arXiv subjects

H. Zainuddin

Publications and source records attributed to H. Zainuddin.

11 recordsLinked to original sources

arXiv2026

Real-time thermal self-energies: In the variational bases and spaces

In this work, we introduce a systematic study for studying the scalar propagator and tadpole self-energy by considering an arbitrary parameter $\sigma$ that allows for a path integral description in real-time formalism (RTF). The closed time path formalism (CTP) and Thermofield Dynamics (TFD) are two popular choices for the parameter $\sigma$ in the Feynman rules. We have constructed a scalar propagator and a tadpole self-energy in two different bases in the momentum space as well as the mixed space. The results show that the diagonal components of self-energy in both spaces for the 1/2 basis are the same in both approaches within RTF, whereas the other off-diagonal components of self-energy are different because they depend on the path parameter. On the other hand, the diagonal components of self-energy in both spaces for the new basis are not the same in both approaches within RTF, whereas the off-diagonal components of self-energy are vanishing. That means the new basis allows one to reduce the components for the quantities studied, like self-energy or other.

hep-th↗

arXiv2026

Real-time thermal photon-photon interactions in the mixed space

Using the effective Lagrangian for the low-energy/temperature of photon-photon interaction and the lowest-order photon self-energy is calculated in the Real Time Formalism (RTF) for an arbitrary path specified by the $\sigma$-parameter within the new basis. The causal Green's functions (without chemical potential) for the scalar field are evaluated to derive the usual thermal propagators in the mixed space. It is shown that the symmetric propagator does not depend on $\sigma-$ parameter. Furthermore, the photon self-energy is used to calculate some electromagnetic properties, such as dielectric tensor and velocity of light from photon self-energy in the mixed space that greatly simplifies calculations in RTF. Their time dependence is investigated, and a comparison between our results and those obtained by other models is discussed.

hep-th↗

arXiv2026

Thermal propagator of the bosons and fermions fields

In a thermodynamic environment, thermal field theory (TFT) describes a large ensemble of interacting particles. This may appear to be the same as in classical statistical mechanics. Therefore, we study the scalar propagator and fermion propagator by considering an arbitrary parameter $\sigma$ that allows for a path integral description in real-time formalism (RTF). We constructed those propagators which allowed us to know how particles moved from one point to another point in momentum space as well as in mixed space, at finite temperature without a chemical potential.

hep-th↗

arXiv2022

Parameter Space of Morse Oscillator

We present the analysis of mathematical structure of SU(2) group, specifically the commutation relation between raising and lowering operators of the Morse oscillator. The relationship between the commutator of operators and other parameters of Morse oscillator is investigated. We show that the mathematical structure of operators which depends on the parameters of Morse oscillator may change our conventional expectation. The parameter space of Morse oscillator is visualized to scrutinize the mathematical relations that are related to the Morse oscillator. This parameter space is the space of possible parameter values that depend on the depth of the Morse potential well and other parameters. The algorithm that we present is also applicable to other quantum systems with certain modifications.

quant-ph↗

arXiv2021

Rotational Symmetry and Gauge Invariant Degeneracies on 2D Noncommutative Plane

We obtain the gauge invariant energy eigenvalues and degeneracies together with rotationally symmetric wavefunctions of a particle moving on 2D noncommutative plane subjected to homogeneous magnetic field $B$ and harmonic potential. This has been done by using the phase space coordinates transformation based on 2-parameter family of unitarily equivalent irreducible representations of the nilpotent Lie group $G_{NC}$. We find that the energy levels and states of the system are unique and hence, same goes to the degeneracies as well since they are heavily reliant on the applied $B$ and the noncommutativity $\theta $ of coordinates. Without $B$, we essentially have a noncommutative planar harmonic oscillator under generalized Bopp shift or Seiberg-Witten map. The degenerate energy levels can always be found if $\theta$ is proportional to the ratio between $\hbar$ and $m\omega$. For the scale $B\theta = \hbar$, the spectrum of energy is isomorphic to Landau problem in symmetric gauge and hence, each energy level is infinitely degenerate regardless of any values of $\theta$. Finally, if $0 < B\theta < \hbar$, $\theta$ has to also be proportional to the ratio between $\hbar$ and $m\omega$ for the degeneracy to occur. These proportionality parameters are evaluated and if they are not satisfied then we will have non-degenerate energy levels. Finally, the probability densities and effects of $B$ and $\theta$ on the system are properly shown for all cases.

quant-ph↗

arXiv2020

Higher order singular value decomposition and the reduced density matrices of three qubits

In this paper, we demonstrate that higher order singular value decomposition (HOSVD) can be used to identify special states in three qubits by local unitary (LU) operations. Since the matrix unfoldings of three qubits are related to their reduced density matrices, HOSVD simultaneously diagonalizes the one-body reduced density matrices of three qubits. From the all-orthogonality conditions of HOSVD, we computed the special states of three qubits. Furthermore, we showed that it is possible to construct a polytope that encapsulates all the special states of three qubits by LU operations with HOSVD.

quant-ph↗

arXiv2019

Effect of Colorlessness Condition on Phase Transition from Hadronic Gas to Partonic Plasma

One of the most important phase transition in physics is the Deconfinement Phase Transition in thermal Quantum ChromoDynamics. Due to the confinement property, we study the effect of colorlessness condition during the Deconfinement Phase Transition from a Hadronic Gas to a Quark-Gluon Plasma. We investigate the behavior of some thermodynamical quantities of the system such as the energy density and the pressure, the colorlessness condition and without colorlessness.

hep-ph↗

arXiv2015

On the Fractal Geometry of the Balance Sheet and the Fractal Index of Insolvency Risk

This paper reviews the economic and theoretical foundations of insolvency risk measurement and capital adequacy rules. The proposed new measure of insolvency risk is constructed by disentangling assets, debt and equity at the micro-prudential firm level. This new risk index is the Firm Insolvency Risk Index (FIRI) which is symmetrical, proportional and scale invariant. We demonstrate that the balance sheet can be shown to evolve with a fractal pattern. As such we construct a fractal index that can measure the risk of assets. This index can differentiate between the similarity and dissimilarity in asset risk, and it will also possess the properties of being self-similar and invariant to firm characteristics that make up its asset composition hence invariant to all types of risk derived from assets. Self-similarity and scale invariance across the cross section allows direct comparison of degrees of risk in assets. This is by comparing the risk dissimilarity of assets. Being naturally bounded to its highest upper bound, (0,2], the fractal index is able to serve like a risk thermometer. We assign geometric probabilities of insolvency P (equity is equal or less than 0 conditional on debt being greater than 0).

q-fin.RM↗

arXiv2005

The Low Energy Effective Equations of Motion for Multibrane World Gravity

The three 3-brane system with both positive or negative tension is studied in a low energy regime by using gradient expansion method. The effective equations of motion on the brane is derived and in particular we examine, in the first order, the radion effective lagrangian for this system. In this case, we show the solution of the modified Friedmann equation with dark radiation on the middle brane and the other 3-branes by direct elimination of the radion fields and Weyl scaling of the metric on the branes. We also derived the scalar-tensor gravity on the branes.

hep-th↗

arXiv2005

On Orbifold Compactification of N=2 Supergravity in Five Dimensions

We study compactification of five dimensional ungauged N=2 supergravity coupled to vector- and hypermultiplets on orbifold $S^1/Z_2$. In the model the vector multiplets scalar manifold is arbitrary while the hypermultiplet scalars span a generalized self dual Einstein manifold constructed by Calderbank and Pedersen. The bosonic and the fermionic sector of the low energy effective N=1 supergravity in four dimensions are derived.

hep-th↗

arXiv2004

Application of Artificial Neural Network in Jitter Analysis of Dispersion-Managed Communication System

Artificial Neural Network (ANN) is used as numerical methode in solving modified Nonlinear Schroedinger (NLS) equation with Dispersion Managed System (DMS) for jitter analysis. We take the optical axis z and the time t as input, and then some relevant values such as the change of position and the center frequency of the pulse, and further the mean square time of incoming pulse which are needed for jitter analysis. It shows that ANN yields numerical solutions which are adaptive with respect to the numerical errors and also verifies the previous numerical results using conventional numerical method. Our result indicates that DMS can minimize the timing jitter induced by some amplifiers.

nlin.PS↗