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Anupam Garg

Publications and source records attributed to Anupam Garg.

At least 19 recordsLinked to original sources

Analyzing LLM Usage in an Advanced Computing Class in India

This study examines the use of large language models (LLMs) by undergraduate and graduate students for programming assignments in advanced computing classes. Unlike existing research, which primarily focuses on introductory classes and lacks in-depth analysis of actual student-LLM interactions, our work fills this gap. We conducted a comprehensive analysis involving 411 students from a Distributed Systems class at an Indian university, where they completed three programming assignments and shared their experiences through Google Form surveys. Our findings reveal that students leveraged LLMs for a variety of tasks, including code generation, debugging, conceptual inquiries, and test case creation. They employed a spectrum of prompting strategies, ranging from basic contextual prompts to advanced techniques like chain-of-thought prompting and iterative refinement. While students generally viewed LLMs as beneficial for enhancing productivity and learning, we noted a concerning trend of over-reliance, with many students submitting entire assignment descriptions to obtain complete solutions. Given the increasing use of LLMs in the software industry, our study highlights the need to update undergraduate curricula to include training on effective prompting strategies and to raise awareness about the benefits and potential drawbacks of LLM usage in academic settings.

cs.HC

Suhl Instabilities in Nanoscopic Spheroids

We simulate the magnetization dynamics of a permalloy spheroid of nanoscopic size in zero external field, such that both dipolar and exchange interactions are important. Low excitation power is used to obtain the frequencies and mode patterns of many normal modes. At higher power, non-linear three and four mode couplings between magnons carrying orbital angular momentum are observed to give rise to Suhl instabilities. Suhl's analysis of the selection rules governing the allowed processes is extended to initial states other than uniform precession. These rules are studied and confirmed by the simulations. Both down- and up-conversion are seen as well as three and four-mode processes. General trends are inferred for preferred instabilities among those that are allowed, although the thresholds for some instabilities appear to be very high.

cond-mat.mes-hall

Ferromagnetic resonance modes in the exchange dominated limit in cylinders of finite length

We analyze the magnetic mode structure of axially-magnetized, finite-length, nanoscopic cylinders in a regime where the exchange interaction dominates, along with simulations of the mode frequencies of the ferrimagnet yttrium iron garnet. For the bulk modes we find that the frequencies can be represented by an expression given by Herring and Kittel by using wavevector components obtained by fitting the mode patterns emerging from these simulations. In addition to the axial, radial, and azimuthal modes that are present in an infinite cylinder, we find localized "cap modes" that are "trapped" at the top and bottom cylinder faces by the inhomogeneous dipole field emerging from the ends. Semi-quantitative explanations are given for some of the modes in terms of a one-dimensional Schrodinger equation which is valid in the exchange dominant case. The assignment of the azimuthal mode number is carefully discussed and the frequency splitting of a few pairs of nearly degenerate modes is determined through the beat pattern emerging from them.

cond-mat.mes-hall

Thermal Resistance at a Twist Boundary and Semicoherent Heterointerface

Traditional models of interfacial phonon scattering, including the acoustic mismatch model (AMM) and diffuse mismatch model (DMM), take into account the bulk properties of the material surrounding the interface, but not the atomic structure and properties of the interface itself. Here, we derive a theoretical formalism for the phonon scattering at a dislocation grid, or two interpenetrating orthogonal arrays of dislocations, as this is the most stable structure of both the symmetric twist boundary and semicoherent heterointerface. With this approach, we are able to separately examine the contribution to thermal resistance due to the step function change in acoustic properties and due to interfacial dislocation strain fields, which induces diffractive scattering. Both low-angle Si-Si twist boundaries and the Si-Ge heterointerfaces are considered here and compared to previous experimental and simulation results. This work indicates that scattering from misfit dislocation strain fields doubles the thermal boundary resistance of Si-Ge heterointerfaces compared to scattering due to acoustic mismatch alone. Scattering from grain boundary dislocation strain fields is predicted to dominate the thermal boundary resistance of Si-Si twist boundaries. This physical treatment can guide the thermal design of devices by quantifying the relative importance of interfacial strain fields, which can be engineered via fabrication and processing methods, versus acoustic mismatch, which is fixed for a given interface. Additionally, this approach captures experimental and simulation trends such as the dependence of thermal boundary resistance on the grain boundary angle and interfacial strain energy.

cond-mat.mtrl-sci

Wigner functions in the Higher-Spin Einstein-Podolsky-Rosen-Bohm Experiment

The spin-$j$ extension of Bohm's version of the Einstein-Podolsky-Rosen experiment is is analysed in terms of the Wigner function when the two spins are in a singlet state. This function is calculated for all $j$, and it is shown that just as Bell inequalities are violated with undiminished range and magnitude for arbitarirly large $j$, this function does not become less negative. On the contrary, the oscillations between positive and negative values grow both in frequency and amplitude. It is argued that this is an alternative way to grasp the approach to classical behavior with increasing quantum number.

quant-ph

Agnostic Detector Error, Wigner Functions, and the Classical Limit of the High-Spin Einstein-Podolsky-Rosen Experiment

The spin-$j$ Einstein-Podolsky-Rosen experiment is studied with a view to understanding how classical behaviour emerges as $j \to \infty$. It is proposed that it is necessary to include detector error, which if it is be to viewed as an essential aspect of the emergence of classicality, should be both minimal, i.e., no more than necessary to wash out quantum mechanical behaviour, and agnostic, by which is meant that one should be able to ascribe it to error in the preparation of the state just as well as to the detector.Errors in the state preparation are discussed via the spin Wigner function. An agnostic error protocol is described which appears to be minimal.

quant-ph

Low-Temperature Phonoemissive Tunneling Rates in Single Molecule Magnets

Tunneling between the two lowest energy levels of single molecule magnets with Ising type anisotropy, accompanied by the emission or absorption of phonons, is considered. Quantitatively accurate calculations of the rates for such tunneling are performed for a model Hamiltonian especially relevant to the best studied example, \Fe8. Two different methods are used: high-order perturbation theory in the spin-phonon interaction and the non-Ising-symmetric parts of the spin Hamiltonian, and a novel semiclassical approach based on spin-coherent-state-path-integral instantons. The methods are found to be in good quantitative agreement with other, and consistent with previous approaches to the problem. The implications of these results for magnetization of molecular solids of these molecules are discussed briefly.

cond-mat.mes-hall

Low-Temperature Magnetization Dynamics of Magnetic Molecular Solids in a Swept Field

The swept-field experiments on magnetic molecular solids such as \Fe8 are studied using Monte Carlo simulations. A kinetic equation is developed to understand the phenomenon. It is found that the simulations provide a quantitatively accurate account of the experiments. The kinetic equation provides a similarly accurate account except at very low sweep velocities, where it fails modestly. This failure is due to the neglect of short-range correlations between the dipolar magnetic fields seen by the molecular spins. Both the simulations and the kinetic equation provide a good understanding of the distribution of these dipolar fields.

cond-mat.stat-mech

The Semiclassical Coherent State Propagator in the Weyl Representation

It is shown that the semiclassical coherent state propagator takes its simplest form when the quantum mechanical Hamiltonian is replaced by its Weyl symbol in defining the classical action, in that there is then no need of a Solari-Kochetov correction. It is also shown that such a correction exists if a symbol other than the Weyl symbol is chosen, and that its form is different depending on the symbol chosen. The various forms of the propagator based on different symbols are shown to be equivalent provided the correspondingly correct Solari-Kochetov correction is included. All these results are shown for both particle and spin coherent state propagators. The global anomaly in the fluctuation determinant is further elucidated by a study of the connection bewteen the discrete fluctuation determinant and the discrete Jacobi equation.

quant-ph

The Weyl-Wigner-Moyal Formalism for Spin

The Weyl-Wigner-Moyal formalism is developed for spin by means of a correspondence between spherical harmonics and spherical harmonic tensor operators. The analogue of the Moyal expansion is developed for the Weyl symbol of the product of two operators in terms of the symbols for the individual operators, and it is shown that in the classical limit, the Weyl symbol for a commutator equals $i$ times the Poisson bracket of the corresponding Weyl symbols. It is also found that, to the same order, there is no correction in the symbol for the anticommutator.

math-ph

Phonoemissive Spin Tunneling in Molecular Nanomagnets

A new mechanism is proposed for the magnetization reversal of molecular nanomagnets such as \Fe8. In this process the spin tunnels from the lowest state near one easy direction to the first excited state near the opposite easy direction, and subsequently decays to the second easy direction with the emission of a phonon, or it first emits a phonon and then tunnels to the final state. This mechanism is the simplest imaginable one that allows magnetization relaxation in the presence of a longitudinal magnetic field that is so large that the nuclear spin environment cannot absorb the energy required for energy conservation to hold. It is proposed as a way of understanding both magnetization realaxation and Landau-Zener-Stückelberg experiments. The requisite Fermi golden rule rate, and the spin-flip rates are calculated, and it is found that these rates are much too low by several orders of magnitude. Thus the understanding of magnetic relaxation in the experiments remains an open question.

cond-mat.mes-hall

Low-Temperature Magnetization Relaxation in Magnetic Molecular Solids

The low temperature relaxation of the magnetization in magnetic molecular solids such as Fe$_8$ is studied using Monte Carlo simulations. A set of rate equations is developed to understand the simulations, and the results are compared. The simulations show that the magnetization of an initially saturated samples deviates as a square-root in time at short times, as observed experimentally, and this law is derived from the rate equations analytically.

cond-mat.stat-mech

Lost and found: The missing diabolical points in the Fe$_8$ molecular magnet

Certain diabolical points in the tunneling spectrum of the single-molecule magnet Fe$_8$ were previously believed to be have been eliminated as a result of a weak fourth-order anisotropy. As shown by Bruno, this is not so, and the points are only displaced in the magnetic field space along the medium anisotropy direction. The previously missing points are numerically located by following the lines of the Berry curvature. The importance of an experimental search for these rediscovered points is discussed.

cond-mat.mes-hall

Incoherent Landau-Zener-Stuckelberg Transitions in Single-Molecule Magnets

It is shown that in experiments on single molecule magnets (SMM's) in which transitions between two lowest spin states are induced by sweeping the applied magnetic field along the easy axis, the transitions are fully incoherent. Nuclear spins and the dipolar coupling of molecular spins are identified as the main sources of decoherence, and the form of the decoherence is calculated. The Landau-Zener-Stuckelberg (LZS) process is examined in light of this decoherence, and it is shown that the correct formula for the spin-flip probability is better given by a more recent formula of Kayanuma's than that of LZS. The two formulas are shown to be identical in the limit of rapid sweeps. An approximate way of incorporating the molecular spin dipole field into the rate equations for this process is developed.

cond-mat.other

Bohr-Sommerfeld quantization of spin Hamiltonians

The Bohr-Sommerfeld rule for a spin system is obtained, including the first quantum corrections. The rule applies to both integer and half-integer spin, and respects Kramers degeneracy for time-reversal invariant systems. It is tested for various models, in particular the Lipkin-Meshkov-Glick model, and found to agree very well with exact results.

cond-mat.mes-hall

Large-field versus discontinuous instantons in spin orientation tunneling

Tunnel splitting oscillations in magnetic molecules are reconsidered within the simplest model for the problem, which does not contain fourth order anisotropy. It is shown that at large magnetic field, there is only one instanton, and it is continuous. This is in contrast to the discontinuous instantons that are induced by the fourth order term [Ersin Keçecioğlu and A. Garg, Phys. Rev. Lett. {\bf 88}, 237205 (2002)].

cond-mat.mes-hall

Spin Tunneling in Magnetic Molecules: Quasisingular Perturbations and Discontinuous SU(2) Instantons

Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the Fe8 molecular solid. It is shown that such paths are essential to a proper understanding of the phenomenon of quenched spin tunneling in these molecules. In the Fe8 problem, such paths are shown to arise as soon as a fourth order anisotropy term in the energy is turned on, making this term a singular perturbation from the semiclassical point of view. The instanton approximation is shown to quantitatively explain the magnetic field dependence of the tunnel splitting, as well as agree with general rules for the number of quenching points allowed for a given value of spin. An accurate approximate formula for the spacing between quenching points is derived.

cond-mat

Spin Coherent-State Path Integrals and the Instanton Calculus

We use an instanton approximation to the continuous-time spin coherent-state path integral to obtain the tunnel splitting of classically degenerate ground states. We show that provided the fluctuation determinant is carefully evaluated, the path integral expression is accurate to order O(1/j). We apply the method to the LMG model and to the molecular magnet Fe_8 in a transverse field.

cond-mat