Arvind
Articles written in Pramana – Journal of Physics
Volume 8 Issue 6 June 1977 pp 500-511 General Relativity
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.
Volume 9 Issue 5 November 1977 pp 441-456 Mathematical Physics
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 (
Volume 11 Issue 2 August 1978 pp 171-185 Astrophysics
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.
Volume 12 Issue 2 February 1979 pp 103-120 General Relativity
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 (the
Volume 45 Issue 6 December 1995 pp 471-497 Review
The real symplectic groups in quantum mechanics and optics
Arvind B Dutta N Mukunda R Simon
We present a utilitarian review of the family of matrix groups Sp(2
Volume 47 Issue 5 November 1996 pp 347-359
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.
Volume 56 Issue 2-3 February 2001 pp 357-365 Quantum Information Processing
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.
Volume 56 Issue 5 May 2001 pp L705-L713 Rapid Communication
Quantum entanglement in the NMR implementation of the Deutsch-Jozsa algorithm
Arvind Kavita Dorai Anil Kumar
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.
Volume 62 Issue 5 May 2004 pp 1015-1028
Brownian motion in a classical ideal gas: A microscopic approach to Langevin’s equation
Rangan Lahiri Arvind Anirban Sain
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 (
Volume 65 Issue 2 August 2005 pp 297-310
Local shell-to-shell energy transfer via nonlocal interactions in fluid turbulence
Mahendra K Verma Arvind Ayyer Olivier Debliquy Shishir Kumar Amar V Chandra
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.
Volume 88 Issue 6 June 2017 Article ID 0082 Research Article
Measurement-based local quantum filters and their ability to transform quantum entanglement
DEBMALYA DAS RITABRATA SENGUPTA ARVIND
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.
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