SECTION 02 // THEORETICAL & COMPUTATIONAL CONDENSED MATTER

RESEARCH INDEX & SCIENTIFIC DOSSIER

Curated ledger of theoretical formulations, active investigations, peer-reviewed articles, and collaborative pedigree.

01 // THEORETICAL FRAMEWORKS & FORMULATIONS

[CONVERGED EQUATIONS]

Bose-Einstein Condensates & Soliton Collisions 1D GPE

In quasi-one-dimensional atomic waveguides, attractive contact interactions ($g_{1D} < 0$) counteract kinetic dispersion, enabling the formation of non-dispersive bright matter-wave solitons. We study phase shifts and quantum corrections beyond mean-field theory:

$$i\hbar \frac{\partial \psi(x,t)}{\partial t} = \left(-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + V(x) - g_{1D}|\psi(x,t)|^2\right)\psi(x,t)$$

Focus: Multi-component Gross-Pitaevskii equations (GPE), collisional phase stability, and second-order Bogoliubov fluctuations.

Real-Time Stochastic FCIQMC Dynamics RIMU.JL

Full Configuration Interaction Quantum Monte Carlo (FCIQMC) resolves exponential Hilbert spaces via walker populations. Extending this to unitary real-time evolution introduces severe sign cancellation:

$$\frac{d C_{\mathbf{i}}(t)}{dt} = -i \sum_{\mathbf{j}} H_{\mathbf{i}\mathbf{j}} C_{\mathbf{j}}(t) - S(t) C_{\mathbf{i}}(t)$$

Innovation: Stabilizing `LeapfrogComplex` propagators via the `InternalCoherence` post-step algorithm developed in `RimuRealTime.jl`.

1D Extended Fermi-Hubbard Lattice CORRELATED FERMIONS

Investigation of competing on-site repulsion ($U$) and nearest-neighbor interaction ($V$) in strongly correlated one-dimensional fermionic lattices subjected to non-Hermitian hoppings:

$$H = -t\sum_{\langle i,j \rangle,\sigma}(c_{i\sigma}^\dagger c_{j\sigma} + \text{h.c.}) + U\sum_i n_{i\uparrow}n_{i\downarrow} + V\sum_{\langle i,j \rangle} n_i n_j$$

Focus: Charge-density-wave (CDW) vs Spin-density-wave (SDW) phases, Floquet periodic driving, and biorthogonal spectral signatures.

Matrix Product States & DMRG TENSOR NETWORKS

Entanglement entropy bounds in one-dimensional systems permit efficient Matrix Product State (MPS) representations of ground states and time-evolved quantum states via DMRG:

$$|\Psi\rangle = \sum_{\{\sigma_i\}} A^{\sigma_1} A^{\sigma_2} \cdots A^{\sigma_L} |\sigma_1 \sigma_2 \cdots \sigma_L\rangle$$

Focus: Truncation errors under time-dependent DMRG (t-DMRG) during non-equilibrium quantum quenches.

ARCHIVAL PLATE 02-B // SPACETIME TRAJECTORY & COLLISIONAL PHASE SHIFT ($\Delta\theta$)

NUMERICAL GPE

Analytical Derivation: In the integrable 1D Lieb-Liniger limit, the asymptotic spatial shift obeys $\Delta x = \frac{2\xi}{N} \ln\left(1 + \frac{4 v^2}{g_{1D}^2}\right)$. Solitons preserve their shape and velocity, acquiring only a net coordinate advancement.

02 // BIBLIOGRAPHIC ARTICLES & PREPRINTS

COLLAPSIBLE BIBTEX INCLUDED

[PREPRINT] DOC-ID: JN-PUB-2026-01

YEAR: 2026 • MASSEY UNIVERSITY

Real-Time Dynamics in Configuration Interaction Quantum Monte Carlo: Stabilizing Stochastic Propagators

Authors: Joachim Brand, Jyotiraj Nath, Matija Čufar, C. J. Bradly

Unitary real-time evolution within Full Configuration Interaction Quantum Monte Carlo suffers from rapid phase cancellation between complex walker populations. Here, we present the mathematical formulation of the InternalCoherence post-step strategy and demonstrate stable quantum propagation using LeapfrogComplex algorithms in open-source Julia.

[arXiv:2602.XXXXX] // [CODE IMPLEMENTATION]

BIBTEX CITATION DOCKET

@article{brand2026realtime,
  title={Real-Time Dynamics in Configuration Interaction Quantum Monte Carlo: Stabilizing Stochastic Propagators},
  author={Brand, Joachim and Nath, Jyotiraj and \v{C}ufar, Matija and Bradly, C. J.},
  journal={arXiv preprint arXiv:2602.XXXXX},
  year={2026},
  institution={Massey University, Auckland, New Zealand}
}

[IN REVIEW] DOC-ID: JN-PUB-2026-02

YEAR: 2026 • MASSEY UNIVERSITY

Collisional Phase Shifts and Quantum Fluctuations of Bright Solitons in Attractive BEC Waveguides

Authors: Jyotiraj Nath, Ray Yang, Elke Pahl, Joachim Brand

We simulate low-velocity collisions of bright matter-wave solitons in tightly confined optical waveguides using a non-polynomial Gross-Pitaevskii solver. Quantum corrections and phase-delay asymptotic shifts are benchmarked against exact Bethe ansatz predictions for integrable Lieb-Liniger regimes.

[SUBMITTED TO PHYSICAL REVIEW A] // [FIELD NOTE ESSAY]

BIBTEX CITATION DOCKET

@article{nath2026collisional,
  title={Collisional Phase Shifts and Quantum Fluctuations of Bright Solitons in Attractive BEC Waveguides},
  author={Nath, Jyotiraj and Yang, Ray and Pahl, Elke and Brand, Joachim},
  journal={Physical Review A (in review)},
  year={2026},
  publisher={APS}
}

[INRIA MONOGRAPH] DOC-ID: JN-INRIA-2025

YEAR: 2025 • INRIA PARIS-SACLAY

Algorithmic Synthesis of Fault-Tolerant Clifford+T Decompositions for Single-Qubit Unitaries

Author: Jyotiraj Nath (Supervised at Inria Saclay, France)

Research monograph conducted during research fellowship at Inria Paris-Saclay (June–July 2025). Focuses on algorithmic gate synthesis routines converting arbitrary single-qubit rotations $R_z(\theta)$ into minimal-depth fault-tolerant Clifford+T sequences over cyclotomic integer rings $\mathbb{Z}[\zeta_8]$.

BIBTEX CITATION DOCKET

@techreport{nath2025algorithmic,
  title={Algorithmic Synthesis of Fault-Tolerant Clifford+T Decompositions for Single-Qubit Unitaries},
  author={Nath, Jyotiraj},
  institution={Inria Paris-Saclay, Palaiseau, France},
  year={2025},
  type={Research Internship Monograph}
}

[PEER-REVIEWED] DOC-ID: JN-PUB-2024

YEAR: 2024 • SVNIT COLLABORATION

Biorthogonal Spectral Flow and Floquet Dynamics in the 1D Extended Fermi-Hubbard Chain

Authors: Jyotiraj Nath, Prasanta K. Panigrahi, Bhaswati Singha Deo, Mayukha Pal, Shreya Banerjee

Theoretical characterization of non-Hermitian generalizations of the 1D extended Fermi-Hubbard model under time-periodic stroboscopic driving. Demonstrates non-reciprocal boundary accumulation and dynamical skin effects in correlated quantum lattices.

BIBTEX CITATION DOCKET

@article{nath2024biorthogonal,
  title={Biorthogonal Spectral Flow and Floquet Dynamics in the 1D Extended Fermi-Hubbard Chain},
  author={Nath, Jyotiraj and Panigrahi, Prasanta K. and Singha Deo, Bhaswati and Pal, Mayukha and Banerjee, Shreya},
  journal={Journal of Physics: Condensed Matter},
  volume={36},
  pages={225601},
  year={2024},
  doi={10.1088/1361-648X/ad2a11}
}

03 // ACADEMIC PEDIGREE & LEADERSHIP LEDGER

[VERIFIED STAMPS]

PERIOD	ROLE / APPOINTMENT	INSTITUTION & LOCATION	STATUS
Jan 2026 – Present	Doctoral Researcher (PhD in Physics)	Massey University (Auckland, NZ) • Prof. Joachim Brand Group	ACTIVE CANDIDATE
Jun 2025 – Jul 2025	Research Fellow / Intern	Inria Paris-Saclay (Palaiseau, France) • Quantum Gate Synthesis	COMPLETED
2021 – 2025	Master of Science in Physics	SVNIT (Sardar Vallabhbhai National Institute of Technology, Surat, India)	CONFERRED
2025	Co-Organizer	QSQT-2025 (Quantum Systems & Quantum Technologies)	ARCHIVED CONV.