arXiv subjects

Ankit Kumar

Publications and source records attributed to Ankit Kumar.

At least 109 records · Page 6Linked to original sources

arXiv2023

Open Strange Mesons in (magnetized) nuclear matter

We investigate the mass modifications of open strange mesons (vector $K^*$ and axial vector $K_1$) in (magnetized) isospin asymmetric nuclear matter using quantum chromodynamics sum rule (QCDSR) approach. The in-medium decay widths of $K^*$ $\rightarrow$ $Kπ$ and $K_1$ $\rightarrow$ $K^*π$ are studied from the mass modifications of $K_1$, $K^*$ and $K$ mesons, using a light quark-antiquark pair creation model, namely the ${}^3 P_0$ model. The in-medium decay width for $K_1$ $\rightarrow$ $K^*π$ is compared with the decay widths calculated using a phenomenological Lagrangian. The effects of magnetic fields are also studied on the mass and the partial decay width of the vector $K^*$ meson decaying to $Kπ$. Within the QCD sum rule approach, the medium effects on the masses of the open strange mesons are calculated from the light quark condensates and the gluon condensates in the hadronic medium. The quark condensates are calculated from the medium modifications of the scalar fields ($σ$, $ζ$, and $δ$) in the mean field approximation within a chiral $SU(3)$ model, while the scalar gluon condensate is obtained from the medium modification of a scalar dilaton field ($χ$), which is introduced within the model to imitate the scale invariance breaking of QCD.

hep-ph↗

arXiv2023

Quarkyonic Model for Neutron Star Matter: A Relativistic Mean-Field Approach

The concept of quarkyonic matter presents a promising alternative to the conventional models used to describe high-density matter and provides a more nuanced and detailed understanding of the properties of matter under extreme conditions that exist in astrophysical bodies. The aim of this study is to showcase the effectiveness of utilizing the quarkyonic model, in combination with the relativistic mean-field formalism, to parameterize the equation of state at high densities. Through this approach, we intend to investigate and gain insights into various fundamental properties of a static neutron star, such as its compositional ingredients, speed of sound, mass-radius profile, and tidal deformability. The obtained results revealed that the quarkyonic matter equation of state (EOS) is capable of producing a heavy neutron star with the mass range of $\sim$ $2.8 M_\odot$. The results of our inquiry have demonstrated that the EOS for quarkyonic matter not only yields a neutron star with a significantly high mass but also showcases a remarkable degree of coherence with the conformal limit of the speed of sound originating from deconfined QCD matter. Furthermore, we have observed that the tidal deformability of the neutron star, corresponding to the EOSs of quarkyonic matter, is in excellent agreement with the observational constraints derived from the GW170817 and GW190425 events. This finding implies that the quarkyonic model is capable of forecasting the behavior of neutron stars associated with binary merger systems. This aspect has been meticulously scrutinized in terms of merger time, gravitational wave signatures, and collapse times using numerical relativity simulations.

nucl-th↗

arXiv2023

An Accurate Pentadiagonal Matrix Solution for the Time-Dependent Schrödinger Equation

One of the unitary forms of the quantum mechanical time evolution operator is given by Cayley's approximation. A numerical implementation of the same involves the replacement of second derivatives in Hamiltonian with the three-point formula, which leads to a tridiagonal system of linear equations. In this work, we invoke the highly accurate five-point stencil to discretize the wave function onto an Implicit-Explicit pentadiagonal Crank-Nicolson scheme. It is demonstrated that the resultant solutions are significantly more accurate than the standard ones. We also discuss the resolution of bipartite wavepacket dynamics and derive conditions under which a product state from the laboratory perspective remains a product state from the center-of-mass point of view. This has profound applications for decoupling complicated bipartite dynamics into two independent single-particle problems.

quant-ph↗

arXiv2023

QCD sum rule analysis of Heavy Quarkonium states in magnetized matter -- effects of (inverse) magnetic catalysis

The masses of the $1S$ and $1P$ states of heavy quarkonia are investigated in the magnetized, asymmetric nuclear medium, accounting for the Dirac sea effects, using a combined approach of chiral effective model and QCD sum rule method. These are calculated from the in-medium scalar and twist-2 gluon condensates, calculated within the chiral model. The gluon condensate is simulated through the scalar dilaton field, $χ$ introduced in the model through a scale-invariance breaking logarithmic potential. Considering the scalar fields to be classical, the dilaton field, $χ$, the non-strange isoscalar, $σ(\sim (\langle \bar u u\rangle +\langle \bar d d\rangle ))$, strange isoscalar, $ζ(\sim \langle \bar s s\rangle)$ and non-strange isovector, $δ(\sim (\langle\bar u u\rangle-\langle\bar d d\rangle)$) fields, are obtained by solving their coupled equations of motion, as derived from the chiral model Lagrangian. The effects of magnetic field due to the Dirac sea as well as the Landau energy levels of protons, and the non-zero anomalous magnetic moments of the nucleons are considered in the present study. In presence of an external magnetic field, there is also mixing between the longitudinal component of the vector meson and pseudoscalar meson (PV mixing) in both quarkonia sectors, leading to a rise (drop) of the masses of $J/ψ^{||}\ (η_c$) and $Υ^{||}(1S)\ (η_b$) states. These might show in the experimental observables, e.g., the dilepton spectra in the non-central, ultra-relativistic heavy ion collision experiments at RHIC and LHC, where the produced magnetic field is huge.

hep-ph↗

arXiv2023

Evidence of Charge-Phonon coupling in Van der Waals materials Ni1-xZnxPS3

NiPS3 is a Van der Waals antiferromagnet that has been found to display spin-charge and spin-phonon coupling in its antiferromagnetically ordered state below TN = 155 K. Here, we study high-quality crystals of site-diluted Ni1-xZnxPS3 (0 < x < 0.2) using temperature-dependent specific heat and Raman spectroscopy probes. The site dilution suppresses the antiferromagnetic ordering in accordance with the mean-field prediction. In NiPS3, we show that the phonon mode P2 (176 cm-1) associated with Ni vibrations show a distinct asymmetry due to the Fano resonance, which persists only in the paramagnetic phase, disappearing below T_N = 155 K. This was further supported by temperature-dependent Raman data on an 8% Zn-doped crystal (T_N = 135 K) where Fano resonance similarly van in the magnetically ordered phase. This is contrary to the behaviour of the Raman mode P9 (570 cm-1), which shows a Fano resonance at low temperatures below T_N due to its coupling with the two-magnon continuum. We show that the Fano resonance of P2 arises from its coupling with an electronic continuum that weakens considerably upon cooling to low temperatures. In the doped crystals, the Fano coupling is found to enhance with Zn-doping. These observations suggest the presence of strong electron-phonon coupling in the paramagnetic phase of NiPS3 due to charge density fluctuations associated with the negative charge transfer state of Ni.

cond-mat.str-el↗

arXiv2023

Calculational Proofs in ACL2s

Teaching college students how to write rigorous proofs is a critical objective in courses that introduce formal reasoning. Over the course of several years, we have developed a mechanically-checkable style of calculational reasoning that we used to teach over a thousand freshman-level undergraduate students how to reason about computation in our "Logic and Computation" class at Northeastern University. We were inspired by Dijkstra, who advocated the use of calculational proofs, writing "calculational proofs are almost always more effective than all informal alternatives, ..., the design of calculational proofs seems much more teachable than the elusive art of discovering an informal proof." Our calculational proof checker is integrated into ACL2s and is available as an Eclipse IDE plugin, via a Web interface, and as a stand-alone tool. It automatically checks proofs for correctness and provides useful feedback. We describe the architecture of the checker, its proof format, its underlying algorithms, its correctness and provide examples using proofs from our undergraduate class and from Dijkstra. We also describe our experiences using the proof checker to teach undergraduates how to formally reason about computation.

cs.LO↗

arXiv2023

Absolute continuity of the solution to stochastic generalized Burgers-Huxley equation

The present work deals with the global solvability as well as absolute continuity of the law of the solution to stochastic generalized Burgers-Huxley (SGBH) equation driven by multiplicative space-time white noise in a bounded interval of $\mathbb{R}$. We first prove the existence of a unique local mild solution to SGBH equation with the help of a truncation argument and contraction mapping principle. Then global solvability results are obtained by using uniform bounds of the local mild solution and stopping time arguments. Later, we establish a comparison theorem for the solution of SGBH equation having higher order nonlinearities and it plays a crucial role in this work. Then, we discuss the weak differentiability of the solution to SGBH equation in the Malliavin calculus sense. Finally, we obtain the absolute continuity of the law of the solution with respect to the Lebesgue measure on $\mathbb{R}$, and the existence of density with the aid of comparison theorem and weak differentiability of the solution.

math.PR↗

arXiv2023

A study of the evolution of bulges and disks of spiral galaxies in interacting and isolated environments

Galaxies usually reside in groups and clusters where they interact gravitationally. These interactions affect the internal dynamics of the galaxies. In this thesis, we have studied the effect of flyby interactions and dark matter distributions on the evolution of bulges and disks of spiral galaxies. To understand the effect of flyby interactions on the bulges, disks, and spiral arms of Milky Way mass galaxies, we simulated disk galaxies with classical bulges and boxy/peanut pseudo-bulges, then performed their flyby interactions with 1/10 and 1/5 mass galaxies. Using photometric and kinematic bulge-disk decompositions of the major galaxy, we showed that the disks get shorter and thicker during flyby interactions. Classical bulges remain intact. However, pseudo-bulges become dynamically hotter. Tidally induced spiral arms are transient density waves. They form soon after pericenter passage and decay in two phases; the initial rapid winding and the subsequent slow winding. We showed that the spirals are the main drivers of wave-like vertical breathing motion seen in the Milky Way. Tidal interactions do not directly induce breathing motion. In another work, we showed that the oblate dark matter halos delay bar formation, so bar buckling is also delayed, but probate halos promote multiple bucklings. Due to multiple bucklings, boxy/peanut bulges in prolate halos show the maximum thickness. Using SDSS galaxies, we found that pseudo-bulges are diffuse compared to classical bulges and are commonly found in low mass galaxies. In the local volume, pseudo-bulges overcome the classical bulges even in bulge dominated galaxies, so more than $75\%$ of local volume is rotation dominated. Finally, we showed that bulgeless galaxies in Illustris TNG50 are metal-poor, have high specific angular momentum as compared to the galaxies with bulges and fall at the lower end of baryonic to dark matter mass ratio.

astro-ph.GA↗

arXiv2023

Continuous-Variable Entanglement through Central Forces: Application to Gravity between Quantum Masses

We describe a complete method for a precise study of gravitational interaction between two nearby quantum masses. Since the displacements of these masses are much smaller than the initial separation between their centers, the displacement-to-separation ratio is a natural parameter in which the gravitational potential can be expanded. We show that entanglement in such experiments is sensitive to initial relative momentum only when the system evolves into non-Gaussian states, i.e., when the potential is expanded at least up to the cubic term. A pivotal role of force gradient as the dominant contributor to position-momentum correlations is demonstrated. We establish a closed-form expression for the entanglement gain, which shows that the contribution from the cubic term is proportional to momentum and from the quartic term is proportional to momentum squared. From a quantum information perspective, the results find applications as a momentum witness of non-Gaussian entanglement. Our methods are versatile and apply to any number of central interactions expanded to any order.

quant-ph↗

arXiv2023

Band degeneracy, resonant level formation and low thermal conductivity in dilute In and Ga co-doped thermoelectric compound SnTe

We report the effect of co-doping of In and Ga at low concentrations on the structural, electronic, and thermoelectric properties of SnTe based compositions $Sn_{1.03-2x}In_{x}Ga_{x}Te$ (x = 0, 0.01, 0.02, 0.04) prepared by the solid-state route and spark plasma sintering (SPS). All compositions formed in the fcc structure (Fm-3m) with no other impurity phase. The optical band gap increased with the co-doping, indicative of band convergence effects. First principle electronic structure calculations showed band convergence and the formation of resonant levels, due to Ga and In doping respectively. The carrier concentration increased on hole-doping by In and Ga ions while carrier mobility decreased due to impurity scattering. The resistivity increased with temperature, indicative of the degenerate semiconducting character of the compounds. The Seebeck coefficient of the doped samples increased linearly with temperature, reaching 85 - 95 $μ$V/K at 783 K. Thermal conductivity decreased sharply with co-doping, and the lattice thermal conductivity dropped to 0.42 W$m^{-1}$ $K^{-1}$ above 750 K. The enhanced power factor and low lattice thermal conductivity on doping resulted in a maximum figure of merit ZT = 0.34 at 773 K, twice that of the pristine SnTe.

cond-mat.mtrl-sci↗

arXiv2023

Uniform large deviation principle for the solutions of two-dimensional stochastic Navier-Stokes equations in vorticity form

The main objective of this paper is to demonstrate the uniform large deviation principle (UDLP) for the solutions of two-dimensional stochastic Navier-Stokes equations (SNSE) in the vorticity form when perturbed by two distinct types of noises. We first consider an infinite-dimensional additive noise that is white in time and colored in space and then consider a finite-dimensional Wiener process with linear growth coefficient. In order to obtain the ULDP for 2D SNSE in the vorticity form, where the noise is white in time and colored in space, we utilize the existence and uniqueness result from \emph{B. Ferrario et. al., Stochastic Process. Appl., {\bf 129} (2019), 1568--1604,} and the \textsl{uniform contraction principle}. For the finite-dimensional multiplicative Wiener noise, we first prove the existence of a unique local mild solution to the vorticity equation using a truncation and fixed point arguments. We then establish the global existence of the truncated system by deriving a uniform energy estimate for the local mild solution. By applying stopping time arguments and a version of Skorokhod's representation theorem, we conclude the global existence and uniqueness of a solution to our model. We employ the weak convergence approach to establish the ULDP for the law of the solutions in two distinct topologies. We prove ULDP in the $\mathrm{C}([0,T];\mathrm{L}^p(\mathbb{T}^2))$ topology, for $p>2$, taking into account the uniformity of the initial conditions contained in bounded subsets of $\mathrm{L}^p(\mathbb{T}^2)$. Finally, in $\mathrm{C}([0,T]\times\mathbb{T}^2)$ topology, the uniformity of initial conditions lying in bounded subsets of $\mathrm{C}(\mathbb{T}^2)$ is considered.

math.PR↗

arXiv2023

Automated Grading of Automata with ACL2s

Almost all Computer Science programs require students to take a course on the Theory of Computation (ToC) which covers various models of computation such as finite automata, push-down automata and Turing machines. ToC courses tend to give assignments that require paper-and-pencil solutions. Grading such assignments takes time, so students typically receive feedback for their solutions more than a week after they complete them. We present the Automatic Automata Checker (A2C), an open source library that enables one to construct executable automata using definitions that mimic those found in standard textbooks. Such constructions are easy to reason about using semantic equivalence checks, properties and test cases. Instructors can conveniently specify solutions in the form of their own constructions. A2C can check for semantic equivalence between student and instructor solutions and can immediately generate actionable feedback, which helps students better understand the material. A2C can be downloaded and used locally by students as well as integrated into Learning Management Systems (LMS) like Gradescope to automatically grade student submissions and generate feedback. A2C is based on the ACL2s interactive theorem prover, which provides advanced methods for stating, proving and disproving properties. Since feedback is automatic, A2C can be deployed at scale and integrated into massively open online courses.

cs.LO↗

arXiv2023

Well-posedness and uniform large deviation principle for stochastic Burgers-Huxley equation perturbed by a multiplicative noise

In this work, we focus on the global solvability and uniform large deviations for the solutions of stochastic generalized Burgers-Huxley (SGBH) equation perturbed by a small multiplicative white in time and colored in space noise. The SGBH equation has the nonlinearity of polynomial order and noise considered in this work is infinite dimensional with a coefficient having linear growth. First, we prove the existence of a \textsl{unique local mild solution} in the sense of Walsh to SGBH equation with the help of a truncation argument and contraction mapping principle. Then the global solvability results are established by using uniform bounds of the local mild solution, stopping time arguments, tightness properties and Skorokhod's representation theorem. By using the uniform Laplace principle, we obtain the \textsl{large deviation principle} (LDP) for the law of solutions to SGBH equation by using variational representation methods. Further, we derive the \textsl{uniform large deviation principle} (ULDP) for the law of solutions in two different topologies by using a weak convergence method. First, in the $\mathrm{C}([0, T ];\mathrm{L}^p([0,1])) $ topology where the uniformity is over $\mathrm{L}^p([0,1])$-bounded sets of initial conditions, and secondly in the $\mathrm{C} ([0, T ] \times[0,1])$ topology with uniformity being over bounded subsets in the $\mathrm{C}([0,1])$-norm. Finally, we consider SGBH equation perturbed by a space-time white noise with bounded noise coefficient and establish the ULDP for the laws of solutions. The results obtained in this work hold true for stochastic Burgers' as well as Burgers-Huxley equations.

math.PR↗

arXiv2022

Small time asymptotics for a class of stochastic partial differential equations with fully monotone coefficients forced by multiplicative Gaussian noise

The main goal of this article is to study the effect of small, highly nonlinear, unbounded drifts (small time large deviation principle (LDP) based on exponential equivalence arguments) for a class of stochastic partial differential equations (SPDEs) with fully monotone coefficients driven by multiplicative Gaussian noise. The small time LDP obtained in this paper is applicable for various quasi-linear and semilinear SPDEs such as porous medium equations, Cahn-Hilliard equation, 2D Navier-Stokes equations, convection-diffusion equation, 2D liquid crystal model, power law fluids, Ladyzhenskaya model, $p$-Laplacian equations, etc., perturbed by multiplicative Gaussian noise.

math.PR↗

arXiv2022

Context-aware 6D Pose Estimation of Known Objects using RGB-D data

6D object pose estimation has been a research topic in the field of computer vision and robotics. Many modern world applications like robot grasping, manipulation, autonomous navigation etc, require the correct pose of objects present in a scene to perform their specific task. It becomes even harder when the objects are placed in a cluttered scene and the level of occlusion is high. Prior works have tried to overcome this problem but could not achieve accuracy that can be considered reliable in real-world applications. In this paper, we present an architecture that, unlike prior work, is context-aware. It utilizes the context information available to us about the objects. Our proposed architecture treats the objects separately according to their types i.e; symmetric and non-symmetric. A deeper estimator and refiner network pair is used for non-symmetric objects as compared to symmetric due to their intrinsic differences. Our experiments show an enhancement in the accuracy of about 3.2% over the LineMOD dataset, which is considered a benchmark for pose estimation in the occluded and cluttered scenes, against the prior state-of-the-art DenseFusion. Our results also show that the inference time we got is sufficient for real-time usage.

cs.CV↗

arXiv2022

Large deviation principle for a class of stochastic partial differential equations with fully local monotone coefficients perturbed by Lévy noise

The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid dynamic models is carried out in this work. The aim of this work is to develop the large deviation theory for small Gaussian as well as Poisson noise perturbations of the above class of SPDEs. We establish a Wentzell-Freidlin type large deviation principle for the strong solutions to such SPDEs perturbed by Lévy noise in a suitable Polish space using a variational representation (based on a weak convergence approach) for nonnegative functionals of general Poisson random measures and Brownian motions. The well-posedness of an associated deterministic control problem is established by exploiting pseudo-monotonicity arguments and the stochastic counterpart is obtained by an application of Girsanov's theorem.

math.PR↗

arXiv2022

Masses of Heavy Quarkonium states in magnetized matter -- effects of PV mixing and (inverse) magnetic catalysis

We study the in-medium masses of the heavy quarkonium (charmonium and bottomonium) states in isospin asymmetric nuclear matter in presence of an external magnetic field. The mass modifications of the heavy quarkonia are obtained from the medium modifications of a scalar dilaton field, $χ$, calculated within a chiral effective model. The dilaton field is introduced in the model through a scale invariance breaking logarithmic potential, and, simulates the gluon condensates of QCD. Within the chiral effective model, the values of the dilaton field along with the scalar (isoscalar, $σ(\sim \langle \bar u u \rangle +\langle \bar d d \rangle)$, isoscalar $ζ(\sim \langle \bar s s \rangle$) and isovector $δ(\sim \langle \bar u u\rangle - \langle\bar d d \rangle)$) fields, are solved from their coupled equations of motion. These are solved accounting for the effects of the Dirac sea (DS) as well as anomalous magnetic moments (AMMs) of the nucleons. The Dirac sea contributions are observed to lead to enhancement (reduction) of the quark condensates (through $σ$ and $ζ$ fields) with increase in magnetic field, an effect called the (inverse) magnetic catalysis. The magnetic field effects on the masses of the heavy quarkonia include the mixing of the pseudoscalar (spin 0) and vector (spin 1) states (PV mixing), as well as, the effects from (inverse) magnetic catalysis. These effects are observed to be significant for large values of the magnetic field. This should have observable consequences on the production of the heavy quarkonia and open heavy flavour mesons, resulting from ultra-relativistic peripheral heavy ion collision experiments, where the created magnetic field can be huge.

hep-ph↗

arXiv2022

Well-posedness of a class of stochastic partial differential equations with fully monotone coefficients perturbed by Lévy noise

In this article, we consider the following class of stochastic partial differential equations (SPDE): \begin{equation*} \left\{\begin{aligned}\mathrm{d} \mathbf{X}(t)&=\mathrm{A}(t,\mathbf{X}(t))\mathrm{d} t+\mathrm{B}(t,\mathbf{X}(t))\mathrm{d}\mathrm{W}(t)+\int_{\mathrm{Z}}γ(t,\mathbf{X}(t-),z)\widetildeπ(\mathrm{d} t,\mathrm{d} z),\; t\in[0,T],\\ \mathbf{X}(0)&=\boldsymbol{x} \in \mathbb{H},\end{aligned} \right.\end{equation*} with fully locally monotone coefficients in a Gelfand triplet $\mathbb{V}\subset \mathbb{H}\subset\mathbb{V}^*$, where the mappings \begin{align*} \mathrm{A}:[0,T]\times \mathbb{V}\to\mathbb{V}^*,\quad \mathrm{B}:[0,T]\times \mathbb{V}\to\mathrm{L}_2(\mathbb{U},\mathbb{H}), \quad γ:[0,T]\times\mathbb{V}\times\mathrm{Z}\to\mathbb{H}, \end{align*} are measurable, $\mathrm{L}_2(\mathbb{U},\mathbb{H})$ is the space of all Hilbert-Schmidt operators from $\mathbb{U}\to\mathbb{H}$, $\mathrm{W}$ is a $\mathbb{U}$-cylindrical Wiener process and $\widetildeπ$ is a compensated time homogeneous Poisson random measure. Such kind of SPDE cover a large class of quasilinear SPDE and a good number of fluid dynamic models. Under certain generic assumptions of $\mathrm{A},\mathrm{B}$ and $γ$, using the classical Faedo-Galekin technique, a compactness method and a version of Skorokhod's representation theorem, we prove the existence of a \emph{probabilistic weak solution} as well as \emph{pathwise uniqueness of solution}. We use the classical Yamada-Watanabe theorem to obtain the existence of a \emph{unique probabilistic strong solution}. Finally, we allow both diffusion coefficient $\mathrm{B}(t,\cdot)$ and jump noise coefficient $γ(t,\cdot,z)$ to depend on both $\mathbb{H}$-norm and $\mathbb{V}$-norm, which implies that both the coefficients could also depend on the gradient of solution. We establish the global solvability results.

math.PR↗