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Ramamurti Rajaraman

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Ramamurti Rajaraman
Born (1939-03-11) 11 March 1939 (age 85)[1]
NationalityIndian
Alma materSt. Stephen's College, Delhi (B.Sc.)
Cornell University (PhD)
Awards1983 Shanti Swarup Bhatnagar Prize
2014 Leo Szilard Lectureship Award by American Physical Society
Scientific career
FieldsPhysics
InstitutionsJawaharlal Nehru University
Doctoral advisorHans Bethe

Ramamurti Rajaraman (born 11 March 1939) is an emeritus professor of theoretical physics at the School of Physical Sciences at Jawaharlal Nehru University.[2] He was also the co-Chairman of the International Panel on Fissile Materials and a member of the Bulletin of the Atomic Scientists' Science and Security Board. He has taught and conducted research in physics at the Indian Institute of Science, the Institute for Advanced Study at Princeton, and as a visiting professor at Stanford, Harvard, MIT, and elsewhere. He received his doctorate in theoretical physics in 1963 from Cornell University. In addition to his physics publications, Rajaraman has written widely on topics including fissile material production in India and Pakistan and the radiological effects of nuclear weapon accidents.

Early life and education

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Rajaraman completed his BSc (Honours) from Delhi University in 1958 and his PhD in theoretical physics in 1963 from Cornell University with Hans Bethe as his supervisor.[3] After a brief postdoctoral stint at TIFR in 1963, he returned to Cornell to teach and continue research. In 1969, after spending two years at the Institute for Advanced Study at Princeton he returned to India, working first at Delhi University (1969–76), then Indian Institute of Science (IISc), Bangalore (1976–93), finally JNU (1994- ) where he is now Emeritus Professor. He spent sabbaticals at the Harvard University, MIT, Stanford University, CERN, University of Illinois and the Institute for Advanced Study in Princeton.

Academic and research achievements

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A notable feature of Rajaraman’s research is the diversity of the areas on which he has worked. In theoretical physics his work spanning four decades (1962-2002) covers nuclear many-body theory, elementary particles, quantum field theory, soliton physics, quantum hall effect and aspects of Statistical Mechanics. In addition, since 2000, he has been deeply engaged in technical and advocative work on public policy, including global nuclear disarmament, India’s civilian and military nuclear programs and higher education. Given below is a summary of some of this work.

Nuclear many-body theory

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In 1962-63, as part of his PhD thesis, Rajaraman demonstrated that the prevalent calculations of the energy of nuclear matter in powers of the Brueckner reaction matrix would not yield a convergent result.[4][5] He suggested instead summing, in closed form, interactions to all orders among any given number of nucleons, thereby generating a density expansion. He also outlined a method for doing so. Subsequently, Hans Bethe converted Rajaraman's outline into a substantive theory for the three-nucleon problem in nuclear matter.[6] These developments, summarized in the 1967 review article by Rajaraman with Bethe,[7] eventually led to the Coupled Cluster method in Many Body theory. Subsequently, B.H.J. McKellar, Rajaraman studied the impact on of intrinsic three-body and higher many-body forces between nucleons, (as distinct from the familiar pairwise nuclear forces) on nuclear matter.[8][9] Separately Rajaraman showed that nucleon-nucleon correlations suppress pion condensation in neutron stars.[10]

Regge poles and particle phenomenology

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During the ‘Seventies, Rajaraman extended his research to include particle physics. At that time, high energy hadron scattering was being analysed using S-matrix and Regge pole techniques. Since the Froissart-Martin asymptotic bounds on hadron scattering is not applicable to Weak Interactions, Rajaraman constructed a self-consistent theory of zero-mass neutrinos and showed that ν- ν and ν- ν(bar) scattering total cross sections asymptotically become equal and approach the same constant value.[11]

Rajaraman gave the first determination from experimental data of the value of the "Triple Pomeron Vertex" as a function of momentum transfer[12] and also derived the consequences of the vanishing of this vertex on high energy hadron scattering.[13] With Finkelstein, he analysed Exchange Degeneracy in inclusive reactions involving the triple-Reggeon vertex[14][15]

With S. Rai Choudhary and G. Rajasekaran, he obtained several results on deep inelastic electron scattering data being then generated at SLAC. These included (i) constraints on its Structure Functions, (ii) its relationship to purely hadronic inclusive scattering (N+N→N+ X) and (iii) discovery of a fixed pole in virtual Compton Scattering.[16][17][18]

Solitons

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Aside from his reviews and his book,[19] Rajaraman’s original results on solitons include exact soliton solutions' of coupled scalar field theories[20] and with E. Weinberg a method for quantizing Solitons with internal symmetries.[21] In 1982, Rajaraman and the theorist John Bell, examined the curious phenomenon of quantum states with fractional fermion number, discovered theoretically by Jackiw and Rebbi and experimentally observed in Polyacetylene. These findings seemed to violate common sense at first sight. Rajaraman and Bell clarified this puzzle, in a pair of papers, one addressing the problem in the continuum Dirac theory, and the other in a lattice model of polyacetylene.[22][23] They showed that the missing fraction of the electron was lurking at the edges of the system, as has also been seen since then in some experiments.[24]

Gauge anomalies

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In 1985, R. Jackiw and Rajaraman showed that gauge theories with anomalies are not necessarily inconsistent, contrary to the general belief till then. They solved the Chiral Schwinger Model (CSM), which is anomalous, exactly and proved that it has a consistent and relativistically covariant spectrum.[25] Following this Rajaraman demonstrated using Dirac’s theory of Constraints that the presence of a gauge anomaly only alters the constraint structure of the theory so that although it is no longer gauge invariant, but it still remains canonically consistent and relativistic.[26] Later, he went on extend these results to different non-abelian gauge theories in two- and four dimensions,[27][28][29] including (with Percacci) the chirally gauged Wess-Zumino-Witten model.[30]

Statistical mechanics

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Motivated by neutron-star calculations which treat the Δ(3-3 ) hadron resonance as a separate species of fermions, Rajaraman and R.F. Dashen analysed the general question of the effective elementarity of narrow resonances in hadronic ensembles.[31][32] Since resonances are naturally described in the S-matrix rather than Hamiltonian formalism, this investigation relied on the S-matrix formulation of Statistical Mechanics developed by R.F. Dashen and S.K. Ma. The criteria derived by Dashen and RR, when applied to the neutron star equation of state, showed that treating the Δ(3-3 ) as an independent elementary particle was a reasonable approximation. Separately Rajaraman studied, with Dashen and Ma, the finite temperature behaviour of the Gross and Neveu model which spontaneously breaks chiral symmetry.[33] Dashen, Ma and Rajaraman found that when temperature is turned on, however slightly, the symmetry is restored. Separately, Ma and Rajaraman gave a pedagogical explanation of when and why broken symmetries are restored by fluctuations.[34] Another intriguing result, obtained with Raj Lakshmi was the symmetry restoration, upon quantisation, of some field theories because of zero-point energy differences.[35]

Quantum hall effect

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Rajaraman and S. L. Sondhi constructed a bosonic field operator for composite bosons, in quantum Hall systems whose condensate yields the Laughlin states at the mean field level.[36] In a similar vein, Rajaraman constructed field operators for Jain’s flux-electron composites.[37] He also studied different features of Bilayer quantum hall systems. A.H. MacDonald and T. Jungwirth and Rajaraman constructed their phase diagram at filling factor of two as a function of the Zeeman coupling, the layer bias and interlayer tunneling. They showed its ground state has a rich structure of broken symmetries including one exhibiting canted anti-ferromagnetism.[38]

Rajaraman and PhD student Sankalpa Ghosh studied topologically non trivial "meron" and bi-meron excitations in layer-spin for bilayer Hall systems taking into account differences in interlayer and intra-layer coulomb energy.[39][40] They also analyzed CP_{3} solitons arising in a four-component description of electrons carrying both spin and layer-spin. These solitons carry nontrivial intertwined windings of real spin and layer degrees of freedom.[41]

Nuclear policy and arms control

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Rajaraman has argued[42] against India developing nuclear weapons long before its first nuclear test at Pokhran in 1974. However even after India and Pakistan officially started building nuclear weapons in 1998, he felt he should stay engaged with the strategic community and strive for nuclear restraint and threat reduction To this end, he educated himself more deeply on nuclear technology and policy. In this he was greatly helped by repeated visits to Princeton University’s Program on Science and Global Security, led by Frank von Hippel, a leader on nuclear arms control.

Since then, through articles, television appearances and lectures at think tanks and universities in India and abroad, Rajaraman has tried to bring clarity to nuclear issues in South Asia and at the global level. His work covers nuclear weapon accidents, civil defense, India’s nuclear doctrine, minimal deterrence and anti-ballistic-missile and early warning systems.[43] He has repeatedly urged capping of India’s nuclear arsenal based on technical and strategic grounds that a small arsenal will suffice to meet the requirements of the Indian government's stated doctrine of minimum deterrence.[44][45][46][47] He has championed nuclear de-alert agreements and other confidence building measures at track II meetings with Pakistani and Chinese colleagues. He has calculated fissile material production and stocks in South Asia [48][49] and analysed the prospects for FMCT.[50][51] More recently argued in favour of India’s joining the Comprehensive Test ban Treaty (CTBT).[52] He has analysed in detail the ramifications of the US-India Nuclear Agreement Nuclear Deal and was an active participant in the contentious public debate surrounding its three-year negotiations (2005–08).[53]

Rajaraman is a founding member and past co-chair of the International Panel on Fissile Materials,[54] of the Council of the Pugwash Conference on Science & World Affairs, and of the Asia Pacific Leadership Network for Nuclear Non-Proliferation and Disarmament, and a member of the Science and Security Board of the Bulletin of the Atomic Scientists for six years (see [55][56][57] ).

For his work on nuclear arms control, Rajaraman received the Leo Szilard Award given by the American Physical Society in 2014.

He has also written on safety, security and transparency in India’s nuclear energy program, from well before the Fukushima tragedy.[58] To help mitigate the contentious views on nuclear energy among the Indian public, he organised and edited a book [59] on India’s nuclear energy program with contributors ranging from leaders of the governmental Department of Atomic Energy to anti-nuclear activists. He was a member of the Expert Committee of the Nuclear Threat Initiative (NTI) for developing their 2012 Nuclear Security Index.[60]

Teaching

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Despite the wide ranging research contributions summarised above, Rajaraman will perhaps be remembered more for his teaching. At all the universities where he has taught for over 50 years, he has been known for his teaching skills in physics, particularly of quantum theory. The same holds for the numerous mini-courses he has given at summer and winter schools in India and abroad, explaining new advances in theoretical physics research.

Perhaps the most widely known examples of this were his monographs on quantum solitons. A new non-perturbative approach to quantum field theory was being developed in the 1970s by quantizing fluctuations around exact classical (soliton) solutions, to get extended quantum particle states with remarkable topological properties. In 1975 Rajaraman published the very first review article on these new methods in the review journal Physics Reports.[61] Subsequently, he developed it as a book, Solitons and Instantons, published in 1982 by Elsevier North Holland.[19] It explained in simple and coherent manner these developments as well as associated techniques of path integrals, instanton induced vacuum tunnelling, Grassman fields, and multiple gauge vacua. Since these methods have found applications in nuclear, particle and condensed matter physics, this book has been widely used around the world by a generation of theoretical physicists. Its translation rights were bought by the Soviet Press MIR, who published it in Russian in 1985.[62] Subsidized copies of the book were made available to most leading physics departments in the Soviet Union and Eastern Europe.

Honours and awards

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He is the recipient of the 2014 Leo Szilard Lectureship Award from the American Physical Society[63] for his “efforts to promote peace and nuclear security in South Asia though extensive engagements and writings” and the Shanti Swarup Bhatnagar Prize in Physical Sciences in 1983.[64] He was also recipient of 1989 Dr. G.P. Chatterjee Memorial Award and 1995 S.N.Bose Medal of the Indian National Science Academy.[citation needed]

Fellowships/memberships

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  • Founding member (2006–present) and past Co-Chairman (2007-2014) of the International Panel on Fissile Materials
  • Fellow, Indian Academy of Sciences, elected 1978
  • Fellow, Indian National Science Academy, elected 1985, council member (2004–06), Vice-President (2010–12)
  • Editor, PRAMANA - Indian Journal of Physics (1989-1992)
  • Council member, Pugwash Conferences (2016–present)
  • Member of the Asia Pacific Leadership Network
  • Member of the Science and Security Board of Bulletin of the Atomic Scientists (2012-2015; 2015-2018)
  • Member, Board of Editors, Science and Global Security, (Taylor & Francis publishers, USA)[65]
  • Member, Permanent Monitoring Panel—Mitigation of Terrorist Acts, World Federation of Scientists, Erice, Italy[66]
  • Member, NTI Verification Pilot Project, Nuclear Threat Initiative, Washington DC

References

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  1. ^ "Prof. R. RAJARAMAN". jnu. Archived from the original on 30 September 2015. Retrieved 29 September 2015.
  2. ^ "Prof. R. RAJARAMAN". The Institute for Advanced Study. Retrieved 29 September 2015.
  3. ^ "Ramamurti Rajaraman". thebulletin.org.
  4. ^ Rajaraman, R. (1963). "Three-Nucleon Clusters in Nuclear Matter". Physical Review. 129 (1): 265. Bibcode:1963PhRv..129..265R. doi:10.1103/PhysRev.129.265.
  5. ^ Rajaraman, R. (1963). "Three-Body Effect in Nuclear Matter to All Orders of Perturbation". Physical Review. 131 (3): 1244. Bibcode:1963PhRv..131.1244R. doi:10.1103/PhysRev.131.1244.
  6. ^ Bethe, H. A. (1965). "Three-Body Correlations in Nuclear Matter". Physical Review. 138 (4B): B804. Bibcode:1965PhRv..138..804B. doi:10.1103/PhysRev.138.B804.
  7. ^ Rajaraman, R.; Bethe, H. A. (1967). "Three-Body Problem in Nuclear Matter". Reviews of Modern Physics. 39 (4): 745. Bibcode:1967RvMP...39..745R. doi:10.1103/RevModPhys.39.745.
  8. ^ McKellar, Bruce H. J.; Rajaraman, R. (1968). "Three-Body Forces in Nuclear Matter". Physical Review Letters. 21 (7): 450. Bibcode:1968PhRvL..21..450M. doi:10.1103/PhysRevLett.21.450.
  9. ^ McKellar, Bruce H. J.; Rajaraman, R. (1971). "Effect of Correlations on the Contribution of Three-Body Forces to the Binding Energy of Nuclear Matter". Physical Review C. 3 (5): 1877. Bibcode:1971PhRvC...3.1877M. doi:10.1103/PhysRevC.3.1877.
  10. ^ Rajaraman, R. (February 1974). "Effect of nucleon correlations on pion condensation in neutron stars". Physics Letters B. 48 (3): 179–182. Bibcode:1974PhLB...48..179R. doi:10.1016/0370-2693(74)90003-3.
  11. ^ Rajaraman, R. (25 February 1969). "Self-Consistent High-Energy Scattering of Zero-Mass Leptons: The Coupled-Channel Case". Physical Review. 178 (5): 2221–2225. Bibcode:1969PhRv..178.2221R. doi:10.1103/PhysRev.178.2221.
  12. ^ Rajaraman, R. (1971). "Evaluation of the Triple-Pomeranchukon-Vertex η PPP ( t ) from Experiment as a Function of t". Physical Review Letters. 27 (10): 693. Bibcode:1971PhRvL..27..693R. doi:10.1103/PhysRevLett.27.693.
  13. ^ Rajaraman, R. (July 1972). "Some consequences of the vanishing of the triple-pomeronchukon-vertex". Physics Letters B. 40 (3): 392–396. Bibcode:1972PhLB...40..392R. doi:10.1016/0370-2693(72)90828-3.
  14. ^ Finkelstein, J.; Rajaraman, R. (1971). "Some consequences of exchange degeneracy and the triple-Regge-hypothesis". Physics Letters B. 36 (5): 459. Bibcode:1971PhLB...36..459F. doi:10.1016/0370-2693(71)90529-6.
  15. ^ Finkelstein, J.; Rajaraman, R. (1 February 1972). "Inclusive Experiments, Exchange Degeneracy, and Reggeon Total Cross Sections". Physical Review D. 5 (3): 672–678. Bibcode:1972PhRvD...5..672F. doi:10.1103/PhysRevD.5.672.
  16. ^ Choudhury, S. Rai; Rajaraman, R. (1970). "Constraint on the Universal Function in Electroproduction". Physical Review D. 2 (11): 2728. Bibcode:1970PhRvD...2.2728C. doi:10.1103/PhysRevD.2.2728.
  17. ^ Choudhury, S. Rai; Rajaraman, R. (1972). "Relationship Between Hadronic and Electronic Excitation of N ∗ Resonances". Physical Review D. 5 (3): 773. Bibcode:1972PhRvD...5..773C. doi:10.1103/PhysRevD.5.773.
  18. ^ Rajaraman, R.; Rajasekaran, G. (1971). "Fixed Pole in the Virtual Compton Amplitude A 2". Physical Review D. 3 (1): 266. Bibcode:1971PhRvD...3..266R. doi:10.1103/PhysRevD.3.266.
  19. ^ a b Rajaraman, R (1 April 1987). An Introduction to Solitons and Instantons in Quantum Field Theory. North Holland. p. 418. ISBN 9780444870476.
  20. ^ Rajaraman, R. (1979). "Solitons of Coupled Scalar Field Theories in Two Dimensions". Physical Review Letters. 42 (4): 200. Bibcode:1979PhRvL..42..200R. doi:10.1103/PhysRevLett.42.200.
  21. ^ Rajaraman, R.; Weinberg, Erick J. (1975). "Internal symmetry and the semiclassical method in quantum field theory". Physical Review D. 11 (10): 2950. Bibcode:1975PhRvD..11.2950R. doi:10.1103/PhysRevD.11.2950.
  22. ^ Rajaraman, R.; Bell, J.S. (1982). "On solitons with half integral charge". Physics Letters B. 116 (2–3): 151. Bibcode:1982PhLB..116..151R. doi:10.1016/0370-2693(82)90996-0.
  23. ^ Bell, J.S.; Rajaraman, R. (1983). "On states, on a lattice, with half-integral charge". Nuclear Physics B. 220 (1): 1. Bibcode:1983NuPhB.220....1B. doi:10.1016/0550-3213(83)90130-X.
  24. ^ Karthick Selvan, M.; Panigrahi, Prasanta K. (2016). "Charge fractionalization in oxide heterostructures: A field-theoretical model". Europhysics Letters. 114 (6): 67005. arXiv:1603.05590. Bibcode:2016EL....11467005K. doi:10.1209/0295-5075/114/67005. S2CID 119216386.
  25. ^ Jackiw, R.; Rajaraman, R. (1985). "Vector-Meson Mass Generation by Chiral Anomalies". Physical Review Letters. 54 (12): 1219–1221. Bibcode:1985PhRvL..54.1219J. doi:10.1103/PhysRevLett.54.1219. PMID 10030968.
  26. ^ Rajaraman, R. (1985). "Hamiltonian formulation of the anomalous chiral Schwinger model". Physics Letters B. 154 (4): 305. Bibcode:1985PhLB..154..305R. doi:10.1016/0370-2693(85)90369-7.
  27. ^ Rajaraman, R. (1985). "Anomalous non-abelian gauge theory in two dimensions". Physics Letters B. 162 (1–3): 148. Bibcode:1985PhLB..162..148R. doi:10.1016/0370-2693(85)91077-9.
  28. ^ Rajaraman, R. (1987). "On anomalous U(1) gauge theory in four dimensions". Physics Letters B. 184 (4): 369. Bibcode:1987PhLB..184..369R. doi:10.1016/0370-2693(87)90182-1.
  29. ^ Lott, J.; Rajaraman, R. (1985). "Degrees of freedom and the quantization of anomalous gauge theories". Physics Letters B. 165 (4–6): 321. Bibcode:1985PhLB..165..321L. doi:10.1016/0370-2693(85)91238-9.
  30. ^ Percacci, R.; Rajaraman, R. (1988). "Gauss law commutator in the chirally gauged Wess-Zumino-Witten model". Physics Letters B. 201 (2): 256. Bibcode:1988PhLB..201..256P. doi:10.1016/0370-2693(88)90224-9.
  31. ^ Dashen, R. F.; Rajaraman, R. (1974). "Narrow resonances in statistical mechanics". Physical Review D. 10 (2): 694. Bibcode:1974PhRvD..10..694D. doi:10.1103/PhysRevD.10.694.
  32. ^ Dashen, R. F.; Rajaraman, R. (1974). "Effective elementarity of resonances and bound states in statistical mechanics". Physical Review D. 10 (2): 708. Bibcode:1974PhRvD..10..708D. doi:10.1103/PhysRevD.10.708.
  33. ^ Dashen, Roger F.; Ma, Shang-Keng; Rajaraman, R. (1975). "Finite-temperature behavior of a relativistic field theory with dynamical symmetry breaking". Physical Review D. 11 (6): 1499. Bibcode:1975PhRvD..11.1499D. doi:10.1103/PhysRevD.11.1499.
  34. ^ Ma, Shang-Keng; Rajaraman, R. (1975). "Comments on the absence of spontaneous symmetry breaking in low dimensions". Physical Review D. 11 (6): 1701. Bibcode:1975PhRvD..11.1701M. doi:10.1103/PhysRevD.11.1701.
  35. ^ Rajaraman, R.; Lakshmi, M. Raj (1981). "Restoration of symmetry by radiative corrections". Physical Review D. 23 (10): 2399. Bibcode:1981PhRvD..23.2399R. doi:10.1103/PhysRevD.23.2399.
  36. ^ Rajaraman, R.; Sondhi, S. L. (1996). "A Field Theory for the Read Operator". International Journal of Modern Physics B. 10 (7): 793. arXiv:cond-mat/9601125. Bibcode:1996IJMPB..10..793R. doi:10.1142/S0217979296000337. S2CID 119091796.
  37. ^ Rajaraman, R. (1997). "Generalized Chern-Simons theory of composite fermions in bilayer Hall systems". Physical Review B. 56 (11): 6788. arXiv:cond-mat/9702076. Bibcode:1997PhRvB..56.6788R. doi:10.1103/PhysRevB.56.6788. S2CID 14873601.
  38. ^ MacDonald, A. H.; Rajaraman, R.; Jungwirth, T. (1999). "Broken-symmetry ground states in ν = 2 bilayer quantum Hall systems". Physical Review B. 60 (12): 8817. arXiv:cond-mat/9903318. Bibcode:1999PhRvB..60.8817M. doi:10.1103/PhysRevB.60.8817. S2CID 119411013.
  39. ^ Ghosh, Sankalpa; Rajaraman, R. (1998). "Meron Pseudospin Solutions in Quantum Hall Systems". International Journal of Modern Physics B. 12 (1): 37. arXiv:cond-mat/9711137. Bibcode:1998IJMPB..12...37G. doi:10.1142/S021797929800003X. S2CID 15964684.
  40. ^ Ghosh, Sankalpa; Rajaraman, R. (1998). "Bimerons in Double Layer Quantum Hall Systems". International Journal of Modern Physics B. 12 (24): 2495. arXiv:cond-mat/9807275. Bibcode:1998IJMPB..12.2495G. doi:10.1142/S0217979298001460. S2CID 119354403.
  41. ^ Ghosh, Sankalpa; Rajaraman, R. (2000). "Quantum Hall solitons with intertwined spin and pseudospin at ν = 1". Physical Review B. 63 (3): 035304. arXiv:cond-mat/0001226. Bibcode:2000PhRvB..63c5304G. doi:10.1103/PhysRevB.63.035304. S2CID 15427095.
  42. ^ R, Rajaraman (12 July 1970). "The Unclear Nuclear Debate". The Illustrated Weekly of India.
  43. ^ Mian, Zia; Rajaraman, R.; Ramana, M. V. (2003). "Early Warning in South Asia – Constraints and Implications". Science and Global Security. 11 (2–3). Gordon and Breach (U.K.): 109–150. Bibcode:2003S&GS...11..109M. doi:10.1080/714041033. S2CID 119571308.
  44. ^ "Cap the Nuclear Arsenal Now". The Hindu (Editorial Page). 25 January 2005.
  45. ^ "Nuclear Posture". The Hindu (Editorial Page). 7 February 2003.
  46. ^ "Minimum Deterrent and Large Arsenal". The Hindu (Editorial Page). 2 July 2014.
  47. ^ "India's Arms Control Quandary (Invited Article)". The Bulletin of the Atomic Scientists (March–April Issue (2010)): 27–36.
  48. ^ Rajaraman, R. (2008). "Estimates of India's Fissile Material Stocks". Science and Global Security (Gordon and Breach, U.K.). 16 (3): 74–87 (2008). Bibcode:2008S&GS...16...74R. doi:10.1080/08929880802570248. S2CID 10258879.
  49. ^ "Exploring Uranium Resource Constraints on Fissile Material Production in Pakistan ( with Zia Mian and A. H. Nayyar)". Science and Global Security ( Gordon and Breach (U.K.)). 17 (2 and 3 (2009)): 77–109.
  50. ^ "" India and the FMCT", Country Perspectives on the Challenges to a Fissile materials (Cutoff) Treaty". IPFM Report September 2008.
  51. ^ "Prospects for a Fissile Materials Treaty and its Implications for India" in "India and Global Nuclear Disarmament" Ed V.R. Raghavan. Macmillan Publishers India Ltd. 2010. pp. 77–105.
  52. ^ "It Is Time India Signs the Nuclear Test Ban Treaty". The Wire. 6 January 2017.
  53. ^ "The India-US Nuclear Deal: The perspective of a non governmental scientist" in "Canadian Policy on Nuclear Cooperation with India", Ed: Sasikumar and Huntley. Simons Centre for Disarmament and Non-Proliferation Research. 2007. ISBN 978-1-4303-0811-9.
  54. ^ "Members". International Panel on Fissile Materials. 3 August 2016. Retrieved 1 April 2019.
  55. ^ "International Panel on Fissile Materials".
  56. ^ "Bulletin of the Atomic Scientists".
  57. ^ "A-PLN - Leadership Network".
  58. ^ "There is no Real Debate on Our Nuclear Programme". The Times of India ( Editorial Page). 28 April 1988.
  59. ^ "India's Nuclear Energy programme" Ed: R.Rajaraman. Academic Foundation and Indian National Science Academy, New Delhi. 2013.
  60. ^ "About the international panel of experts" (PDF). Nuclear Threat Initiative. January 2012. p. 86. Archived from the original (PDF) on 14 February 2014. Retrieved 14 August 2023.
  61. ^ Rajaraman, R. (1975). "Some non-perturbative semi-classical methods in quantum field theory (a pedagogical review)". Physics Reports. 21 (5): 227–313. Bibcode:1975PhR....21..227R. doi:10.1016/0370-1573(75)90016-2.
  62. ^ Солитоны и Инстаптоны. Mir Press ( Moscow) and North Holland. 1985.
  63. ^ "2014 Leo Szilard Lectureship Award Recipient". American Physical Society. Retrieved 18 September 2015.
  64. ^ Handbook of Shanti Swarup Bhatnagar Prize Winners (1958–1988) (PDF). Council of Scientific & Industrial Research. 1999.
  65. ^ "Editors -Science and Global Security".
  66. ^ "Permanent Monitoring Panel - Mitigation of Terrorist Acts". federationofscientists.org. Retrieved 29 September 2015.
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