Dr. Bijan Bagchi received his B.Sc., M.Sc., and Ph.D. degrees from the University of Calcutta. After Ph.D. he joined as an associate at the Raychaudhuri lab of Presidency College, Calcutta. Subsequently he went to the Institute for Theoretical Physics, University of Bern, Switzerland as a visiting scientist. A former Professor with the University of Calcutta he has served as its Head of the Department and also as the Coordinator of the UGC Special Assistance Programme. He later became a UGC Emeritus Fellow in the Department of Physics, Shiv Nadar University where he is currently holding the post of a Professor. Dr. Bagchi has held several research positions in Europe and the US including Visiting Professorships at Physique Nucleaire Theorique et Physique Mathematique, University of Libre, Brussels and also at Laboratoire de Physique et Chimie Theoriques, University of Lorraine, Metz, France and National Cheng Kung University, Tainan. During the past few years his research has focused in developing models for position-dependent mass systems, generating solutions of the Dirac equation using supersymmetric methods, seeking exceptional points for certain class of non-Hermitian systems, extensively studying parity-time symmetric models, estimating tunneling of Hawking radiation, analysing group theoretic approach for rationally extended shape invariant potentials, systematically analysing generalised oscillators by casting them as model for dynamical systems, and inquiring into the role of bi-complex Hamiltonians in quantum mechanics. He has published about 170 research articles in various international and national journals in the area of theoretical physics and is the author of the books entitled Supersymmetry in Quantum and Classical Mechanics, Advanced Classical Mechanics and Partial Differential Equations for Mathematical Physicists, all published by the CRC Press, UK, respectively in the years 2000, 2017 and 2019.

** Research Interests:**

** **

- Exactly and quasi exactly solvable systems
- Parity-time symmetry and pseudo-Hermitian models
- Lie algebraic techniques
- Supersymmetric quantum mechanics
- Non-commutative algebra
- Nonlinear dynamics
- Alternative theories of gravity
- Integrable systems
- Dirac equation
- Hawking radiation

**Some current research:**

We proposed [1] an interacting nonhermitian model described by a two-mode quadratic Hamiltonian along with an interaction term to locate and analyze the presence of an exceptional point in the system. Each mode is guided by a Swanson-like quadratic Hamiltonian and a suitable choice is made for the interaction term. The parity-time symmetric transformation is adopted in the standard way relevant for a coupled system.

We investigated [2] the most general form of the one-dimensional Dirac Hamiltonian HD in the presence of scalar and pseudoscalar potentials. To seek embedding of supersymmetry (SUSY) in it, as an alternative procedure to directly employing the intertwining relations, we constructed a quasi-Hamiltonian K, defined as the square of HD, to explore the consequences. We showed that the diagonal elements of K under a suitable approximation reflects the presence of a superpotential thus proving a useful guide in unveiling the role of SUSY. For illustrative purpose we applied our scheme to the transformed one-dimensional version of the planar electron Hamiltonian under the influence of a magnetic field. We generated spectral solutions for a class of isochronous potentials.

We re-examined [3] Hawking radiation for a nonrotating (2+1)-dimensional BTZ black hole and evaluated the transmission probability of tunneling through the barrier of the event horizon employing the standard method of WKB approximation. We obtained results for both uncharged and charged cases. We explored the associated thermodynamics in terms of Hawking temperature and provide estimates of black hole parameters like the surface gravity and entropy.

We examined the possibility of artificial Hawking radiation by proposing a non-PT - symmetric weakly pseudo-Hermitian two band model containing a tilting parameter. We also determined the tunneling probability using our Hamiltonian through the event horizon that acts as a classically forbidden barrier.

We reviewed [4] the theoretical underpinnings of coherent states and squeezed states which are conventionally generated from the prototype harmonic oscillator but not always restricting to it. Noting that the treatments of building up such states have a long history, we collected the important ingredients and reproduced them from a fresh perspective but refrained from delving into detailed derivation of each topic. In this way, we re-captured some of the essential results and pointed out their inter-connectivity.

We derived [5] new families of non-parity-time-symmetric complex potentials with all-real spectra by the supersymmetry method and the pseudo-Hermiticity method. We found families of non-parity-time-symmetric complex partner potentials, which share the same spectrum as base potentials with known real spectra, such as the (complex) Wadati potentials. Different from previous derivations of supersymmetric potentials with real spectra, the present method does not utilize discrete eigenmodes of base potentials. As a result, our partner potentials feature explicit analytical expressions, which contain free functions. With the pseudo-Hermiticity method, we derived a new class of non-parity-time-symmetric complex potentials with free functions and constants, whose eigenvalues appear as conjugate pairs. This eigenvalue symmetry forces the spectrum to be all-real for a wide range of choices of these functions and constants in the potential. Tuning these free functions and constants, phase transition can also be induced, where conjugate pairs of complex eigenvalues emerge in the spectrum

We considered [6] the problem of determining the disentangled form of the evolution operator U(t) for a class of time-dependent non-Hemitian Hamiltonians. It was shown that this amounts to a transformation of the whole scheme in terms of addressing a nonlinear Riccati equation the existence of whose solutions depends on the fulfillment of a certain accompanying integrabilty condition. The evolution operator was constructed as the product of independent exponential operators by means of some Baker-Campbell-Hausdorff identities. The method was applied to a two level spin model.

[1] B. Bagchi, R. Ghosh and S. Sen Europhys. Lett in press (2022)

[2] B. Bagchi and R. Ghosh J. Math. Phys. 62, 072101 (2021)

[3] B. Bagchi and S. Sen Int. J. Mod. Phys. A37, 2150252 (2022)

[4] B.Bagchi, R. Ghosh and A. Khare Int. J. Mod. Phys. A 35 2030011 (2020)

[5] B. Bagchi and J. Yang, J. Math. Phys. 61 063506 (2020)

[6] B. Bagchi Lett. High Energy Physics 3 (2018) 04

**Teaching at SNU:**

- Quantum Field Theory (PHY409)
- General Theory of Relativity (PHY413)
- Advanced Mathematical Methods for Physicists (PHY547)
- Review of Classical Mechanics (PHY506)
- Review of Quantum Mechanics (PHY508)

** Advisor:**

- Current PhD students: Dibyendu Ghosh (CU), Rahul Ghosh (SNU) and Sauvik Sen (SNU).

**SOME SELECTED PUBLICATIONS:**

Journal of Mathematical Physics 62, 072101 (2021)- New families of non-parity-time-symmetric complex potentials with all-real spectra (with J. Yang) Journal of Mathematical Physics 61 063506 (2020)
- Quantum, noncommutative and MOND corrections to the entropic law of gravitation (with A. Fring), International Journal of Modern Physics B33 (2019) 1950018
- Non-standard Lagrangians and branching: the case of some nonlinear Liénard systems (with Dibyendu Ghosh, S. Modak and P.K. Panigrahi Modern Physics Letters A34 (2019) 1950110
- Evolution operator for time-dependnet non-Hermitian Hamiltonians Lett High Energy Physics 3 (2018) 04
- Scattering amplitudes for the rationally extended complex potentials (with N. Kumari, R.K.Yadav. A.Khare and B.P.Mandal) Annals of Physics 373, 163 (2016)
- Qualitative analysis of certain generalized classes of quadratic oscillator systems (with S. Ghosh, B. Pal and S. Poria
**)**Journal of Mathematical Physics 57,022701(2016) - Parametric symmetries in exactly solvable real and PT-symmetric complex potentials (with R.K.Yadav, A.Khare, N.Kumari and B.P.Mandal
**)**Journal of Mathematical Physics 57 062106 (2016). - Qualitative analysis of certain generalized classes of quadratic oscillator systems (with S. Ghosh, B. Pal and S.Poria) Journal of Mathematical Physics 57 022701(2016).
- Bicomplex Hamiltonian systems in quantum mechanics (with A.Banerjee) Journal of Physics A48 505201 (2015).
- Exploring branched Hamiltonians for a class of nonlinear systems (with S. Modak, P.K.Panigrahi, F. Ruzicka and M. Znojil) Modern Physics Letters A30 1550213 (2015).
- Rational extensions of trigonometric Poschl-Teller potential based on para-Jacobi polynomials (with Y. Grandati and C. Quesne) Journal of Mathematical Physics 56 062103 (2015).
- On Generalized Lienard oscillator and momentum dependent mass (with A Ghose Choudhury and P. Guha) Journal of Mathematical Physics 56 012015 (2015).
- New 1-step extension of the Swanson oscillator and superintegrability of its two-dimensional generalisation (with I. Marquette) Physics Letters A379 1584 (2015).
- Competing PT-potentials and re-entrant PT-symmetric phase for a particle in a box (with Y.Joglekar) Journal of Physics A45 402001 (2012 FTC).
- Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems (with A. Fring) Physics Letters A373 4307 (2009).
- Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry (with T. Tanaka) Annals of Physics 324 2438 (2009)

** Service to Profession:**

- Frequent referee for a number of international journals in theoretical physics.
- Served on CSIR, UGC and UPSC committees.
- Reviewer for fund proposals of DST, New Delhi.
- Expert of various selection committees in India and abroad.
- Member of PhD committee and Board of Studies of various Universities.
- Visiting Associate to Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune.
- Thesis evaluator for various Universities.

**Recent Academic Visits:**

- University of Vermont, Burlington, USA, May 2019
- University of Indianapolis, USA, May 2019
- University of Texas, Austin, May 2019
- Queen's College, CUNY, USA, May 2019