arXiv subjects

M. Sivakumar

Publications and source records attributed to M. Sivakumar.

At least 19 recordsLinked to original sources

arXiv2022

Transmission across non-Hermitian $\mathcal{PT}$-symmetric quantum dots and ladders

A non-Hermitian region connected to semi-infinite Hermitian lattices acts either as a source or as a sink and the probability current is not conserved in a scattering typically. Even a $\mathcal{P}\mathcal{T}$-symmetric region that contains both a source and a sink does not lead to current conservation plainly. We propose a model and study the scattering across a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric two-level quantum dot~(QD) connected to two semi-infinite one-dimensional lattices in a special way so that the probability current is conserved. Aharonov-Bohm type phases are included in the model, which arise from magnetic fluxes ($\hbar\phi_{L} /e,~\hbar\phi_{R} /e$) through two loops in the system. We show that when $\phi_L=\phi_R$, the probability current is conserved. We find that the transmission across the QD can be perfect in the $\mathcal{P}\mathcal{T}$-unbroken phase (corresponding to real eigenenergies of the isolated QD) whereas the transmission is never perfect in the $\mathcal{P}\mathcal{T}$-broken phase (corresponding to purely imaginary eigenenergies of the QD). The two transmission peaks have the same width only for special values of the fluxes (being odd multiples of $\pi\hbar/2e$). In the broken phase, the transmission peak is surprisingly not at zero energy. We give an insight into this feature through a four-site toy model. We extend the model to a $\mathcal{P}\mathcal{T}$-symmetric ladder connected to two semi-infinite lattices. We show that the transmission is perfect in unbroken phase of the ladder due to Fabry-P\'erot type interference, that can be controlled by tuning the chemical potential. In the broken phase of the ladder, the transmission is substantially suppressed.

cond-mat.mes-hall↗

arXiv2020

Nonadiabatic charge pumping across two superconductors connected through a normal metal region by periodically driven potentials

Periodically driven systems exhibit resonance when the difference between an excited state energy and the ground state energy is an integer multiple of $\hbar$ times the driving frequency. On the other hand, when a superconducting phase difference is maintained between two superconductors, subgap states appear which carry a Josephson current. A driven Josephson junction therefore opens up an interesting avenue where the excitations due to applied driving affect the current flowing from one superconductor to the other. Motivated by this, we study charge transport in a superconductor-normal metal-superconductor (SNS) junction where oscillating potentials are applied to the normal metal region. We find that for small amplitudes of the oscillating potential, driving at one site reverses the direction of current at the superconducting phase differences when difference between the subgap eigenenergies of the undriven Hamiltonian is integer multiple of $\hbar$ times the driving frequency. For larger amplitudes of oscillating potential, driving at one site exhibits richer features. We show that even when the two superconductors are maintained at same superconducting phase, a current can be driven by applying oscillating potentials to two sites in the normal metal differing by a phase. We find that when there is a nonzero Josephson current in the undriven system, the local peaks and valleys in current of the system driven with an amplitude of oscillating potential smaller than the superconducting gap indicates sharp excitations in the system. In the adiabatic limit, we find that charge transferred in one time period diverges as a powerlaw with pumping frequency when a Josephson current flows in the undriven system. Our calculations are exact and can be applied to finite systems. We discuss possible experimental setups where our predictions can be tested.

cond-mat.mes-hall↗

arXiv2013

Consistent Non-Minimal Couplings of Massive Higher-Spin Particles

The mutual compatibility of the dynamical equations and constraints describing a massive particle of arbitrary spin, though essential for consistency, is generically lost in the presence of interactions. The conventional Lagrangian approach avoids this difficulty, but fails to ensure light-cone propagation and becomes very cumbersome. In this paper, we take an alternative route--the involutive form of the equations and constraints--to guarantee their algebraic consistency. This approach enormously simplifies the search for consistent interactions, now seen as deformations of the involutive system, by keeping manifest the causal propagation of the correct number of degrees of freedom. We consider massive particles of arbitrary integer spin in electromagnetic and gravitational backgrounds to find their possible non-minimal local couplings. Apart from easily reproducing some well-known results, we find restrictions on the backgrounds for consistent propagation of such a particle in isolation. The results can be altered by non-local interactions that may arise from additional massive states in the interacting theory.

hep-th↗

arXiv2011

$κ$-deformed Dirac Equation

We construct a Dirac equation in $κ$-Minkowski spacetime and analyse its implications. This $κ$-deformed Dirac equation is expanded as a power series involving derivatives with respect to commutative coordinates and the deformation parameter, $a$. We show that the $κ$-deformation breaks the charge conjugation invariance but preserves parity and time reversal. We then study how the Hydrogen atom spectrum is modified due to the $κ$-deformation, applying perturbation theory. Using this, we obtain bounds on the deformation parameter $a$, which are few orders higher than the Planck length. We also show that the effects of deformation on the spectrum are distinct from that of Moyal deformation and generalized uncertainty principle.

hep-th↗

arXiv2010

Emergent Geometry from Quantized Spacetime

We examine the picture of emergent geometry arising from a mass-deformed matrix model. Because of the mass-deformation, a vacuum geometry turns out to be a constant curvature spacetime such as d-dimensional sphere and (anti-)de Sitter spaces. We show that the mass-deformed matrix model giving rise to the constant curvature spacetime can be derived from the d-dimensional Snyder algebra. The emergent geometry beautifully confirms all the rationale inferred from the algebraic point of view that the d-dimensional Snyder algebra is equivalent to the Lorentz algebra in (d+1)-dimensional {\it flat} spacetime. For example, a vacuum geometry of the mass-deformed matrix model is completely described by a G-invariant metric of coset manifolds G/H defined by the Snyder algebra. We also discuss a nonlinear deformation of the Snyder algebra.

hep-th↗

arXiv2010

Geometric Finiteness, Holography and Quasinormal Modes for the Warped AdS_3 Black Hole

We show that there exists a precise kinematical notion of holography for the Euclidean warped $AdS_3$ black hole. This follows from the fact that the Euclidean warped $AdS_3$ black hole spacetime is a geometrically finite hyperbolic manifold. For such manifolds a theorem of Sullivan provides a one-to-one correspondence between the hyperbolic structure in the bulk and the conformal structure of its boundary. Using this theorem we obtain the holographic quasinormal modes for the warped $AdS_3$ black hole.

hep-th↗

arXiv2010

ECG Feature Extraction Techniques - A Survey Approach

ECG Feature Extraction plays a significant role in diagnosing most of the cardiac diseases. One cardiac cycle in an ECG signal consists of the P-QRS-T waves. This feature extraction scheme determines the amplitudes and intervals in the ECG signal for subsequent analysis. The amplitudes and intervals value of P-QRS-T segment determines the functioning of heart of every human. Recently, numerous research and techniques have been developed for analyzing the ECG signal. The proposed schemes were mostly based on Fuzzy Logic Methods, Artificial Neural Networks (ANN), Genetic Algorithm (GA), Support Vector Machines (SVM), and other Signal Analysis techniques. All these techniques and algorithms have their advantages and limitations. This proposed paper discusses various techniques and transformations proposed earlier in literature for extracting feature from an ECG signal. In addition this paper also provides a comparative study of various methods proposed by researchers in extracting the feature from ECG signal.

cs.NE↗

arXiv2010

The Central Charge of the Warped AdS^3 Black Hole

The AdS/CFT conjecture offers the possibility of a quantum description for a black hole in terms of a CFT. This has led to the study of general AdS^3 type black holes with a view to constructing an explicit toy quantum black hole model. Such a CFT description would be characterized by its central charge and the dimensions of its primary fields. Recently the expression for the central charges (C_L, C_R) of the CFT dual to the warped AdS^3 have been determined using asymptotic symmetry arguments. The central charges depend, as expected, on the warping factor. We show that topological arguments, used by Witten to constrain central charges for the BTZ black hole, can be generalized to deal with the warped AdS^3 case. Topology constrains the warped factor to be rational numbers while quasinormal modes are conjectured to give the dimensions of primary fields. We find that in the limit when warping is large or when it takes special rational values the system tends to Witten's conjectured unique CFT's with central charges that are multiples of 24.

hep-th↗

arXiv2008

Aspects of Noncommutative Scalar/Tensor Duality

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical U(1) gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in $θ$. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The p-form generalization of the Seiberg-Witten map to order $θ$ is also derived.

hep-th↗

arXiv2008

Bose-Fermi Equivalence in Three Dimensional Non-commutative Space-Time

We study the Fermionisation of Seiberg-Witten mapped action (to order $θ$) of the $λϕ^{4}$ theory coupled minimally with U(1) gauge field governed by Chern-Simon action. Starting from the corresponding partition function we derive non-perturbatively (in coupling constant) the partition function of the spin 1/2 theory following Polyakov spin factor formalism. We find the dual interacting fermionic theory is non local. This feature persist also in the limit of vanishing self coupling. In $θ\to 0$ limit, the commutative result is regained.

hep-th↗

arXiv2006

Particle size dependence of magnetization and phase transition near T_N in multiferroic BiFeO3

We report results of a comprehensive study of the phase transition at T_N (~643 K) as a function of particle size in multiferroic BiFeO3 system. We employed electrical, thermal, and temperature dependent X-ray diffraction (XRD) studies in order to characterize the transition in a host of samples. We also carried out detailed magnetic measurements over a temperature regime 2-300 K under a magnetic field 100-10000 Oe both on bulk and nano-crystalline systems. While in the bulk system a sharp endothermic peak at T_N together with a broad feature, ranging over nearly ~150 K (Delta_T), could be observed in calorimetry, the nanoscale systems exhibit only the broad feature. The characteristic dielectric anomaly, expected at T_N, is found to occur both at T_O and T_N across Delta_T in the bulk sample. The Maxwell-Wagner component due to interfaces between heterogenous regions with different conductivities is also present. The magnetic properties, measured at lower temperature, corroborate our observations in calorimetry. The metastability increases in the nanoscale BiFeO3 with divergence between zero-field cooled (ZFC) and field cooled (FC) magnetization below ~100 K and faster magnetic relaxation. Interestingly, in nanoscale BiFeO3, one also observes finite coercivity at lower temperature which points out that suitable design of particle size and shape may induce ferromagnetism. The inhomogeneous distribution of Bi/Fe-ions and/or oxygen non-stoichiometry seems to be giving rise to broad features in thermal, magnetic as well as in electrical responses.

cond-mat.mtrl-sci↗

arXiv2005

Dual Linearised Gravity in Arbitrary Dimensions

We construct dual formulation of linearised gravity in first order tetrad formalism in arbitrary dimensions within the path integral framework following the standard duality algorithm making use of the global shift symmetry of the tetrad field. The dual partition function is in terms of the (mixed symmetric) tensor field $Φ_{[ν_{1}ν_{2}...ν_{d-3}]ν}$ in {\it frame-like} formulation. We obtain in d-dimensions the dual Lagrangian in a closed form in terms of field strength of the dual frame-like field. Next by coupling a source with the (linear) Riemann tensor in d-dimensions, dual generating functional is obtained. Using this an operator mapping between (linear) Riemann tensor and Riemann tensor corresponding to the dual field is derived and we also discuss the exchange of equations of motion and Bianchi identity.

hep-th↗

arXiv2001

Born-Infeld Chern-Simons Theory: Hamiltonian Embedding, Duality and Bosonization

In this paper we study in detail the equivalence of the recently introduced Born-Infeld self dual model to the Abelian Born-Infeld-Chern-Simons model in 2+1 dimensions. We first apply the improved Batalin, Fradkin and Tyutin scheme, to embed the Born-Infeld Self dual model to a gauge system and show that the embedded model is equivalent to Abelian Born-Infeld-Chern-Simons theory. Next, using Buscher's duality procedure, we demonstrate this equivalence in a covariant Lagrangian formulation and also derive the mapping between the n-point correlators of the (dual) field strength in Born-Infeld Chern-Simons theory and of basic field in Born-Infeld Self dual model. Using this equivalence, the bosonization of a massive Dirac theory with a non-polynomial Thirring type current-current coupling, to leading order in (inverse) fermion mass is also discussed. We also re-derive it using a master Lagrangian. Finally, the operator equivalence between the fermionic current and (dual) field strength of Born-Infeld Chern-Simons theory is deduced at the level of correlators and using this the current-current commutators are obtained.

hep-th↗

arXiv2001

The Hydrodynamical Limit of Quantum Hall system

We study the current algebra of FQHE systems in the hydrodynamical limit of small amplitude, long-wavelength fluctuations. We show that the algebra simplifies considerably in this limit. The hamiltonian is expressed in a current-current form and the operators creating inter-Landau level and lowest Landau level collective excitations are identified.

cond-mat↗

arXiv2001

Topologically Massive Non-Abelian Gauge Theories: Constraints and Deformations

We study the relationship between three non-Abelian topologically massive gauge theories, viz. the naive non-Abelian generalization of the Abelian model, Freedman-Townsend model and the dynamical 2-form theory, in the canonical framework. Hamiltonian formulation of the naive non-Abelian theory is presented first. The other two non-Abelian models are obtained by deforming the constraints of this model. We study the role of the auxiliary vector field in the dynamical 2-form theory in the canonical framework and show that the dynamical 2-form theory cannot be considered as the embedded version of naive non-Abelian model. The reducibility aspect and gauge algebra of the latter models are also discussed.

hep-th↗

arXiv2001

Hamiltonian vs Lagrangian Embedding of a Massive Spin-one Theory Involving 2-form Field

We consider the Hamiltonian and Lagrangian embedding of a first-order, massive spin-one, gauge non-invariant theory involving anti-symmetric tensor field. We apply the BFV-BRST generalised canonical approach to convert the model to a first class system and construct nil-potent BFV-BRST charge and an unitarising Hamiltonian. The canonical analysis of the Stückelberg formulation of this model is presented. We bring out the contrasting feature in the constraint structure, specifically with respect to the reducibility aspect, of the Hamiltonian and the Lagrangian embedded model. We show that to obtain manifestly covariant Stückelberg Lagrangian from the BFV embedded Hamiltonian, phase space has to be further enlarged and show how the reducible gauge structure emerges in the embedded model.

hep-th↗

arXiv2000

Hodge decomposition theorem for Abelian two form gauge theory

We show that the BRST/anti-BRST invariant 3+1 dimensional 2-form gauge theory has further nilpotent symmetries (dual BRST /anti-dual BRST) that leave the gauge fixing term invariant. The generator for the dual BRST symmetry is analogous to the co-exterior derivative of differential geometry. There exists a bosonic symmetry which keeps the ghost terms invariant and it turns out to be the analogue of the Laplacian operator. The Hodge duality operation is shown to correspond to a discrete symmetry in the theory. The generators of all these continuous symmetries are shown to obey the algebra of the de Rham cohomology operators of differential geometry. We derive the extended BRST algebra constituted by six conserved charges and discuss the Hodge decomposition theorem in the quantum Hilbert space of states.

hep-th↗

arXiv1999

On the equivalence between topologically and non-topologically massive abelian gauge theories

We analyse the equivalence between topologically massive gauge theory (TMGT) and different formulations of non-topologically massive gauge theories (NTMGTs) in the canonical approach. The different NTMGTs studied are Stückelberg formulation of (A) a first order formulation involving one and two form fields, (B) Proca theory, and (C) massive Kalb-Ramond theory. We first quantise these reducible gauge systems by using the phase space extension procedure and using it, identify the phase space variables of NTMGTs which are equivalent to the canonical variables of TMGT and show that under this the Hamiltonian also get mapped. Interestingly it is found that the different NTMGTs are equivalent to different formulations of TMGTs which differ only by a total divergence term. We also provide covariant mappings between the fields in TMGT to NTMGTs at the level of correlation function.

hep-th↗