Research

Exploring the fundamental nature of reality through mathematical physics.

Postdoctoral Research Focus

My postdoctoral research interest is in applying concepts from non-Hermitian and fractional quantum mechanics to the design of advanced photonic sensors. My focus is on developing fractal and PT-symmetric waveguide structures—such as fiber gratings and micro-ring resonators—for enhanced light localization and exceptional-point-based sensing.

Key Research Areas

Photonic Sensors

Design of advanced photonic sensors using non-Hermitian and fractional quantum mechanics. Developing fractal and PT-symmetric waveguide structures for enhanced light localization.

Non-Hermitian Quantum Mechanics

Exploring Non-Hermitian Quantum Theories and their applications, specifically Parity-Time (PT) reversal phase transitions and Exceptional Points.

Fractal Quantum Systems

Investigating tunneling features in fractal potentials and Generalized Smith-Volterra-Cantor potentials.

Quantum Entanglement

Study of Quantum Entanglement, Quantum Computation, and complex scattering phenomena in quantum systems.

Graphene Tunneling

Researching Graphene tunneling prospects and their applications in modern quantum devices.

Journal Articles

1

M. Umar, V. N. Singh, and B. P. Mandal , “Tunneling time in non-hermitian space fractional quantum mechanics” Journal of Mathematical Physics, 2025. URL

                    https://doi.org/10.48550/arXiv.2504.04082
                

2

V. N. Singh, M. Hasan, M. Umar, and B. P. Mandal , “Polyadic cantor potential of minimum lacunarity: Special case of super periodic generalized unified cantor potential” J. Phys. A: Math. Theor., 2025. URL

                    https://doi.org/10.1088/1751-8121/ada987
                

3

V. N. Singh, M. Hasan, M. Umar, and B. P. Mandal , “Quantum tunneling from a new type of generalized smith-volterra-cantor potential” Journal of Mathematical Physics, 2025. URL

                    https://doi.org/10.1063/5.0203470
                

4

M. Umar, V. N. Singh, M. Hasan, and B. P. Mandal , “Quantum tunneling from a new type of unified cantor potential” Annals of Physics, vol. 458, p. 169 485, 2023. URL

                    https://doi.org/10.1016/j.aop.2023.169485
                

5

V. N. Singh, M. Umar, M. Hasan, and B. P. Mandal , “Quantum tunneling from family of cantor potentials in fractional quantum mechanics” Annals of Physics, vol. 450, p. 169 236, 2023. URL

                    https://doi.org/10.1016/j.aop.2023.169236
                

6

V. N. Singh, M. Umar, M. Hasan, and B. Prasad Mandal , “Tunneling from general smith–volterra–cantor potential” Journal of Mathematical Physics, vol. 64, no. 3, 2023. URL

                    https://doi.org/10.1063/5.0109426
                

7

M. Hasan, V. N. Singh, and B. P. Mandal , “Role of pt-symmetry in understanding hartman effect” The European Physical Journal Plus, vol. 135, pp. 1-25, 2020. URL

                    https://doi.org/10.1140/epjp/s13360-020-00664-6
                