arXiv subjects

A. Saxena

Publications and source records attributed to A. Saxena.

At least 91 records · Page 5Linked to original sources

arXiv2017

Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum

In the present work, we explore a nonlinear Dirac equation motivated as the continuum limit of a binary waveguide array model. We approach the problem both from a near-continuum perspective as well as from a highly discrete one. Starting from the former, we see that the continuum Dirac solitons can be continued for all values of the discretization (coupling) parameter, down to the uncoupled (so-called anti-continuum) limit where they result in a 9-site configuration. We also consider configurations with 1- or 2-sites at the anti-continuum limit and continue them to large couplings, finding that they also persist. For all the obtained solutions, we examine not only the existence, but also the spectral stability through a linearization analysis and finally consider prototypical examples of the dynamics for a selected number of cases for which the solutions are found to be unstable.

nlin.PS↗

arXiv2016

Neutron capture cross section measurement of 238U at the n TOF CERN facility with C6D6 scintillation detectors in the energy region from 1 eV to 700 keV

The aim of this work is to provide a precise and accurate measurement of the 238U(n,g) reaction cross section in the energy region from 1 eV to 700 keV. This reaction is of fundamental importance for the design calculations of nuclear reactors, governing the behaviour of the reactor core. In particular, fast reactors, which are experiencing a growing interest for their ability to burn radioactive waste, operate in the high energy region of the neutron spectrum. In this energy region most recent evaluations disagree due to inconsistencies in the existing measurements of up to 15%. In addition, the assessment of nuclear data uncertainty performed for innovative reactor systems shows that the uncertainty in the radiative capture cross-section of 238U should be further reduced to 1-3% in the energy region from 20 eV to 25 keV. To this purpose, addressed by the Nuclear Energy Agency as a priority nuclear data need, complementary experiments, one at the GELINA and two at the n_TOF facility, were proposed and carried out within the 7th Framework Project ANDES of the European Commission. The results of one of these 238U(n,g) measurements performed at the n_TOF CERN facility are presented in this work. The gamma-ray cascade following the radiative neutron capture has been detected exploiting a setup of two C6D6 liquid scintillators. Resonance parameters obtained from this work are on average in excellent agreement with the ones reported in evaluated libraries. In the unresolved resonance region, this work yields a cross section in agreement with evaluated libraries up to 80 keV, while for higher energies our results are significantly higher.

nucl-ex↗

arXiv2016

The WEAVE-LOFAR Survey

In these proceedings we highlight the primary scientific goals and design of the WEAVE-LOFAR survey, which will use the new WEAVE spectrograph on the 4.2m William Herschel Telescope to provide the primary source of spectroscopic information for the LOFAR Surveys Key Science Project. Beginning in 2018, WEAVE-LOFAR will generate more than 10$^6$ R=5000 365-960 nm spectra of low-frequency selected radio sources, across three tiers designed to efficiently sample the redshift-luminosity plane, and produce a data set of enormous legacy value. The radio frequency selection, combined with the high multiplex and throughput of the WEAVE spectrograph, make obtaining redshifts in this way very efficient, and we expect that the redshift success rate will approach 100 per cent at $z < 1$. This unprecedented spectroscopic sample - which will be complemented by an integral field component - will be transformational in key areas, including studying the star formation history of the Universe, the role of accretion and AGN-driven feedback, properties of the epoch of reionisation, cosmology, cluster haloes and relics, as well as the nature of radio galaxies and protoclusters. Each topic will be addressed in unprecedented detail, and with the most reliable source classifications and redshift information in existence.

astro-ph.GA↗

arXiv2016

Complete integrability of Nonlocal Nonlinear Schrödinger equation

Based on the completeness relation for the squared solutions of the Lax operator $L$ we show that a subset of nonlocal equations from the hierarchy of nonlocal nonlinear Schrödinger equations (NLS) is a completely integrable system. The spectral properties of the Lax operator indicate that there are two types of soliton solutions. The relevant action-angle variables are parametrized by the scattering data of the Lax operator. The notion of the symplectic basis, which directly maps the variations of the potential of $L$ to the variations of the action-angle variables has been generalized to the nonlocal case. We also show that the inverse scattering method can be viewed as a generalized Fourier transform. Using the trace identities and the symplectic basis we construct the hierarchy Hamiltonian structures for the nonlocal NLS equations.

nlin.SI↗

arXiv2016

Stability of solitary waves and vortices in a 2D nonlinear Dirac model

We explore a prototypical two-dimensional model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis, illustrating the potential of spinor solutions consisting of a soliton in one component and a vortex in the other to be neutrally stable in a wide parametric interval of frequencies. Solutions of higher vorticity are generically unstable and split into lower charge vortices in a way that preserves the total vorticity. These results pave the way for a systematic stability and dynamics analysis of higher dimensional waveforms in a broad class of nonlinear Dirac models and a comparison revealing nontrivial differences with respect to their better understood non-relativistic analogue, the nonlinear Schrödinger equation.

nlin.PS↗

arXiv2016

Integral measurement of the $^{12}$C(n,p)$^{12}$B reaction up to 10 GeV

The integral measurement of the $^{12}$C(n,p)$^{12}$B reaction was performed at the neutron time of flight facility n_TOF at CERN. The total number of $^{12}$B nuclei produced per neutron pulse of the n_TOF beam was determined using the activation technique in combination with a time of flight technique. The cross section is integrated over the n_TOF neutron energy spectrum from reaction threshold at 13.6 MeV to 10 GeV. Having been measured up to 1 GeV on basis of the $^{235}$U(n,f) reaction, the neutron energy spectrum above 200 MeV has been reevaluated due to the recent extension of the cross section reference for this particular reaction, which is otherwise considered a standard up to 200 MeV. The results from the dedicated GEANT4 simulations have been used to evaluate the neutron flux from 1 GeV up to 10 GeV. The experimental results related to the $^{12}$C(n,p)$^{12}$B reaction are compared with the evaluated cross sections from major libraries and with the predictions of different GEANT4 models, which mostly underestimate the $^{12}$B production. On the contrary, a good reproduction of the integral cross section derived from measurements is obtained with TALYS-1.6 calculations, with optimized parameters.

nucl-ex↗

arXiv2015

PT Meets Supersymmetry and Nonlinearity: An Analytically Tractable Case Example

In the present work, we combine the notion of $\mathcal{PT}$-symmetry with that of super-symmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called P{ö}schl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which the corresponding solution of the regular nonlinear Schr{ö}dinger equation with arbitrary power law nonlinearity does not possess. The spectral properties and dynamical implications of this instability are examined. We believe that these findings may pave the way towards initiating a fruitful interplay between the notions of $\mathcal{PT}$-symmetry, super-symmetric partner potentials and nonlinear interactions.

nlin.PS↗

arXiv2014

Solitons and Vortices in Two-dimensional Discrete Nonlinear Schrodinger Systems with Spatially Modulated Nonlinearity

We consider a two-dimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anti-continuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual "extended" unstaggered bright solitons, in which all sites are excited in the AC limit, with the same sign across the lattice (they represent the most robust states supported by the lattice, their 1D counterparts being what was considered as 1D bright solitons in the above-mentioned work), and the vortex cross, which is specific to the 2D setting. For all the existing states, we explore their stability (analytically, whenever possible). Typical scenarios of instability development are exhibited through direct simulations.

nlin.PS↗

arXiv2014

When Does Linear Stability Not Exclude Nonlinear Instability ?

We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization's internal modes of negative energy with the wave continuum. In a broad class of nonlinear Schr{ö}dinger (NLS) equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an anti-symmetric soliton in a double-well potential, (b) a twisted localized mode in a one-dimensional lattice with cubic nonlinearity, and (c) a discrete vortex in a two-dimensional saturable lattice. In all cases, we observe a weak nonlinear instability, despite the linear stability of the respective states.

nlin.PS↗

arXiv2014

High accuracy determination of the $^{238}$U/$^{235}$U fission cross section ratio up to $\sim$1 GeV at n_TOF (CERN)

The $^{238}$U to $^{235}$U fission cross section ratio has been determined at n_TOF up to $\sim$1 GeV, with two different detection systems, in different geometrical configurations. A total of four datasets have been collected and compared. They are all consistent to each other within the relative systematic uncertainty of 3-4%. The data collected at n_TOF have been suitably combined to yield a unique fission cross section ratio as a function of the neutron energy. The result confirms current evaluations up to 200 MeV. A good agreement is also observed with theoretical calculations based on the INCL++/Gemini++ combination up to the highest measured energy. The n_TOF results may help solving a long-standing discrepancy between the two most important experimental dataset available so far above 20 MeV, while extending the neutron energy range for the first time up to $\sim$1 GeV.

nucl-ex↗

arXiv2014

PT-Symmetric dimer in a generalized model of coupled nonlinear oscillators

In the present work, we explore the case of a general PT-symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrödinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations.

nlin.PS↗

arXiv2014

Measurement of the $^{12}$C($n,p$)$^{12}$B cross section at n_TOF (CERN) by in-beam activation analysis

The integral cross section of the $^{12}$C($n,p$)$^{12}$B reaction has been determined for the first time in the neutron energy range from threshold to several GeV at the n_TOF facility at CERN. The measurement relies on the activation technique, with the $β$-decay of $^{12}$B measured over a period of four half-lives within the same neutron bunch in which the reaction occurs. The results indicate that model predictions, used in a variety of applications, are mostly inadequate. The value of the integral cross section reported here can be used as a benchmark for verifying or tuning model calculations.

nucl-ex↗

arXiv2014

Solitary Waves in a Discrete Nonlinear Dirac equation

In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross-Neveu model. The motivation for this discrete model proposal is both computational (near the continuum limit) and theoretical (using the understanding of the anti-continuum limit of vanishing coupling). Numerous unexpected features are identified including a staggered solitary pattern emerging from a single site excitation, as well as two- and three-site excitations playing a role analogous to one- and two-site, respectively, excitations of the discrete nonlinear Schrödinger analogue of the model. Stability exchanges between the two- and three-site states are identified, as well as instabilities that appear to be persistent over the coupling strength $ε$, for a subcritical value of the propagation constant $Λ$. Variations of the propagation constant, coupling parameter and nonlinearity exponent are all examined in terms of their existence and stability implications and long dynamical simulations are used to unravel the evolutionary phenomenology of the system (when unstable).

nlin.PS↗

arXiv2014

GEANT4 simulation of the neutron background of the C$_6$D$_6$ set-up for capture studies at n_TOF

The neutron sensitivity of the C$_6$D$_6$ detector setup used at n_TOF for capture measurements has been studied by means of detailed GEANT4 simulations. A realistic software replica of the entire n_TOF experimental hall, including the neutron beam line, sample, detector supports and the walls of the experimental area has been implemented in the simulations. The simulations have been analyzed in the same manner as experimental data, in particular by applying the Pulse Height Weighting Technique. The simulations have been validated against a measurement of the neutron background performed with a $^\mathrm{nat}$C sample, showing an excellent agreement above 1 keV. At lower energies, an additional component in the measured $^\mathrm{nat}$C yield has been discovered, which prevents the use of $^\mathrm{nat}$C data for neutron background estimates at neutron energies below a few hundred eV. The origin and time structure of the neutron background have been derived from the simulations. Examples of the neutron background for two different samples are demonstrating the important role of accurate simulations of the neutron background in capture cross section measurements.

physics.ins-det↗

arXiv2014

Generalized Dimers and their Stokes-variable Dynamics

In the present work, we generalize the setting of dimers with potential gain and loss which have been extensively considered recently in $\mathcal{P T}$-symmetric contexts. We consider a pair of waveguides which are evanescently coupled but may also be actively coupled and may possess onsite gain and loss, as well as (possibly non-uniform) nonlinearity. We identify (and where appropriate review from earlier work) a plethora of interesting dynamical scenaria ranging from the existence of stable and unstable fixed points and integrable dynamics, to the emergence of pitchfork or Hopf bifurcations and the generation of additional fixed points and limit cycles, respectively, as well as the potential deviation of trajectories to infinity. Thus, a catalogue of a large number of possible cases is given and their respective settings physically justified (where appropriate).

nlin.PS↗

arXiv2014

Spin and Valley Noise in Two-Dimensional Dirac Materials

We develop a theory for optical Faraday rotation noise in two-dimensional Dirac materials. In contrast to spin noise in conventional semiconductors, we find that the Faraday rotation fluctuations are influenced not only by spins but also the valley degrees of freedom attributed to intervalley scattering processes. We illustrate our theory with two-dimensional transition metal dichalcogenides and discuss signatures of spin and valley noise in the Faraday noise power spectrum. We propose optical Faraday noise spectroscopy as a technique for probing both spin and valley relaxation dynamics in two-dimensional Dirac materials.

cond-mat.mes-hall↗

arXiv2013

PT-Symmetric Dimer of Coupled Nonlinear Oscillators

We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from the linear limit of the system, we extend considerations to the nonlinear case for both soft and hard cubic nonlinearities identifying symmetric and anti-symmetric breather solutions, as well as symmetry breaking variants thereof. We propose a reduction of the system to a Schrödinger type PT-symmetric dimer, whose detailed earlier understanding can explain many of the phenomena observed herein, including the PT phase transition. Nevertheless, there are also significant parametric as well as phenomenological potential differences between the two models and we discuss where these arise and where they are most pronounced. Finally, we also provide examples of the evolution dynamics of the different states in their regimes of instability.

nlin.PS↗

arXiv2012

Role of Nuclear Quadrupole Coupling on Decoherence and Relaxation of Central Spins in Quantum Dots

Strain-induced gradients of local electric fields in semiconductor quantum dots can couple to the quadrupole moments of nuclear spins. We develop a theory describing the influence of this quadrupolar coupling (QC) on the spin correlators of electron and hole "central" spins localized in such dots. We show that when the QC strength is comparable to or larger than the hyperfine coupling strength between nuclei and the central spin, the relaxation rate of the central spin is strongly enhanced and can be exponential. We demonstrate a good agreement with recent experiments on spin relaxation in hole-doped (In,Ga)As self-assembled quantum dots.

cond-mat.mes-hall↗