• Arvind

Articles written in Pramana – Journal of Physics

• Dirac equation in Kerr space-time

The weak field-low velocity approximation of Dirac equation in Kerr space-time is investigated. The interaction terms admit of an interpretation in terms of a ‘dipole-dipole’ interaction in addition to coupling of spin with the angular momentum of the rotating source. The gravitational gyro-factor for spin is identified. The charged case (Kerr-Newman) is studied using minimal prescription for electromagnetic coupling in the locally inertial frame and to the leading order the standard electromagnetic gyro-factor is retrieved. A first order perturbation calculation of the shift of the Schwarzschild energy level yields the main interesting result of this work: the anomalous Zeeman splitting of the energy level of a Dirac particle in Kerr metric.

• Green’s functions for spin half field theory in Rindler space

The solutions of Dirac equation in different regions of the complete extension of Rindler space are obtained near the event horizons and in the asymptotic limits. Continuity of these solutions across the event horizons is established. The Green’s functions are written down in the two causally disconnected regions, continued in the future (F) and past (P) regions using the techniques a la Boulware and a consistent scheme of Green’s functions in all regions is exhibited.

• Spontaneous creation of massive spin half particles by a rotating block hole

The techniques of second quantization in Kerr metric for the scalar and neutrino (massless) fields are extended to the massive spin half case. The normal modes of Dirac field in Kerr metric are obtained in Chandrasekhar’s representation and the field is quantized as usual by imposing equal-time anti-commutation relations. The vacuum expectation value of energy-momentum tensor is evaluated asymptotically, leading to the result that a Kerr black hole spontaneously creates, in addition to scalar and neutrino quanta, massive Dirac particles in the classical superradiant modes.

• Hawking radiation of scalar and Dirac quanta from a Kerr black hole

Unruh’s technique of replacing collapse by boundary conditions on the past horizon (theξ-quantisation scheme) for the derivation of the well-known Hawking radiation is extended to the Kerr black hole for the scalar and especially for the spin half field. The expectation value of the energy momentum tensor is evaluated asymptotically in theξ-vacuum state yielding explicitly the net Hawking flux of scalar and spin half quanta. The appropriate statistical distribution that emerges naturally for Dirac quanta validates the ξ-scheme for fermions and confirms the association of temperature with a Kerr black hole.

• The real symplectic groups in quantum mechanics and optics

We present a utilitarian review of the family of matrix groups Sp(2n, ℛ), in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of Sp(2n, ℛ). Global decomposition theorems, interesting subgroups and their generators are described. Turning ton-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and develop a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under Sp(2n, ℛ) action are delineated.

• Relativistic operator description of photon polarization

We present an operator approach to the description of photon polarization, based on Wigner’s concept of elementary relativistic systems. The theory of unitary representations of the Poincarè group, and of parity, is exploited to construct spinlike operators acting on the polarization states of a photon at each fixed energy momentum. The nontrivial topological features of these representations relevant for massless particles, and the departures from the treatment of massive finite spin representations are highlighted and addressed.

• Quantum entanglement and quantum computational algorithms

The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We demonstrate that the one- and the two-bit Deutsch-Jozsa algorithm does not require entanglement and can be mapped onto a classical optical scheme. It is only for three and more input bits that the DJ algorithm requires the implementation of entangling transformations and in these cases it is impossible to implement this algorithm classically.

• Quantum entanglement in the NMR implementation of the Deutsch-Jozsa algorithm

A scheme to execute an 𝑛-bit Deutsch-Jozsa (DJ) algorithm using 𝑛 qubits has been implemented for up to three cubits on an NMR quantum computer. For the one- and the two-bit Deutsch problem, the qubits do not get entangled, and the NMR implementation is achieved without using spin-spin interactions. It is for the three-bit case, that the manipulation of entangled states becomes essential. The interactions through scalar 𝐽-couplings in NMR spin systems have been exploited to implement entangling transformations required for the three bit DJ algorithm.

• Brownian motion in a classical ideal gas: A microscopic approach to Langevin’s equation

We present an insightful ‘derivation’ of the Langevin equation and the fluctuation dissipation theorem in the specific context of a heavier particle moving through an ideal gas of much lighter particles. The Newton’s law of motion (mx = F) for the heavy particle reduces to a Langevin equation (valid on a coarser time-scale) with the assumption that the lighter gas particles follow a Boltzmann velocity distribution. Starting from the kinematics of the random collisions we show that (1) the average force 〈F〉 ∞ −x and (2) the correlation function of the fluctuating forceη = F — 〈F〉 is related to the strength of the average force.

• Local shell-to-shell energy transfer via nonlocal interactions in fluid turbulence

In this paper we analytically compute the strength of nonlinear interactions in a triad, and the energy exchanges between wave-number shells in incompressible fluid turbulence. The computation has been done using first-order perturbative field theory. In three dimensions, magnitude of triad interactions is large for nonlocal triads, and small for local triads. However, the shell-to-shell energy transfer rate is found to be local and forward. This result is due to the fact that the nonlocal triads occupy much less Fourier space volume than the local ones. The analytical results on three-dimensional shell-to-shell energy transfer match with their numerical counterparts. In two-dimensional turbulence, the energy transfer rates to the nearby shells are forward, but to the distant shells are backward; the cumulative effect is an inverse cascade of energy.

• Measurement-based local quantum filters and their ability to transform quantum entanglement

We introduce local filters as a means to detect the entanglement of bound entangled states which do not yield to detection by witnesses based on positive maps which are not completely positive.We demonstrate how suchnon-detectable bound entangled states can be locally filtered into detectable bound entangled states. Specifically, we show that a bound entangled state in the orthogonal complement of the unextendible product bases (UPB), canbe locally filtered into another bound entangled state that is detectable by the Choi map. We reinterpret these filters as local measurements on locally extended Hilbert spaces. We give explicit constructions of a measurement-basedimplementation of these filters for 2$\otimes$2 and 3$\otimes$3 systems. This provides us with a physical mechanism to implement such local filters.

• Commissioning and validation of the injector and electron beam transport systems for the IR-FEL at RRCAT

The first observation of lasing in an infra-red free electron laser (IR-FEL) at the Raja Ramanna Centre for Advanced Technology has been reported recently with a measured power output, i.e. $\sim10^{5}$ times higher than the expected spontaneous radiation power for the electron beam parameters used in the experiment. IR-FEL design simulations, however, estimate a power gain of $10^{7}$ which is three orders of magnitude higher than the experimentally achieved value. To understand this difference between the measured and the expected power output from the IR-FEL, the electron beam used in the experiments has been characterised and FEL simulations have been repeated after considering the measured electron beam parameters. A reasonably good agreement is obtained between the measured results and those predicted by FEL simulations. Experiments have also been performed to study the expected variation in electron beam properties over a macropulse, which should be minimum for an oscillator FEL like the IR-FEL. This paper reports the results from the experiments for characterisation of the electron beam in the IR-FEL set-up and the results from FEL simulations, considering these measured electron beam parameters.

• Single and multiband THz metamaterial polarisers

We report single and multiband linear polarisers for terahertz (THz) frequencies using cut-wire metamaterials (MM). The MMs were designed by finite-element method (FEM), fabricated by electron beam lithography, and characterised by THz time-domain spectroscopy. The MM unit cells consist of single or multiple length cut-wire pads of gold on semi-insulating gallium arsenide (GaAs) for single or multiple band polarisers. For example, a MM with a square unit cell of 50 $\mu$m size on 1 mm GaAs substrate with a gold cut wire of 65 $\mu$m length, 2 $\mu$m width, and 150 nm height gives a resonance around 1.05 THz. The dependence of the resonance frequency of the single-band polariser on the length of the cut-wires was explained based on transmission line model.

• # Pramana – Journal of Physics

Volume 94, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019