arXiv subjects

J. Lages

Publications and source records attributed to J. Lages.

At least 19 recordsLinked to original sources

arXiv2026

Small-world structure of quantum computer hardware

We show that the network of quantum register states of a quantum computer (QC), coupled through residual two-body interactions between qubits, exhibits small-world properties analogous to those of complex networks found in human society. The most probable Erd\H{o}s number between any two states is about 9, comparable to the six degrees of separation reported by Milgram for social networks. Using the $\mathring{A}$berg criterion, which retains only interactions exceeding the local energy spacing, we construct an effective ($\mathring{A}$berg) network and show that, above a critical coupling strength, this network percolates into a giant component spanning nearly the whole quantum register space. This percolation transition closely matches the onset of quantum chaos and dynamical thermalization established previously via costly exact diagonalization, while our approach extends the accessible system size up to $n_q=30$ qubits.

cond-mat.stat-mech↗

arXiv2016

Fractal structures for the Jacobi Hamiltonian of restricted three-body problem

We study the dynamical chaos and integrable motion in the planar circular restricted three-body problem and determine the fractal dimension of the spiral strange repeller set of non-escaping orbits at different values of mass ratio of binary bodies and of Jacobi integral of motion. We find that the spiral fractal structure of the Poincaré section leads to a spiral density distribution of particles remaining in the system. We also show that the initial exponential drop of survival probability with time is followed by the algebraic decay related to the universal algebraic statistics of Poincaré recurrences in generic symplectic maps.

astro-ph.EP↗

arXiv2015

Chaotic enhancement of dark matter density in binary systems

We study the capture of galactic dark matter particles (DMP) in two-body and few-body systems with a symplectic map description. This approach allows modeling the scattering of $10^{16}$ DMPs after following the time evolution of the captured particle on about $10^9$ orbital periods of the binary system. We obtain the DMP density distribution inside such systems and determine the enhancement factor of their density in a center vicinity compared to its galactic value as a function of the mass ratio of the bodies and the ratio of the body velocity to the velocity of the galactic DMP wind. We find that the enhancement factor can be on the order of tens of thousands.

astro-ph.EP↗

arXiv2015

Symplectic map description of Halley's comet dynamics

The main features of 1P/Halley chaotic dynamics can be described by a two dimensional symplectic map. Using Mel'nikov integral we semi-analytically determine such a map for 1P/Halley taking into account gravitational interactions from the Sun and the eight planets. We determine the Solar system kick function ie the energy transfer to 1P/Halley along one passage through the Solar system. Our procedure allows to compute for each planet its contribution to the Solar system kick function which appears to be the sum of the Keplerian potential of the planet and of a rotating circular gravitational dipole potential due to the Sun movement around Solar system barycenter. We test the robustness of the symplectic Halley map by directly integrating Newton's equations over $\sim 2.4\cdot 10^4$ yr around Y2K and by reconstructing the Solar system kick function. Our results show that the Halley map with fixed parameters gives a reliable description of comet dynamics on time scales of $10^4$ yr while on a larger scales the parameters of the map are slowly changing due to slow oscillations of orbital momentum.

astro-ph.EP↗

arXiv2013

Geometric phase and Pancharatnam phase induced by light wave polarization

We use the quantum kinematic approach to revisit geometric phases associated with polarizing processes of a monochromatic light wave. We give the expressions of geometric phases for any, unitary or non-unitary, cyclic or non-cyclic transformations of the light wave state. Contrarily to the usually considered case of absorbing polarizers, we found that a light wave passing through a polarizer may acquire in general a non zero geometric phase. This geometric phase exists despite the fact that initial and final polarization states are in phase according to the Pancharatnam criterion and can not be measured using interferometric superposition. Consequently, there is a difference between the Pancharatnam phase and the complete geometric phase acquired by a light wave passing through a polarizer. We illustrate our work with the particular example of total reflection based polarizers.

physics.optics↗

arXiv2012

Dark matter chaos in the Solar System

We study the capture of galactic dark matter particles in the Solar System produced by rotation of Jupiter. It is shown that the capture cross section is much larger than the area of Jupiter orbit being inversely diverging at small particle energy. We show that the dynamics of captured particles is chaotic and is well described by a simple symplectic dark map. This dark map description allows to simulate the scattering and dynamics of $10^{14}$ dark matter particles during the life time of the Solar System and to determine dark matter density profile as a function of distance from the Sun. The mass of captured dark matter in the radius of Neptune orbit is estimated to be $2 \cdot 10^{15} g$. The radial density of captured dark matter is found to be approximately constant behind Jupiter orbit being similar to the density profile found in galaxies.

astro-ph.EP↗

arXiv2010

Superinsulator as a phase of bi-particle localized states

We propose a physical picture of superinsulator observed recently in experiments with superconducting films in a magnetic field. On the basis of previous numerical studies we argue that a moderate attraction creates bi-particle localized states at intermediate disorder strength when noninteracting electron states are delocalized and metallic. Our present numerical study show that such localized pairs are broken by a static electric field which strength is above a certain threshold. We argue that such a breaking of localized pairs by a static field is at the origin of superinsulator breaking with a current jump observed experimentally above a certain critical voltage.

cond-mat.supr-con↗

arXiv2009

Generalized composition law from 2x2 matrices

Many results that are difficult can be found more easily by using a generalization in the complex plane of Einstein's addition law of parallel velocities. Such a generalization is a natural way to add quantities that are limited to bounded values. We show how this generalization directly provides phase factors such as the Wigner angle in special relativity and how this generalization is connected in the simplest case with the composition of 2x2 S matrices.

physics.optics↗

arXiv2008

Composition law for polarizers

The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption - as in a polaroid film - and the second one is based on total reflection at the interface with a birefringent medium. Using the Stokes vector representation, we determine explicitly the trajectories of the wave light polarization during the polarization process. We find that such trajectories are not always geodesics of the Poincaré sphere as it is usually thought. Using the analogy between light polarization and special relativity, we find that the action of successive polarizers on the light wave polarization is equivalent to the action of a single resulting polarizer followed by a rotation achieved for example by a device with optical activity. We find a composition law for polarizers similar to the composition law for noncollinear velocities in special relativity. We define an angle equivalent to the relativistic Wigner angle which can be used to quantify the quality of two composed polarizers.

physics.optics↗

arXiv2007

Noncommutative Quantum Mechanics Viewed from Feynman Formalism

Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This proof is based on the assumption of simple commutation relations between position and velocity. We first study a nonrelativistic particle using Feynman formalism. We show that Poincaré's magnetic angular momentum and Dirac magnetic monopole are the direct consequences of the structure of the sO(3) Lie algebra in Feynman formalism. Then we show how to extend this formalism to the dual momentum space with the aim of introducing Noncommutative Quantum Mechanics which was recently the subject of a wide range of works from particle physics to condensed matter physics.

hep-th↗

arXiv2007

From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics

In 1990, Dyson published a proof due to Feynman of the Maxwell equations assuming only the commutation relations between position and velocity. With this minimal assumption, Feynman never supposed the existence of Hamiltonian or Lagrangian formalism. In the present communication, we review the study of a relativistic particle using ``Feynman brackets.'' We show that Poincaré's magnetic angular momentum and Dirac magnetic monopole are the consequences of the structure of the Lorentz Lie algebra defined by the Feynman's brackets. Then, we extend these ideas to the dual momentum space by considering noncommutative quantum mechanics. In this context, we show that the noncommutativity of the coordinates is responsible for a new effect called the spin Hall effect. We also show its relation with the Berry phase notion. As a practical application, we found an unusual spin-orbit contribution of a nonrelativistic particle that could be experimentally tested. Another practical application is the Berry phase effect on the propagation of light in inhomogeneous media.

hep-th↗

arXiv2006

Effects of disorder on the vortex charge

We study the influence of disorder on the vortex charge, both due to random pinning of the vortices and due to scattering off non-magnetic impurities. In the case when there are no impurities present, but the vortices are randomly distributed, the effect is very small, except when two or more vortices are close by. When impurities are present, they have a noticeable effect on the vortex charge. This, together with the effect of temperature, changes appreciably the vortex charge. In the case of an attractive impurity potential the sign of the charge naturally changes.

cond-mat.supr-con↗

arXiv2005

Suppression of quantum chaos in a quantum computer hardware

We present numerical and analytical studies of a quantum computer proposed by the Yamamoto group in Phys. Rev. Lett. 89, 017901 (2002). The stable and quantum chaos regimes in the quantum computer hardware are identified as a function of magnetic field gradient and dipole-dipole couplings between qubits on a square lattice. It is shown that a strong magnetic field gradient leads to suppression of quantum chaos.

cond-mat.dis-nn↗

arXiv2005

Local density of states of a strongly type-II d-wave superconductor: The binary alloy model in a magnetic field

We calculate self-consistently the local density of states (LDOS) of a d-wave superconductor considering the scattering of the quasiparticles off randomly distributed impurities and off externally induced vortices. The impurities and the vortices are randomly distributed but the vortices are preferably located near the impurities. The increase of either the impurity repulsive potential or the mpurity density only affects the density of states (DOS) slightly. The dominant effect is due to the vortex scattering. The results for the LDOS agree qualitatively with experimental results considering that most vortices are pinned at the impurities.

cond-mat.supr-con↗

arXiv2004

Decoherence by a chaotic many-spin bath

We numerically investigate decoherence of a two-spin system (central system) by a bath of many spins 1/2. By carefully adjusting parameters, the dynamical regime of the bath has been varied from quantum chaos to regular, while all other dynamical characteristics have been kept practically intact. We explicitly demonstrate that for a many-body quantum bath, the onset of quantum chaos leads to significantly faster and stronger decoherence compared to an equivalent non-chaotic bath. Moreover, the non-diagonal elements of the system's density matrix decay differently for chaotic and non-chaotic baths. Therefore, knowledge of the basic parameters of the bath (strength of the system-bath interaction, bath's spectral density of states) is not always sufficient, and much finer details of the bath's dynamics can strongly affect the decoherence process.

quant-ph↗

arXiv2003

Angular Symmetry Breaking Induced by Electromagnetic Field

It is well known that velocities does not commute in presence of an electromagnetic field. This property implies that angular algebra symmetries, such as the sO(3) and Lorentz algebra symmetries, are broken. To restore these angular symmetries we show the necessity of adding the Poincare momentum M to the simple angular momentum L. These restorations performed succesively in a flat space and in a curved space lead in each cases to the generation of a Dirac magnetic monopole. In the particular case of the Lorentz algebra we consider an application of our theory to the gravitoelectromagnetism. In this last case we establish a qualitative relation giving the mass spectrum for dyons.

hep-th↗

arXiv2003

Interplay of disorder and magnetic field in the superconducting vortex state

We calculate the density of states of an inhomogeneous superconductor in a magnetic field where the positions of vortices are distributed completely at random. We consider both the cases of s-wave and d-wave pairing. For both pairing symmetries either the presence of disorder or increasing the density of vortices enhances the low energy density of states. In the s-wave case the gap is filled and the density of states is a power law at low energies. In the d-wave case the density of states is finite at zero energy and it rises linearly at very low energies in the Dirac isotropic case (α_D=t/Δ_0=1, where t is the hopping integral and Δ_0 is the amplitude of the order parameter). For slightly higher energies the density of states crosses over to a quadratic behavior. As the Dirac anisotropy increases (as Δ_0 decreases with respect to the hopping term) the linear region decreases in width. Neglecting this small region the density of states interpolates between quadratic and back to linear as α_D increases. The low energy states are strongly peaked near the vortex cores.

cond-mat.supr-con↗

arXiv2003

Classical spinning particle assuming a covariant Hamiltonian

We consider a classical spinning particle in the frame of the relativistic physics by means of a covariant Hamiltonian and of a generalization of Poisson brackets which take into account the gauge fields. We obtain different equations of motion and evolution in this context and we compare our results with those of Bargmann-Michel-Telegdi. An extension to the case of a curved space and a link towards quantum theory are given at the end of the paper.

hep-th↗