arXiv subjects

Amrita Mandal

Publications and source records attributed to Amrita Mandal.

12 recordsLinked to original sources

arXiv2026

Infinite reduction in absorbing time in quantum walks over classical ones

We study the absorption time and spreading rate of the discrete-time quantum walk propagating on a line in the presence or absence of an absorber. We analytically establish that in the presence of an absorber, the average absorption time of the quantum walker is finite, contrary to the behavior of a classical random walker, indicating an infinite resource reduction on moving over to a quantum version of a walker. Furthermore, numerical simulations indicate a reversal of this behavior due to the insertion of disorder in the walker's step lengths. Additionally, we demonstrate that in the presence of an absorber, there is a speed-up in the spreading rate, and that a disordered quantum walk that is sub-ballistic regains the ballistic spreading of a clean quantum walk.

quant-ph↗

arXiv2025

Intelligent backpropagated neural networks application on Couette-Poiseuille flow of variable viscosity in a composite porous channel filled with an anisotropic porous layer

This study examines Couette-Poiseuille flow of variable viscosity within a channel that is partially filled with a porous medium. To enhance its practical relevance, we assume that the porous medium is anisotropic with permeability varying in all directions, making it a positive semidefinite matrix in the momentum equation. We assume the Navier-Stokes equations govern the flow in the free flow region, while the Brinkman-Forchheimer-extended Darcy's equation governs the flow inside the porous medium. The coupled system contains a nonlinear term from the Brinkman-Forchheimer equation. We propose an approximate solution using an iterative method valid for a wide range of porous media parameter values. For both high and low values of the Darcy number, the asymptotic solutions derived from the regular perturbation method and matched asymptotic expansion show good agreement with the numerical results. However, these methods are not effective in the intermediate range. To address this, we employ the artificial Levenberg-Marquardt method with a back-propagated neural network (ALMM-BNN) paradigm to predict the solution in the intermediate range. While it may not provide the exact solutions, it successfully captures the overall trend and demonstrates good qualitative agreement with the numerical results. This highlights the potential of the ALMM-BNN paradigm as a robust predictive tool in challenging parameter ranges where numerical solutions are either difficult to obtain or computationally expensive. The current model provides valuable insights into the shear stress distribution of arterial blood flow, taking into account the variable viscosity of the blood in the presence of inertial effects. It also offers a framework for creating glycocalyx scaffolding and other microfluidic systems that can mimic the biological glycocalyx.

physics.flu-dyn↗

arXiv2024

On the trace-zero doubly stochastic matrices of order 5

We propose a graph theoretic approach to determine trace of product of two permutation matrices through a weighted digraph representation of the permutation matrices. Consequently, we derive trace-zero doubly stochastic (DS) matrices of order $5$ whose $k$-th power is also a trace-zero DS matrix for $k\in\{2,3,4,5\}$. Then, we determine necessary conditions for the coefficients of a generic polynomial of degree $5$ to be realizable as the characteristic polynomial of a trace-zero DS matrix of order $5$. Finally, we approximate the eigenvalue region of trace-zero DS matrices of order $5.$

math.CO↗

arXiv2023

Stronger resilience to disorder in 2D quantum walks than in 1D

We study the response of spreading behavior, of two-dimensional discrete-time quantum walks, to glassy disorder in the jump length. We consider different discrete probability distributions to mimic the disorder, and three types of coin operators, viz., Grover, Fourier, and Hadamard, to analyze the scale exponent of the disorder-averaged spreading. We find that the ballistic spreading of the clean walk is inhibited in presence of disorder, and the walk becomes sub-ballistic but remains super-diffusive. The resilience to disorder-induced inhibition is stronger in two-dimensional walks, for all the considered coin operations, in comparison to the same in one dimension. The quantum advantage of quantum walks is therefore more secure in two dimensions than in one.

quant-ph↗

arXiv2023

A characterization of orthogonal permutative matrices of order 4

Orthogonal matrices which are linear combinations of permutation matrices have attracted enormous attention in quantum information and computation. In this paper, we provide a complete parametric characterization of all complex, real and rational orthogonal permutative matrices of order $4.$ We show that any such matrix can always be expressed as a linear combination of up to four permutation matrices. Finally we determine several matrix spaces generated by linearly independent permutation matrices such that any orthogonal matrix in these spaces is always permutative or direct sum of orthogonal permutative matrices up to permutation of its rows and columns.

math.CO↗

arXiv2022

Localization of two-dimensional quantum walks defined by generalized Grover coins

Localization phenomena of quantum walks makes the propagation dynamics of a walker strikingly different from that corresponding to classical random walks. In this paper, we study the localization phenomena of four-state discrete-time quantum walks on two-dimensional lattices with coin operators as one-parameter orthogonal matrices that are also permutative, a combinatorial structure of the Grover matrix. We show that the proposed walks localize at its initial position for canonical initial coin states when the coin belongs to classes which contain the Grover matrix that we consider in this paper, however, the localization phenomena depends on the coin parameter when the class of parametric coins does not contain the Grover matrix.

quant-ph↗

arXiv2022

Limit theorems and localization of three state quantum walks on a line defined by generalized Grover coins

In this article, we undertake a detailed study of the limiting behavior of a three-state discrete-time quantum walk on one dimensional lattice with generalized Grover coins. Two limit theorems are proved and consequently we show that the quantum walk exhibits localization at its initial position, for a wide range of coin parameters. Finally, we discuss the effect of the coin parameters on the peak velocities of probability distributions of the underlying quantum walks.

quant-ph↗

arXiv2020

On the eigenvalue region of permutative doubly stochastic matrices

This paper is devoted to the study of eigenvalue region of the doubly stochastic matrices which are also permutative, that is, each row of such a matrix is a permutation of any other row. We call these matrices as permutative doubly stochastic (PDS) matrices. A method is proposed to obtain symbolic representation of all PDS matrices of order $n$ by finding equivalence classes of permutationally similar symbolic PDS matrices. This is a hard problem in general as it boils down to finding all Latin squares of order $n.$ However, explicit symbolic representation of matrices in these classes are determined in this paper when $n=2, 3, 4.$ It is shown that eigenvalue regions are same for doubly stochastic matrices and PDS matrices when $n=2, 3.$ It is also established that this is no longer true for $n=4,$ and two line segments are determined which belong to the eigenvalue region of doubly stochastic matrices but not in the eigenvalue region of PDS matrices. Thus a conjecture is developed for the boundary of the eigenvalue region of PDS matrices of order $4.$ Finally, inclusion theorems for eigenvalue region of PDS matrices are proved when $n\geq 2.$

math.CO↗

arXiv2020

Periodicity of lively quantum walks on cycles with generalized Grover coin

In this paper we extend the study of three state lively quantum walks on cycles by considering the coin operator as a linear sum of permutation matrices, which is a generalization of the Grover matrix. First we provide a complete characterization of orthogonal matrices of order $3\times 3$ which are linear sum of permutation matrices. Consequently, we determine several groups of complex, real and rational orthogonal matrices. We establish that an orthogonal matrix of order $3\times 3$ is a linear sum of permutation matrices if and only if it is permutative. Finally we determine period of lively quantum walk on cycles when the coin operator belongs to the group of orthogonal (real) linear sum of permutation matrices.

quant-ph↗

arXiv2012

Ferromagnetic behavior of ultrathin manganese nanosheets

Ferromagnetic behaviour has been observed experimentally for the first time in nanostructured Manganese. Ultrathin ($\sim$ 0.6 nm) Manganese nanosheets have been synthesized inside the two dimensional channels of sol-gel derived Na-4 mica. The magnetic properties of the confined system are measured within 2K-300K temperature range. The confined structure is found to show a ferromagnetic behaviour with a nonzero coercivity value. The coercivity value remains positive throughout the entire temperature range of measurement. The experimental variation of susceptibility as a function of temperature has been satisfactorily explained on the basis of a two dimensional system with a Heisenberg Hamiltonian involving direct exchange interaction.

cond-mat.mes-hall↗

arXiv2012

Magnetodielectric effect in nickel nanosheet-Na-4 mica composites

Nickel nanosheets of thickness 0.6 nm were grown within the nanochannels of Na-4 mica template. The specimens show magnetodielectric effect at room temperature with a change of dielectric constant as a function of magnetic field, the electric field frequency varying from 100 to 700 kHz. A decrease of 5% in the value of dielectric constant was observed up to a field of 1.2 Tesla. This is explained by an inhomogeneous two-component composite model as theoretically proposed recently. The present approach will open up synthesis of various nanocomposites for sensor applications.

cond-mat.mes-hall↗

arXiv2012

Enhanced magnetic anisotropy of Nickel nanosheet prepared in Na-4 mica

Nanosheets of nickel with thickness equal to 0.6 nm have been grown within the interlayer spaces of Na-4 mica. The sheets are made up of percolative clusters of nanodisks. Magnetization characteristics indicate a superparamagnetic behavior with a blocking temperature of 428 K.The magnetic anisotropy constant as extracted from the coercivity data has been found to be higher than that of bulk nickel by two orders of magnitude. This is ascribed to a large aspect ratio of the nickel nanophase. The Bloch exponent is also found to be considerably different from that of bulk nickel because of a size effect. The Bloch Equation is still found to be valid for the two dimensional structures.

cond-mat.mes-hall↗