arXiv subjects

Santosh Kumar

Publications and source records attributed to Santosh Kumar.

At least 91 records · Page 5Linked to original sources

arXiv2019

Recursion for the smallest eigenvalue density of $β$-Wishart-Laguerre ensemble

The statistics of the smallest eigenvalue of Wishart-Laguerre ensemble is important from several perspectives. The smallest eigenvalue density is typically expressible in terms of determinants or Pfaffians. These results are of utmost significance in understanding the spectral behavior of Wishart-Laguerre ensembles and, among other things, unveil the underlying universality aspects in the asymptotic limits. However, obtaining exact and explicit expressions by expanding determinants or Pfaffians becomes impractical if large dimension matrices are involved. For the real matrices ($β=1$) Edelman has provided an efficient recurrence scheme to work out exact and explicit results for the smallest eigenvalue density which does not involve determinants or matrices. Very recently, an analogous recurrence scheme has been obtained for the complex matrices ($β=2$). In the present work we extend this to $β$-Wishart-Laguerre ensembles for the case when exponent $α$ in the associated Laguerre weight function, $λ^αe^{-βλ/2}$, is a non-negative integer, while $β$ is positive real. This also gives access to the smallest eigenvalue density of fixed trace $β$-Wishart-Laguerre ensemble, as well as moments for both cases. Moreover, comparison with earlier results for the smallest eigenvalue density in terms of certain hypergeometric function of matrix argument results in an effective way of evaluating these explicitly. Exact evaluations for large values of $n$ (the matrix dimension) and $α$ also enable us to compare with Tracy-Widom density and large deviation results of Katzav and Castillo. We also use our result to obtain the density of the largest of the proper delay times which are eigenvalues of the Wigner-Smith matrix and are relevant to the problem of quantum chaotic scattering.

math-ph↗

arXiv2018

Mode-selective Image Upconversion

We study selective upconversion of optical signals according to their detailed transverse electromagnetic modes, and demonstrate its proof of operations in a nonlinear crystal. The mode selectivity is achieved by preparing the pump wave in an optimized spatial profile to drive the upconversion. For signals in the Laguerre-Gaussian modes, we show that a mode can be converted with up to 60 times higher efficiency than an overlapping but orthogonal mode. This nonlinear-optical approach may find applications in compressive imaging, pattern recognition, quantum communications, and others where the existing linear-optical methods are limited.

physics.optics↗

arXiv2018

Field-induced canting of magnetic moments in GdCo5 at finite temperature: first-principles calculations and high-field measurements

We present calculations and experimental measurements of the temperature-dependent magnetization of a single crystal of GdCo$_5$ in magnetic fields of order 60 T. At zero temperature the calculations, based on density-functional theory in the disordered-local-moment picture, predict a field-induced transition from an antiferromagnetic to a canted alignment of Gd and Co moments at 46.1 T. At higher temperatures the calculations find this critical field to increase along with the zero-field magnetization. The experimental measurements observe this transition to occur between 44-48 T at 1.4 K. Up to temperatures of at least 100 K, the experiments continue to observe the transition; however, at variance with the calculations, no strong temperature dependence of the critical field is apparent. We assign this difference to the inaccurate description of the zero-field magnetization of the calculations at low temperatures, due to the use of classical statistical mechanics. Correcting for this effect, we recover a consistent description of the high-field magnetization of GdCo$_5$ from theory and experiment.

cond-mat.mtrl-sci↗

arXiv2018

Exact distribution of spacing ratios for random and localized states in quantum chaotic systems

Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of states violate this principle and display eigenstate localization, a counter-intuitive feature known to arise due to purely quantum or semiclassical effects. In the spectrum of chaotic systems, the localized and random states interact with one another and modifies the spectral statistics. In this work, a $3 \times 3$ random matrix model is used to obtain exact result for the ratio of spacing between a generic and localized state. We consider time-reversal-invariant as well as non-invariant scenarios. These results agree with the spectra computed from realistic physical systems that display localized eigenmodes.

quant-ph↗

arXiv2018

Calculating the Magnetic Anisotropy of Rare-Earth-Transition-Metal Ferrimagnets

Magnetocrystalline anisotropy, the microscopic origin of permanent magnetism, is often explained in terms of ferromagnets. However, the best performing permanent magnets based on rare earths and transition metals (RE-TM) are in fact ferrimagnets, consisting of a number of magnetic sublattices. Here we show how a naive calculation of the magnetocrystalline anisotropy of the classic RE-TM ferrimagnet GdCo$_5$ gives numbers which are too large at 0 K and exhibit the wrong temperature dependence. We solve this problem by introducing a first-principles approach to calculate temperature-dependent magnetization vs. field (FPMVB) curves, mirroring the experiments actually used to determine the anisotropy. We pair our calculations with measurements on a recently-grown single crystal of GdCo$_5$, and find excellent agreement. The FPMVB approach demonstrates a new level of sophistication in the use of first-principles calculations to understand RE-TM magnets.

cond-mat.mtrl-sci↗

arXiv2017

Relativistic nature of carriers: Origin of electron-hole conduction asymmetry in m o n o l a ye r gr a p h e n e

We report electron-hole conduction asymmetry in monolayer graphene. Previously, it has been claimed that electron-hole conduction asymmetry is due to imbalanced carrier injection from metallic electrodes. Here, we show that metallic contacts have negligible impact on asymmetric conduction and may be either sample or device-dependent phenomena. Electrical measurements show that monolayer graphene based devices exhibit suppressed electron conduction compared to hole conduction due to the presence of donor impurities which scatter electrons more efficiently. This can be explained by the relativistic nature of charge carriers in a graphene monolayer and can be reconciled with the fact that in a relativistic quantum system transport cross section does depend on the sign of scattering potential in contrast to a nonrelativistic quantum system.

cond-mat.mes-hall↗

arXiv2017

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is ap- plicable to a wide range of quantum chaotic systems. We thus eventually fully solve a problem which already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

quant-ph↗

arXiv2017

The stratified micro-randomized trial design: sample size considerations for testing nested causal effects of time-varying treatments

Technological advancements in the field of mobile devices and wearable sensors have helped overcome obstacles in the delivery of care, making it possible to deliver behavioral treatments anytime and anywhere. Increasingly the delivery of these treatments is triggered by predictions of risk or engagement which may have been impacted by prior treatments. Furthermore the treatments are often designed to have an impact on individuals over a span of time during which subsequent treatments may be provided. Here we discuss our work on the design of a mobile health smoking cessation experimental study in which two challenges arose. First the randomizations to treatment should occur at times of stress and second the outcome of interest accrues over a period that may include subsequent treatment. To address these challenges we develop the "stratified micro-randomized trial," in which each individual is randomized among treatments at times determined by predictions constructed from outcomes to prior treatment and with randomization probabilities depending on these outcomes. We define both conditional and marginal proximal treatment effects. Depending on the scientific goal these effects may be defined over a period of time during which subsequent treatments may be provided. We develop a primary analysis method and associated sample size formulae for testing these effects.

stat.AP↗

arXiv2017

Quantum Airy Photons

With exotic propagation properties, optical Airy beams have been well studied for innovative applications in communications, biomedical imaging, micromachining, and so on. Here we extend those studies to the quantum domain, creating quantum correlated photons in finite-energy Airy transverse modes via spontaneous parametric down conversion and sub-sequential spatial light modulation. Through two-photon coincidence measurements, we verify their Airy spatial wavefunctions, propagation along a parabolic trajectory, and that the spatial modulation does not introduce any observable degradation of quantum correlation between the photons. These results suggest the feasibility of using spatially structured photons for practically advantageous quantum applications.

quant-ph↗

arXiv2017

Rare-earth/transition-metal magnetic interactions in pristine and (Ni,Fe)-doped YCo5 and GdCo5

We present an investigation into the intrinsic magnetic properties of the compounds YCo5 and GdCo5, members of the RETM5 class of permanent magnets (RE = rare earth, TM = transition metal). Focusing on Y and Gd provides direct insight into both the TM magnetization and RE-TM interactions without the complication of strong crystal field effects. We synthesize single crystals of YCo5 and GdCo5 using the optical floating zone technique and measure the magnetization from liquid helium temperatures up to 800 K. These measurements are interpreted through calculations based on a Green's function formulation of density-functional theory, treating the thermal disorder of the local magnetic moments within the coherent potential approximation. The rise in the magnetization of GdCo5 with temperature is shown to arise from a faster disordering of the Gd magnetic moments compared to the antiferromagnetically aligned Co sublattice. We use the calculations to analyze the different Curie temperatures of the compounds and also compare the molecular (Weiss) fields at the RE site with previously published neutron scattering experiments. To gain further insight into the RE-TM interactions, we perform substitutional doping on the TM site, studying the compounds RECo4.5Ni0.5, RECo4Ni, and RECo4.5Fe0.5. Both our calculations and experiments on powdered samples find an increased/decreased magnetization with Fe/Ni doping, respectively. The calculations further reveal a pronounced dependence on the location of the dopant atoms of both the Curie temperatures and the Weiss field at the RE site.

cond-mat.mtrl-sci↗

arXiv2017

Smallest eigenvalue density for regular or fixed-trace complex Wishart-Laguerre ensemble and entanglement in coupled kicked tops

The statistical behaviour of the smallest eigenvalue has important implications for systems which can be modeled using a Wishart-Laguerre ensemble, the regular one or the fixed trace one. For example, the density of the smallest eigenvalue of the Wishart-Laguerre ensemble plays a crucial role in characterizing multiple channel telecommunication systems. Similarly, in the quantum entanglement problem, the smallest eigenvalue of the fixed trace ensemble carries information regarding the nature of entanglement. For real Wishart-Laguerre matrices, there exists an elegant recurrence scheme suggested by Edelman to directly obtain the exact expression for the smallest eigenvalue density. In the case of complex Wishart-Laguerre matrices, for finding exact and explicit expressions for the smallest eigenvalue density, existing results based on determinants become impractical when the determinants involve large-size matrices. In this work, we derive a recurrence scheme for the complex case which is analogous to that of Edelman's for the real case. This is used to obtain exact results for the smallest eigenvalue density for both the regular, and the fixed trace complex Wishart-Laguerre ensembles. We validate our analytical results using Monte Carlo simulations. We also study scaled Wishart-Laguerre ensemble and investigate its efficacy in approximating the fixed-trace ensemble. Eventually, we apply our result for the fixed-trace ensemble to investigate the behaviour of the smallest eigenvalue in the paradigmatic system of coupled kicked tops.

math-ph↗

arXiv2017

Intracavity Rydberg atom electromagnetically induced transparency using a high finesse optical cavity

We present an experimental study of cavity assisted Rydberg atom electromagnetically induced transparency (EIT) using a high-finesse optical cavity ($F \sim 28000$). Rydberg atoms are excited via a two-photon transition in a ladder-type EIT configuration. A three-peak structure of the cavity transmission spectrum is observed when Rydberg EIT is generated inside the cavity. The two symmetrically spaced side peaks are caused by bright-state polaritons, while the central peak corresponds to a dark-state polariton. Anti-crossing phenomenon and the effects of mirror adsorbate electric fields are studied under different experimental conditions. We determine a lower bound on the coherence time for the system of $7.26 \pm 0.06 \,μ$s, most likely limited by laser dephasing. The cavity-Rydberg EIT system can be useful for single photon generation using the Rydberg blockade effect, studying many-body physics, and generating novel quantum states amongst many other applications.

physics.atom-ph↗

arXiv2017

The Probability That All Eigenvalues are Real for Products of Truncated Real Orthogonal Random Matrices

The probability that all eigenvalues of a product of $m$ independent $N \times N$ sub-blocks of a Haar distributed random real orthogonal matrix of size $(L_i+N) \times (L_i+N)$, $(i=1,\dots,m)$ are real is calculated as a multi-dimensional integral, and as a determinant. Both involve Meijer G-functions. Evaluation formulae of the latter, based on a recursive scheme, allow it to be proved that for any $m$ and with each $L_i$ even the probability is a rational number. The formulae furthermore provide for explicit computation in small order cases.

math-ph↗

arXiv2017

Research Opportunities and Visions for Smart and Pervasive Health

Improving the health of the nation's population and increasing the capabilities of the US healthcare system to support diagnosis, treatment, and prevention of disease is a critical national and societal priority. In the past decade, tremendous advances in expanding computing capabilities--sensors, data analytics, networks, advanced imaging, and cyber-physical systems--have, and will continue to, enhance healthcare and health research, with resulting improvements in health and wellness. However, the cost and complexity of healthcare continues to rise alongside the impact of poor health on productivity and quality of life. What is lacking are transformative capabilities that address significant health and healthcare trends: the growing demands and costs of chronic disease, the greater responsibility placed on patients and informal caregivers, and the increasing complexity of health challenges in the US, including mental health, that are deeply rooted in a person's social and environmental context.

cs.CY↗

arXiv2017

Rydberg-atom based radio-frequency electrometry using frequency modulation spectroscopy in room temperature vapor cells

Rydberg atom-based electrometry enables traceable electric field measurements with high sensitivity over a large frequency range, from gigahertz to terahertz. Such measurements are particularly useful for the calibration of radio frequency and terahertz devices, as well as other applications like near field imaging of electric fields. We utilize frequency modulated spectroscopy with active control of residual amplitude modulation to improve the signal to noise ratio of the optical readout of Rydberg atom-based radio frequency electrometry. Matched filtering of the signal is also implemented. Although we have reached similarly, high sensitivity with other read-out methods, frequency modulated spectroscopy is advantageous because it is well-suited for building a compact, portable sensor. In the current experiment, $\sim 3 μV cm^{-1}Hz^{-1/2}$ sensitivity is achieved and is found to be photon shot noise limited.

quant-ph↗

arXiv2016

Atom-Based Sensing of Weak Radio Frequency Electric Fields Using Homodyne Readout

We utilize a homodyne detection technique to achieve a new sensitivity limit for atom-based, absolute radio-frequency electric field sensing of $\mathrm{5 μV cm^{-1} Hz^{-1/2} }$. A Mach-Zehnder interferometer is used for the homodyne detection. With the increased sensitivity, we investigate the dominant dephasing mechanisms that affect the performance of the sensor. In particular, we present data on power broadening, collisional broadening and transit time broadening. Our results are compared to density matrix calculations. We show that photon shot noise in the signal readout is currently a limiting factor. We suggest that new approaches with superior readout with respect to photon shot noise are needed to increase the sensitivity further.

quant-ph↗

arXiv2016

Deterministic strain-induced arrays of quantum emitters in a two-dimensional semiconductor

An outstanding challenge in quantum photonics is scalability, which requires positioning of single quantum emitters in a deterministic fashion. Site positioning progress has been made in established platforms including defects in diamond and self-assembled quantum dots, albeit often with compromised coherence and optical quality. The emergence of single quantum emitters in layered transition metal dichalcogenide semiconductors offers new opportunities to construct a scalable quantum architecture. Here, using nanoscale strain engineering, we deterministically achieve a two-dimensional lattice of quantum emitters in an atomically thin semiconductor. We create point-like strain perturbations in mono- and bi-layer WSe2 which locally modify the band-gap, leading to efficient funneling of excitons towards isolated strain-tuned quantum emitters that exhibit high-purity single photon emission. These arrays of non-classical light emitters open new vistas for two-dimensional semiconductors in cavity quantum electrodynamics and integrated on-chip quantum photonics.

cond-mat.mes-hall↗

arXiv2016

Learning Shallow Detection Cascades for Wearable Sensor-Based Mobile Health Applications

The field of mobile health aims to leverage recent advances in wearable on-body sensing technology and smart phone computing capabilities to develop systems that can monitor health states and deliver just-in-time adaptive interventions. However, existing work has largely focused on analyzing collected data in the off-line setting. In this paper, we propose a novel approach to learning shallow detection cascades developed explicitly for use in a real-time wearable-phone or wearable-phone-cloud systems. We apply our approach to the problem of cigarette smoking detection from a combination of wrist-worn actigraphy data and respiration chest band data using two and three stage cascades.

stat.ML↗