arXiv subjects

Javier Garcia

Publications and source records attributed to Javier Garcia.

At least 55 records · Page 3Linked to original sources

arXiv2018

Communication Using Eigenvalues of Higher Multiplicity of the Nonlinear Fourier Transform

A generalized Nonlinear Fourier Transform (GNFT), which includes eigenvalues of higher multiplicity, is considered for information transmission over fiber optic channels. Numerical algorithms are developed to compute the direct and inverse GNFTs. For closely-spaced eigenvalues, examples suggest that the GNFT is more robust than the NFT to the practical impairments of truncation, discretization, attenuation and noise. Communication using a soliton with one double eigenvalue is numerically demonstrated, and its information rates are compared to solitons with one and two simple eigenvalues.

cs.IT↗

arXiv2018

Statistics of the Eigenvalues of a Noisy Multi-Soliton Pulse

For Nonlinear-Frequency Division-Multiplexed (NFDM) systems, the statistics of the received nonlinear spectrum in the presence of additive white Gaussian noise (AWGN) is an open problem. We present a novel method, based on the Fourier collocation algorithm, to compute these statistics.

cs.IT↗

arXiv2017

Energy Conservation in Optical Fibers with Distributed Brick-Walls Filters

A band-pass filtering scheme is proposed to mitigate spectral broadening and channel coupling in the Nonlinear Schrödinger (NLS) fiber optic channel. The scheme is modeled by modifying the NLS Equation to include an attenuation profile with multiple brick-wall filters centered at different frequencies. It is shown that this brick-walls profile conserves the total in-band energy of the launch signal. Furthermore, energy fluctuations between the filtered channels are characterized, and conditions on the channel spacings are derived that ensure energy conservation in each channel. The maximum spectral efficiency of such a system is derived, and a constructive rule for achieving it using Sidon sequences is provided.

cs.IT↗

arXiv2017

Spectrum and normal modes of non-hermitian quadratic boson operators

We analyze the spectrum and normal mode representation of general quadratic bosonic forms $H$ not necessarily hermitian. It is shown that in the one-dimensional case such forms exhibit either an harmonic regime where both $H$ and $H^\dagger$ have a discrete spectrum with biorthogonal eigenstates, and a coherent-like regime where either $H$ or $H^\dagger$ have a continuous complex two-fold degenerate spectrum, while its adjoint has no convergent eigenstates. These regimes reflect the nature of the pertinent normal boson operators. Non-diagonalizable cases as well critical boundary sectors separating these regimes are also analyzed. The extension to $N$-dimensional quadratic systems is as well discussed.

quant-ph↗

arXiv2017

The X-ray reflection spectrum of the radio-loud quasar 4C 74.26

The relativistic jets created by some active galactic nuclei are important agents of AGN feedback. In spite of this, our understanding of what produces these jets is still incomplete. X-ray observations, which can probe the processes operating in the central regions in immediate vicinity of the supermassive black hole, the presumed jet launching point, are potentially particularly valuable in illuminating the jet formation process. Here, we present the hard X-ray NuSTAR observations of the radio-loud quasar 4C 74.26 in a joint analysis with quasi-simultaneous, soft X-ray Swift observations. Our spectral analysis reveals a high-energy cut-off of 183$_{-35}^{+51}$ keV and confirms the presence of ionized reflection in the source. From the average spectrum we detect that the accretion disk is mildly recessed with an inner radius of $R_\mathrm{in}=4-180\,R_\mathrm{g}$. However, no significant evolution of the inner radius is seen during the three months covered by our NuSTAR campaign. This lack of variation could mean that the jet formation in this radio-loud quasar differs from what is observed in broad-line radio galaxies.

astro-ph.HE↗

arXiv2017

The response of relativistic outflowing gas to the inner accretion disk of a black hole

Active galactic nucleus (AGN) feedback is the process by which supermassive black holes in the centres of galaxies may moderate the growth of their hosts. Gas outflows from supermassive black holes release huge quantities of energy into the interstellar medium, clearing the surrounding gas. The most extreme of these, the ultra-fast outflows (UFOs), are the subset of X-ray detected outflows with velocities higher than 10,000 km/s, believed to originate in relativistic disc winds, a few hundred gravitational radii from the black hole. The absorption features produced by these outflows are variable, but no clear link has been found between the behaviour of the X-ray continuum and the energy or equivalent width of the outflow features due to the long time-scales of quasar variability. Here, we present the detection of multiple absorption lines from an extreme ultra-fast gas flow in the X-ray spectrum of the active galactic nucleus IRAS 13224-3809, at 0.236+/-0.006 times the speed of light (71,000 km/s), where the absorption is strongly anti-correlated with the emission from the inner regions of the accretion disk. If the gas flow is identified as a genuine outflow then it is in the fastest 5 per cent of such winds, and its variability is hundreds of times faster than in other variable winds, allowing us to observe in hours what would take months in a quasar. We find signatures of the wind simultaneously in both low and high energy detectors, which are consistent with a single ionized outflow, linking the two phenomena. The detection of the wind responding to the emission from the inner disk demonstrates a connection between accretion processes occurring on very different scales, with the X-rays from within a few gravitational radii of the black hole ionizing the relativistically outflowing gas as the flux rises.

astro-ph.HE↗

arXiv2016

Intra-wire coupling in segmented Ni/Cu nanowires deposited by electrodeposition

Segmented magnetic nanowires are a promising route for the development of three dimensional data storage techniques. Such devices require a control of the coercive field and the coupling mechanisms between individual magnetic elements. In our study, we investigate electrodeposited nanomagnets within host templates using vibrating sample magnetometry and observe a strong dependence between nanowire length and coercive field (25 nm to 5 $μ$m) and diameter (25 nm to 45 nm). A transition from a magnetization reversal through coherent rotation to domain wall propagation is observed at an aspect ratio of approximately 2. Our results are further reinforced via micromagnetic simulations and angle dependent hysteresis loops. The found behavior is exploited to create nanowires consisting of a fixed and a free segment in a spin-valve like structure. The wires are released from the membrane and electrically contacted, displaying a giant magnetoresistance effect that is attributed to individual switching of the coupled nanomagnets. We develop a simple analytical model to describe the observed switching phenomena and to predict stable and unstable regimes in coupled nanomagnets of certain geometries.

cond-mat.mtrl-sci↗

arXiv2016

On two different kinds of resonances in one-dimensional quantum-mechanical models

We apply the Riccati-Padé method and the Rayleigh-Ritz method with complex rotation to the study of the resonances of a one-dimensional well with two barriers. The model exhibits two different kinds of resonances and we calculate them by means of both approaches. While the Rayleigh-Ritz method reveals each set at a particular interval of rotation angles the Riccati Padé method yields both of them as roots of the same Hankel determinants.

quant-ph↗

arXiv2015

Three PT-symmetric Hamiltonians with completely different spectra

We discuss three Hamiltonians, each with a central-field part $H_{0}$ and a PT-symmetric perturbation $igz$. When $H_{0}$ is the isotropic Harmonic oscillator the spectrum is real for all $g$ because $H$ is isospectral to $H_{0}+g^{2}/2$. When $H_{0}$ is the Hydrogen atom then infinitely many eigenvalues are complex for all $g$. If the potential in $H_{0}$ is linear in the radial variable $r$ then the spectrum of $H$ exhibits real eigenvalues for $0<g<g_{c}$ and a PT phase transition at $g_c$.

quant-ph↗

arXiv2015

Highly accurate calculation of the resonances in the Stark effect in hydrogen

We obtained accurate resonances for the Stark effect in hydrogen by means of three independent methods. Two of them are based on complex rotation of the coordinates and diagonalization of the Hamiltonian matrix (CRLM and CRCH). The other one is based on the Riccati equations for the logarithmic derivatives of factors of the wavefunction (RPM). The latter approach enabled us to obtain the most accurate results and extremely sharp resonances.

quant-ph↗

arXiv2015

On recent calculations of resonances for the Stark effect in hydrogen

We show that the resonances of the Stark effect in hydrogen reported in Phys. Rev. A \textbf{88}, 022509 (2013) are considerably less accurate than the number of digits appear to suggest. In particular, the imaginary part of the lowest resonance is several orders of magnitude greater than it should be. We compare the results of that paper with those provided by the Riccati-Padé method, perturbation theory and an asymptotic expansion for the resonance width. The inaccuracy of those results can be traced back to the lack of precision in the calculation of the matrix elements of the secular equation. We carry out a more accurate calculation with the same method and show that the agreement with earlier results of other authors is greatly improved.

quant-ph↗

arXiv2014

Ad hoc physical Hilbert spaces in Quantum Mechanics

The overall principles of what is now widely known as PT-symmetric quantum mechanics are listed, explained and illustrated via a few examples. In particular, models based on an elementary local interaction V(x) are discussed as motivated by the naturally emergent possibility of an efficient regularization of an otherwise unacceptable presence of a strongly singular repulsive core in the origin. The emphasis is put on the constructive aspects of the models. Besides the overall outline of the formalism we show how the low-lying energies of bound states may be found in closed form in certain dynamical regimes. Finally, once these energies are found real we explain that in spite of a manifest non-Hermiticity of the Hamiltonian the time-evolution of the system becomes unitary in a properly amended physical Hilbert space.

quant-ph↗

arXiv2014

Unitary transformations of a family of two-dimensional anharmonic oscillators

In this paper we analyze a recent application of perturbation theory by the moment method to a family of two-dimensional anharmonic oscillators. By means of straightforward unitary transformations we show that two of the models studied by the authors are separable. Other is unbounded from below and therefore cannot be successfully treated by perturbation theory unless a complex harmonic frequency is introduced in the renormalization process. We calculate the lowest resonance by means of complex-coordinate rotation and compare its real part with the eigenvalue estimated by the authors. A pair of the remaining oscillators are equivalent as they can be transformed into one another by unitary transformations.

quant-ph↗

arXiv2014

Non-Hermitian oscillators with $T_{d}$ symmetry

We analyse some PT-symmetric oscillators with $T_{d}$ symmetry that depend on a potential parameter $g$. We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of $g$. Pairs of eigenvalues coalesce at exceptional points $g_c$; their magnitude roughly decreasing with the magnitude of the eigenvalues. It is difficult to estimate whether there is a phase transition at a nonzero value of $g$ as conjectured in earlier papers. Group theory and perturbation theory enable one to predict whether a given space-time symmetry leads to real eigenvalues for sufficiently small nonzero values of $g$.

quant-ph↗

arXiv2014

An Empirical Method for Improving the Quality of RXTE PCA Spectra

We fitted all of the several hundred {\it RXTE} PCA spectra of the Crab individually to a simple power-law model; the total number of counts in the composite spectrum is $>10^9$. We then used the spectrum of residuals to derive a calibration tool, called {\tt pcacorr}, that we apply to large samples of spectra for GX~339--4, H1743--322, and XTE J1550--564. Application of the tool improved the quality of all the fits, and the improvement is dramatic for spectra with $\gtrsim10^7$ counts. The Crab residual spectrum is somewhat different for each of the five PCA detectors, but it was relatively stable over the course of the mission. We recommend that {\tt pcacorr} be routinely applied to spectra with $\gtrsim10^6$ counts and that one include a systematic error of 0.1\%, rather than the 0.5--1\% value that has customarily been used. We expect that application of the tool will result in an increase in sensitivity of the PCA to faint spectral features by up to an order of magnitude.

astro-ph.HE↗

arXiv2014

Is space-time symmetry a suitable generalization of parity-time symmetry?

We discuss space-time symmetric Hamiltonian operators of the form $% H=H_{0}+igH^{\prime}$, where $H_{0}$ is Hermitian and $g$ real. $H_{0}$ is invariant under the unitary operations of a point group $G$ while $H^{\prime}$ is invariant under transformation by elements of a subgroup $G^{\prime}$ of $G$. If $G$ exhibits irreducible representations of dimension greater than unity, then it is possible that $H$ has complex eigenvalues for sufficiently small nonzero values of $g$. In the particular case that $H$ is parity-time symmetric then it appears to exhibit real eigenvalues for all $% 0 0$. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.

quant-ph↗

arXiv2014

Non-hermitean hamiltonians with unitary and antiunitary symmetry

We analyze several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyze their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry $C_{2v}$ exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry.

quant-ph↗

arXiv2014

On the eigenvalues of some non-Hermitian Hamiltonians with space-time symmetry

We calculate the eigenvalues of some two-dimensional non-Hermitian Hamiltonians by means of a pseudospectral method and straightforward diagonalization of the Hamiltonian matrix in a suitable basis set. Both sets of results agree remarkably well but differ considerably from the eigenvalues obtained some time ago by other authors. In particular, we do not observe the multiple phase transitions claimed to occur in one of the anharmonic oscillators.

quant-ph↗