be supersymmetric?

We search for the possibility to have supersymmetric string bits at finite discretization $J$. From a general setup we find that the string bits can be made supersymmetric modulo a single defect mode which is not expected to have any sensible effect in the continuum limit.

hep-th↗
arXiv2003

Four-dimensional Hall mechanics as a particle on $\DC P^3$

In order to establish an explicit connection between four-dimensional Hall effect on $S^4$ and six-dimensional Hall effect on $\DC P^3$, we perform the Hamiltonian reduction of a particle moving on $\DC P^3$ in a constant magnetic field to the four-dimensional Hall mechanics (i.e. a particle on $S^4$ in a SU(2) instanton field). This reduction corresponds to fixing the isospin of the latter system.

hep-th↗
arXiv2003

Many-Body Superconformal Systems from Hamiltonian Reductions

We propose a new reduction mechanism which allows one to construct n-particle (super)conformal theories with pairwise interaction starting from a composite system involving n(n-1)/2+1 copies of the ordinary (super)conformal mechanics. Applications of the scheme include an N=4 superconformal extension for a complexification of the Calogero model and a D(2,1|α)-invariant n-particle system.

hep-th↗
arXiv2003

Fermion Doubling and Berenstein--Maldacena--Nastase Correspondence

We show that the string bit model suffers from doubling in the fermionic sector. The doubling leads to strong violation of supersymmetry in the limit $N\to\infty$. Since there is an exact correspondence between string bits and the algebra of BMN operators even at finite $N$, doubling is expected also on the side of super-Yang--Mills theory. We discuss the origin of the doubling in the BMN sector.

hep-th↗