Open research questions in Quantum Mechanics and Non-Hermitian Physics
205 gap statements mined from Quantum Mechanics and Non-Hermitian Physics papers in our 7.9M-paper local library, which holds 1,143 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.
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What the literature leaves open
The description is limited to the broadband case. An overall bandwidth limitation about some nominal operating frequency may be modelled by a single pole low pass-filter.
PT-SYMMETRIC TIME DELAY OSCILLATOR MODELLING BEYOND THE WEAK COUPLING LIMIT VIA A SCATTERING MATRIX FORMULATION · 2026 · DOIExisting coupled-mode formulations are limited to weak coupling and small gain/loss contrast. The need for a more general and accurate model that treats propagation delay explicitly. The lack of a complete characterization of the unbroken and broken symmetry regimes.
PT-SYMMETRIC TIME DELAY OSCILLATOR MODELLING BEYOND THE WEAK COUPLING LIMIT VIA A SCATTERING MATRIX FORMULATION · 2026 · DOILack of understanding of the properties of non-Hermitian Hamiltonians. Limited knowledge of the interplay of interactions and non-Hermiticity in the dynamics of two bosons. Need for a systematic study of the dynamics of two bosons on the one-dimensional Hatano-Nelson lattice with non-reciprocal tunneling.
The lack of understanding of exceptional points and topological phases in non-Hermitian systems. The need for a systematic study of the exceptional point structure and topological properties of generalized non-Hermitian models.
Tuning topological phases and exceptional points in a non-Hermitian Rice–Mele model beyond nearest neighbors · 2026 · DOINon-Hermitian systems exhibit great potential for quantum-enhanced sensing, yet a unified information-theoretic framework to quantify their sensing capabilities remains elusive.
Bloch representation of quantum Fisher information in phase estimations with non-Hermitian Hamiltonians · 2025 · DOIFuture research should investigate the behavior of bound states in more complex non-Hermitian systems. The study of non-Hermitian impurity problems can be extended to other areas, such as quantum many-body systems.
The non-Hermitian impurity problem is a key area of research in non-Hermitian physics, with a lack of understanding of bound-state formation in different lattice dimensions.
The lack of understanding of how supersymmetry affects information-theoretic and complexity measures in quantum mechanics. The need for a comprehensive analysis of the Dunkl-supersymmetric harmonic oscillator using these measures. The gap in comparing the properties of supersymmetric systems with those of standard quantum harmonic oscillators.
The existing work on quantum state discrimination in non-Hermitian systems is mostly limited to PT-symmetric or pseudo-Hermitian systems with real spectra. There is a need to explore the underlying physics of quantum state discrimination in non-Hermitian systems with complex spectra.
The paper suggests further research into the quantization of confined systems. The study highlights the need for a more general solution to the problem.
The study highlights the need for a self-adjoint Hamiltonian and the challenges in achieving this.
The formulation of D_ij(q) in equations (12)-(16) is restricted to the long-wavelength limit and specific Brillouin zone sampling. Extension to higher-order Brillouin zones and application to systems exhibiting phonon softening or structural instabilities has not been investigated for two-body central interactions.
The treatment of the coupling parameters α₁ and α₂ in equations (4)-(6) is presented for a single set of values derived from atomic coordinates. The sensitivity analysis of the dynamical matrix eigenvalues and eigenvectors to variations in α₁ and α₂, particularly for systems with competing interactions, remains unexplored.
Future research could focus on the development of new optical devices or technologies based on the time-dependent Dirac oscillator. The work could be extended to include a more comprehensive analysis of the limitations of the model. Further research could explore the applications of the Jaynes-Cummings and anti-Jaynes-Cummings models.
The work addresses the need for a novel analysis of the model. The paper contributes to the development of new approaches to simulating relativistic phenomena in optical platforms.
The paper identifies a gap in the literature by noting that the spectrum and Green functions for one-dimensional Schrödinger operators related to the hypergeometric equation have not been computed. The paper notes that prior work has focused on similar problems using the confluent equation.
The study of nonequilibrium systems is challenging due to the lack of a clear understanding of their behavior under slow transformations. The calculation of the Berry curvature and the quasipotential V A λ is complex and requires careful consideration of the system's parameters. The identification of no-localization conditions in terms of mean first-passage times is a challenging task.
Quasistatic response for nonequilibrium processes: evaluating the Berry potential and curvature · 2026 · DOIFuture research should investigate the application of the Berry potential and curvature to other nonequilibrium systems. The study of no-localization conditions in terms of mean first-passage times could be extended to other systems. The paper's findings could be used to inform the design of experiments to test the predictions of the theory.
Quasistatic response for nonequilibrium processes: evaluating the Berry potential and curvature · 2026 · DOIThe lack of experimental evidence for tachyons. The need for a clear experimental proposal for testing the TPG. The speculative nature of the paper, with no physical realization of the TPG.
The Tachyon as a Quantum Gate: Tachyonic Phase Gate (TPG) and Superluminal Quantum Operations in Imaginary-Mass Field Theory · 2026 · DOIThe calculation is limited to a specific interaction time T = 150 × 2π/ω. The results are based on a perturbative solution, which may not be valid for all regimes.
The Kerr nonlinearity considered here is chosen within the weak-to-moderate regime so that the generated states remain approximately Gaussian. The system is described within the Lindblad master-equation formalism, which may not capture all possible quantum dynamics.
While the paper demonstrates unambiguous discrimination with P-pseudo-Hermitian and PT-symmetric Hamiltonians, the feasibility and practical implementation of unambiguous discrimination with generic non-Hermitian Hamiltonians requires further experimental validation.
Investigating the effects of stronger Kerr nonlinearities on entanglement dynamics. Exploring the role of other system parameters, such as the initial coherent-state amplitudes, on the generated entanglement.
Further exploration of pseudo-Hermitian systems. Investigation of applications for nonreciprocal microwave propagation and unidirectional invisibility.
Experimental realization of the TPG. Further exploration of potential connections with phenomena such as closed time-curves, relativistic causality, and advanced computational complexity. Development of a clear experimental proposal for testing the TPG.
The Tachyon as a Quantum Gate: Tachyonic Phase Gate (TPG) and Superluminal Quantum Operations in Imaginary-Mass Field Theory · 2026 · DOI
Most-cited papers in Quantum Mechanics and Non-Hermitian Physics
- Non-Hermitian physics · Advances In Physics · 2020 · 1,890 citations
- Exceptional topology of non-Hermitian systems · Reviews of Modern Physics · 2021 · 1,653 citations
- Topological Origin of Non-Hermitian Skin Effects · Physical Review Letters · 2020 · 1,230 citations
- Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits · Nature Physics · 2020 · 924 citations
- Non-Hermitian bulk–boundary correspondence in quantum dynamics · Nature Physics · 2020 · 867 citations
- Non-Hermitian Boundary Modes and Topology · Physical Review Letters · 2020 · 851 citations
- Topological funneling of light · Science · 2020 · 804 citations
- Observation of intrinsic chiral bound states in the continuum · Nature · 2023 · 619 citations
- Observation of non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial · Proceedings of the National Academy of Sciences · 2020 · 560 citations
- Non-Hermitian Bulk-Boundary Correspondence and Auxiliary Generalized Brillouin Zone Theory · Physical Review Letters · 2020 · 520 citations
Most recent work
- Predicting PT-symmetric solitons in competing cubic–quintic saturable medium via enhanced PINN with quadratic residual and reinforcement learning-based sampling · Optics & Laser Technology · 2026
- A nonlinear parity–time-symmetric system for robust phase sensing · Nature Electronics · 2026
- Self-trapping and skin solitons in two-dimensional non-Hermitian lattices · Communications Physics · 2026
- Fibonacci Waveguide Quantum Electrodynamics · Quantum · 2026
- Optics in spiral dislocation spacetime: torsion as a geometric waveguide and frequency-filtering mechanism · The European Physical Journal C · 2026
- Quantum geometrical effects in non-Hermitian systems · Physical Review Research · 2026
- Non-Hermitian optical bistability with polarization quantization in Sm3+:BiPO4 · Applied Physics Letters · 2026
- On-chip non-Hermitian cavity quantum electrodynamics · Nature Nanotechnology · 2026
- Dissipative solitons in mode-locked parity–time-symmetric lasers · Nature Photonics · 2026
- High and low-frequency multi-pole solitons and multi-ring solitons in PT-symmetric gain-loss-balanced planar waveguides · Chaos Solitons & Fractals · 2026
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