arXiv subjects

Kaushik Ghosh

Publications and source records attributed to Kaushik Ghosh.

16 recordsLinked to original sources

arXiv2026

A Few Comments on Classical Electrodynamics

In this article we will discuss a few aspects of the spacetime description of matter and fields. In Section:1 we will discuss the completeness of real numbers in the context of an alternate definition of the straight line as a geometric continuum. According to this definition, points are not regarded as the basic constituents of a line segment and a line segment is considered to be a fundamental geometric object. This definition is in particular suitable to coordinatize different points on the straight line preserving the order properties of real numbers. Geometrically fundamental nature of line segments are required in physical theories like the string theory. We will discuss the cardinality of rational numbers in the later half of Section:1. We will first discuss what we do in an actual process of counting and define functions well-defined on the set of all positive integers. We will follow an alternate approach that depends on the Hausdorff topology of real numbers to demonstrate that the set of positive rationals can have a greater cardinality than the set of positive integers. This approach is more consistent with an actual act of counting used in statistical mechanics. This article indicates that the axiom of choice is a better technique to prove theorems that use second-countability. This is important for the metrization theorems and physics of spacetime. In Section:2 we will discuss an improved proof of the Poisson's equation. We will show that the self energy of a point charge can be zero in the potential approach to evaluate it. In Section:3 we will discuss a few aspects of the equivalence of the Schwarzschild coordinates and the Kruskal-Szekeres coordinates. In Section:4 we will make a few comments on general physics including the special theory of relativity and hydrodynamics.

physics.gen-ph↗

arXiv2026

Quantum entropy and cardinality of the rational numbers

We compare two methods for evaluating the cardinality of the Cartesian product $N \times N$ of the set of natural numbers $N$. The first is used to explain the thermodynamics of black body radiation by using convergent functions on $N \times N$. The cardinality of $N \times N$ enters through the partition function, internal energy and entropy for every macrostate given by a normal mode of electromagnetic wave. Here, $N \times N$ is assigned a greater cardinality than $N$. The second method was devised in analysis to count the rational numbers by using divergent functions on $N \times N$. Here, $N \times N$ is not assigned a greater cardinality than $N$. In this article, we show that the experimentally confirmed first approach is mathematically more consistent with the definition of the real line and foundations of topology. It also provides a quantitative measure of the cardinality of $N \times N$ relative to that of N. Similar arguments show that the set of rational numbers is not countable. This article suggests that the axiom of choice is a more rigorous technique to prove the existence theorems for connection and metric on the spacetime manifold than the usual application of second-countability.

physics.gen-ph↗

arXiv2026

Quantum Resistance in Multilayer Graphene-BiFeO3 Memristor for Brain-Inspired Computing

In the era of big data and the Internet of Things, quantum-level control of conductance states offers a promising route toward high-density data storage and brain-inspired neuromorphic computing. Although quantum conductance (QC) phenomena have been demonstrated in various metal oxide memristors, achieving reliable and precise control over quantized states remains in its infancy. Here, we demonstrate bidirectional quantum conductance states in multifunctional BiFeO3 (BFO) perovskite memristors integrated with multilayer-graphene contacts, enabling higher-order tunability and revealing the potential of perovskite-2D heterostructures for quantum-engineered memory and computing devices. XPS analysis provides detailed insights into oxygen vacancy dynamics in BFO, whereas first-principles density functional theory calculations clearly reveal a strong localized electric field at the graphene-BFO interface. Our devices exhibit current-controlled higher-order QC transitions facilitated by quantum point contact formation, giving rise to quantized conductance states during both SET and RESET processes. Time-lag correlation maps quantify the stochastic evolution of QC states under dynamic voltage-pulse tuning schemes. Notably, the quantized conductance states effectively emulate synaptic potentiation and depression, enabling precise weight modulation for high-accuracy image and digit recognition in convolutional neural networks. These findings establish perovskite-2D heterostructures as promising candidates for QC-driven resistive switching and demonstrate their potential for developing controllable quantum memristors.

cond-mat.mes-hall↗

arXiv2025

Affine Connection and Quantum Theory

In a few recent manuscripts, we used the affine connection to introduce two massless scalar fields in the Einstein-Palatini action. These fields lead to non-metricity. In this article, we will discuss the significance of these fields in inflation and dark energy. We will construct a Lagrangian formalism to include these scalar fields in a theory of gravity coupled with ordinary matter and radiation. We will find that these fields need not to be included in the actions of interacting gauge theories coupled with conserved fermionic vector currents as a part of the connection. The same remains valid for ordinary scalar fields. We can couple the connection-scalars with ordinary matter by adding suitable interaction terms. In this context, we will find that Stokes' theorem leads us to include the right-handed neutrinos in the electroweak theory in curved spacetime even with the Levi-Civita connection. This is required to obtain consistent equations of motion and anomaly-free conserved vector current for the neutrinos. Axial vector currents for different Dirac fields may remain anomalous. The right-handed neutrinos can be useful to explain neutrino oscillation and dark matter. We will also discuss the possibility of introducing massless finite integer spin particles using second rank symmetric traceless tensors with reference to the corresponding little group in flat spacetime. We will show that we can use massless (A,A) type fields in Minkowski space to introduce massless finite integer spin particles.

gr-qc↗

arXiv2025

Modeling Insurance Claims using Bayesian Nonparametric Regression

The prediction of future insurance claims based on observed risk factors, or covariates, help the actuary set insurance premiums. Typically, actuaries use parametric regression models to predict claims based on the covariate information. Such models assume the same functional form tying the response to the covariates for each data point. These models are not flexible enough and can fail to accurately capture at the individual level, the relationship between the covariates and the claims frequency and severity, which are often multimodal, highly skewed, and heavy-tailed. In this article, we explore the use of Bayesian nonparametric (BNP) regression models to predict claims frequency and severity based on covariates. In particular, we model claims frequency as a mixture of Poisson regression, and the logarithm of claims severity as a mixture of normal regression. We use the Dirichlet process (DP) and Pitman-Yor process (PY) as a prior for the mixing distribution over the regression parameters. Unlike parametric regression, such models allow each data point to have its individual parameters, making them highly flexible, resulting in improved prediction accuracy. We describe model fitting using MCMC and illustrate their applicability using French motor insurance claims data.

stat.ME↗

arXiv2024

Affine Connections in Quantum Gravity and New Scalar Fields

In this manuscript, we will discuss the construction of covariant derivative operator in quantum gravity. We will find it is more perceptive alternative to use affine connections more general than metric compatible connections in quantum gravity. We will demonstrate this using the canonical quantization procedure. This is valid irrespective of the presence and nature of sources. The conventional Palatini and metric-affine formalisms, where the actions are linear in the scalar curvature with metric and affine connections being the the independent variables, are not much suitable to construct a source-free theory of gravity with general affine connections. This is also valid for many minimally coupled interacting theories where sources only couple with metric by using the Levi-Civita connections exclusively. We will discuss potential formalism of affine connections to introduce affine connections more general than metric compatible connections in gravity. We will also discuss possible extensions of the actions for this purpose. General affine connections introduce new fields in gravity besides metric. In this article, we will consider a simple potential formalism with symmetric affine connections and symmetric Ricci tensor. Corresponding affine connections introduce two massless scalar fields. One of these fields contributes a stress-tensor with opposite sign to the sources of Einstein's equation when we state the equation using the Levi-Civita connections. This means we have a massless scalar field with negative stress-tensor in Einstein's equation. This field brings us beyond strict local Minkowski geometries. These scalar fields can be useful to explain inflation and dark energy.

gr-qc↗

arXiv2023

Near-Horizon Geometry and the Entropy of a Minimally Coupled Scalar Field in the Kerr Black Hole

In this article we will discuss a Lorentzian sector calculation of the entropy of a minimally coupled scalar field in the Kerr black hole background. We will use the brick wall model of G.'t Hooft. In the Kerr black hole, complications arise due to the absence of a global timelike Killing field and the presence of the ergosphere. Nevertheless, it is possible to calculate the entropy of a thin shell of matter field in the near-horizon region using the brick wall model. The corresponding leading order entropy of the nonsuperradiant modes is found to be proportional to the area of the horizon and is logarithmically divergent. Thus, to the leading order, the entropy of a three-dimensional system in the near-horizon region is proportional to the boundary surface. This aspect is also valid in the Schwarzschild black hole. The corresponding internal energy remains finite if the entropy is chosen to be of the order of the black hole entropy itself. For a fixed value of the brick wall cut-off, the leading order entropy in the Kerr black hole is found to be half of the corresponding term in the Schwarzschild black hole. This is due to rotation and is consistent with the preferential emission of particles in the Kerr black hole with azimuthal angular momentum in the same direction as that of the black hole itself. However, we can obtain the Schwarzschild case expression by including a subleading term and taking the appropriate slow rotation limit. In this version, we will discuss a sub-leading term for the scalar field entropy in Schwarzschild black hole. This term reduces to an expression similar to the corresponding flat spacetime entropy in the limit when radius of event horizon is vanishing.

gr-qc↗

arXiv2023

Photo-Rechargeable Li Ion Batteries using TiS2 Cathode

Photo-rechargeable (solar) battery can be considered as an energy harvesting cum storage system, where it can charge the conventional metal-ion battery using light instead of electricity, without having other parasitic reactions. Here we demonstrate a two-electrode lithium ion solar battery with multifaceted TiS2-TiO2 hybrid sheets as cathode. Choice of TiS2-TiO2 electrode ensures the formation of a type II semiconductor heterostructure while the lateral heterostructure geometry ensures high mass/charge transfer and light interactions with the electrode. TiS2 has a higher lithium binding energy (1.6 eV) than TiO2 (1.03 eV), ensuring the possibilities of higher amount of Li ion insertion to TiS2 and hence the maximum recovery with the photocharging, as further confirmed by the experiments. Apart from the demonstration of solar solid-state batteries, the charging of lithium ion full cell with light indicates the formation of lithium intercalated graphite compounds, ensuring the charging of the battery without any other parasitic reactions at the electrolyte or electrode-electrolyte interfaces. Possible mechanisms proposed here for the charging and discharging processes of solar batteries, based on our experimental and theoretical results, indicate the potential of such systems in forthcoming era of renewable energies.

physics.app-ph↗

arXiv2021

An Efficient Scheme for Sampling in Constrained Domains

The creation of optimal samplers can be a challenging task, especially in the presence of constraints on the support of parameters. One way of mitigating the severity of this challenge is to work with transformed variables, where the support is more conducive to sampling. In this work, a particular transformation called inversion in a sphere is embedded within the popular Metropolis-Hastings paradigm to effectively sample in such scenarios. The method is illustrated on three domains: the standard simplex (sum-to-one constraint), a sector of an $n$-sphere, and hypercubes. The method's performance is assessed using simulation studies with comparisons to strategies from existing literature.

stat.ME↗

arXiv2021

Demystifying Algorithmic Complexities and Geometric Review of the 'h'-Index

The current discourse delves into the effectiveness of h-index as an author level metric. It further reviews and explains the algorithmic complexity of calculating h-index through algebraic method. To conduct the algebraic analysis propositional algebra, algorithm and coding techniques have been used. Some use cases have been identified with a finite-data-set/set-of-array to demonstrate the coding techniques and for further analysis. Finally, the explanation and calculative complexities to determine the index have been further simplified through geometric method of calculating the h-index using the similar use cases that was used for coding. It is concluded that determination of the h-index using Euclidean geometric method with Cartesian frame of reference provides a through and visual clarification. Finally, a set of postulates has been proposed at the end of the paper, based on the case studies.

cs.DL↗

arXiv2019

On Gauge Theories and Covariant Derivatives in Metric Spaces

In this manuscript, we will discuss the construction of covariant derivative operator in quantum gravity. We will find it is more perceptive to use affine connections more general than metric compatible connections in quantum gravity. We will demonstrate this using the canonical quantization procedure. This is valid irrespective of the presence and nature of sources. The Palatini and metric-affine formalisms, where metric and affine connections are the independent variables, are not sufficient to construct a source-free theory of gravity with affine connections more general than the metric compatible Levi-Civita connections. This is also valid for many minimally coupled interacting theories where sources only couple with metric by using the Levi-Civita connections exclusively. We will discuss potential formalism of affine connections to introduce affine connections more general than metric compatible connections in gravity. We will also discuss possible extensions of the actions for this purpose. General affine connections introduce new fields in gravity besides metric. In this article, we will consider a simple potential formalism with symmetric Ricci tensor. Corresponding affine connections introduce two massless scalar fields. One of these fields contributes a stress-tensor with opposite sign to the sources of Einstein's equation when we state the equation using the Levi-Civita connections. This means we have a massless scalar field with negative stress-tensor in the familiar Einstein equation. These scalar fields can be useful to explain dark energy and inflation. These fields bring us beyond strict local Minkowski geometries.

physics.gen-ph↗

arXiv2019

Interdigitated flexible supercapacitor using activated carbon synthesized from biomass for wearable energy storage

We have developed a flexible, interdigitated supercapacitor with high energy storing capacity for wearable, flexible electronic application. Locally obtained low cost biomass (banana peel) was impregnated with KOH under high temperature under an inert atmosphere to synthesize activated carbon with significant Brunauer Emmett Teller surface area of 62.03m2/g. The supercapacitor was fabricated by screen printing interdigitated current collector of conducting silver ink on a thin flexible PET substrate and subsequent deposition of activated carbon and drop casting of gel electrolyte. Fabricated supercapacitor exhibits high capacitance of 33.18 mF/cm2 at 1mV/s scan rate and 20.12 mF/cm2 at a discharge current of 1mA and high energy density of 5.87 micro Wh/cm2. The developed flexible supercapacitor retains its energy storing capacity (90%) over several cycles of mechanical bending and repetitive electronic cycling tests (5000 cycles). Locally available biomass based activated carbon and low cost screen printing technique can be used for large scale fabrication of supercapacitor. The flexible supercapacitor demonstrates high energy storing capacity and mechanical durability through multiple bending and charging and discharging through LED. Therefore, it can be used for further developing integrated wearable and printed electronic devices.

physics.app-ph↗

arXiv2016

Near-Horizon Geometry and the Entropy of a Minimally Coupled Scalar Field in the Schwarzschild Black Hole

In this article, we will discuss a Lorentzian sector calculation of the entropy of a minimally coupled scalar field in the Schwarzschild black hole background using the brick wall model of 't Hooft. In the original article, the WKB approximation was used for the modes that are globally stationary. In a previous article, we found that the WKB quantization rule together with a proper counting of the states, leads to a new expression of the scalar field entropy which is not proportional to the area of the horizon. The expression of the entropy is logarithmically divergent in the brick wall cut-off parameter in contrast to an inverse power divergence obtained earlier. In this article, we will consider the entropy for a thin shell of matter field of a given thickness surrounding the black hole horizon. The thickness is chosen to be large compared with the Planck length and is of the order of the atomic scale. When expressed in terms of a covariant cut-off parameter, the entropy of a thin shell of matter field of a given thickness and surrounding the horizon in the Schwarzschild black hole background is given by an expression proportional to the area of the black hole horizon. This leading order divergent term in the cut-off parameter remains to be logarithmically divergent. The logarithmic divergence is expected from the nature of the solution in the near-horizon region. We will find that these discussions are significant in the context of the continuation to the Euclidean sector and the corresponding regularization schemes used to evaluate the thermodynamical properties of matter fields in curved spaces. These are related with the geometric aspects of curved spaces. The above discussions are also important in presence of cosmological event horizon.

gr-qc↗

arXiv2016

On the Origins of Near-Surface Stresses in Silicon around Cu-filled and CNT-filled Through Silicon Vias

Micro-Raman spectroscopy was employed to study the near-surface stress distributions and origins in Si around through silicon vias (TSVs) at both room temperature and elevated temperatures for Cu-filled and CNT-filled TSV samples. From the observations, we proved that the stresses near TSVs are mainly from two sources: 1) pre-existing stress before via filling, and 2) coefficients of thermal expansion (CTE) mismatch-induced stress. CTE-mismatch-induced stress is shown to dominate the compressive regime of the near-surface stress distribution around Cu-filled TSV structures, while pre-existing stress dominates the full range of the stress distribution in the CNT-filled TSV structures. Once the pre-existing stress is minimized, the total stress around CNT-filled TSVs can be minimized accordingly. Therefore, compared to Cu-filled TSVs, CNT-filled TSVs hold the potential to circumvent the hassle of stress-aware circuit layout and to solve the stress-related reliability issues.

cond-mat.mtrl-sci↗

arXiv2010

I-Min: An Intelligent Fermat Point Based Energy Efficient Geographic Packet Forwarding Technique for Wireless Sensor and Ad Hoc Networks

Energy consumption and delay incurred in packet delivery are the two important metrics for measuring the performance of geographic routing protocols for Wireless Adhoc and Sensor Networks (WASN). A protocol capable of ensuring both lesser energy consumption and experiencing lesser delay in packet delivery is thus suitable for networks which are delay sensitive and energy hungry at the same time. Thus a smart packet forwarding technique addressing both the issues is thus the one looked for by any geographic routing protocol. In the present paper we have proposed a Fermat point based forwarding technique which reduces the delay experienced during packet delivery as well as the energy consumed for transmission and reception of data packets.

cs.NI↗

arXiv2008

Separation of Dirac equation in the 3+1 dimensional constant curvature black hole background and its solution

The behavior of spin-half particles is discussed in the 3 + 1-dimensional constant curvature black hole (CCBH) spacetime. We use Schwarzschild-like coordinates, valid outside the black hole event horizon. The constant time surfaces corresponding to the time-like Killing vector are degenerate at the black hole event horizon and also along an axis. We write down the Dirac equation in this spacetime using Newman-Penrose formalism which is not easily separable unlike that in the Kerr metric. However, with a particular choice of basis system the equation is separable and we obtain the solutions. We discuss the structural difference in the Dirac equation in the CCBH spacetime with that in the Kerr geometry, due to difference in the corresponding spacetime metric, resulting complexity arised in separation in the earlier case.

gr-qc↗