Search Results (56)

The universal operator-growth hypothesis (OGH) states that, in a closed chaotic system, the Lanczos coefficients grow linearly, $b_n\simeq \alpha n$. We ask how this structure is modified when the system is coupled to a Markovian environment, so that the generator becomes non-Hermitian. Applying the Arnoldi recursion to the vectorized Lindbladian in the infinite-temperature Wightman inner product, we organize the resulting pair of growth rates ${\alpha }_{\mathbb{C}}\equiv {\alpha }_R+i{\alpha }_I$—defined as effective slopes of the sub-diagonal and diagonal Arnoldi coefficients over a pre-registered fit window—around two statements whose logical status we delimit precisely. First, whenever the dissipator acts as $\mathcal{D}=-2\gamma \widehat{G}$ with $\widehat{G}$, a Hermitian grading (all dephasing-type baths), the diagonal obeys the identity $\mathrm{Re}{a}_n=-2\gamma {⟨\widehat{G}⟩}_n$: the imaginary rate measures how fast the growing operator accumulates weight in the dissipation channels. Second, we prove a conditional parity theorem: if the Hamiltonian, jump operators, and seeds can be made simultaneously real in some basis (an antiunitary condition), then $b_n$ is even, and $\mathrm{Re}{a}_n$ is odd in $\gamma$ exactly, so ${\alpha }_R$ is renormalized only at $O\left({\gamma }^2\right)$, and ${\alpha }_I=2{\kappa }_0\gamma$ follows from closed-system data alone. We exhibit a one-qubit Lindbladian that satisfies the often-assumed generator symmetry ${\mathcal{G}}^{†}\left(\gamma \right)=-\mathcal{G}(-\gamma )$ yet violates parity ($b_1=|1-\gamma |$), showing that the extra condition is essential; all models studied here satisfy it bit-exactly. For large-q SYK, these ingredients predict ${\alpha }_{\mathbb{C}}=J^{(-)}2i(q-2)\gamma$, whose imaginary part is fixed solely by the interaction range; the first ladder step is exact, and the multi-step increments approach $q-2$ with system size ($1.92\pm 0.04$ at $N=12$, $q=4$). Under a common fit protocol, the closed-system rates saturate by $N=10$ (${\alpha }_R\left(0\right)\to 0.437$, $2{\kappa }_0\to 0.224$). The imaginary rate is not an independent observable at leading order—its content is its sign, which resolves how the growing operator meets its environment (opposite for spin chains and SYK). Full article

We propose a physics-informed neural network (PINN) scheme for designing shortcuts to adiabaticity in a three-level non-Hermitian quantum system. The PINN is used to solve an inverse control problem in which the state amplitudes and the auxiliary driving field are learned simultaneously from the Schrödinger residual, the initial and target population constraints and a probability conservation constraint on the control pulse. The learned compensation field counteracts the loss of the intermediate state and enables high-fidelity population inversion in an open-system setting. Importantly, the imposed probability conservation is treated as an auxiliary constraint along the learned trajectory rather than as an intrinsic property of the non-Hermitian Hamiltonian. Under this constrained evolution, the Hamiltonian expectation value evaluated on the obtained state remains real within numerical accuracy. Numerical simulations and independent propagation with the fitted control field verify the population inversion and exhibit strong generalization capability over a range of coupling strengths and dissipation rates, as verified by retraining the network independently for each parameter set. The results demonstrate that PINNs provide a flexible inverse design tool for non-Hermitian shortcut to adiabaticity protocols when the governing dynamics and physical constraints are explicitly incorporated into the loss function. Full article

Anisotropic, Tellegen, chiral, moving-medium-type, omega, gyrotropic, hyperbolic, and multi-hyperbolic materials form an important class of isotropy-broken photonic media in which wave propagation can no longer be characterized by the Fresnel wave surface alone. Here we show that Fresnel wave surfaces can be converted into propagation maps that organize positive- and negative-phase-velocity propagation together with attenuation and amplification. In Hermitian media, the boundary between forward and backward propagation forms the orthogonal-phase-velocity separatrix. This separatrix is also a continuous locus of orthogonal-phase-velocity exceptional points, where the index-of-refraction operator becomes defective even though the material medium remains Hermitian. In non-Hermitian media, the attenuation–amplification boundary forms the loss–gain separatrix. The associated loss–gain singularities occur where the handedness remains continuous while the gain–loss character changes sign. Their physical importance is revealed by the momentum-resolved density of states: at these points, the Lorentzian linewidth of the non-Hermitian momentum-resolved density of states (DOS) collapses, producing sharp DOS peaks whose sign reverses across the separatrix. Thus, loss–gain singularities are threshold-like singularities of the Fresnel wave-surface propagation map, generated by non-Hermitian linewidth collapse. The result is a compact geometric language for describing how handedness, degeneracy, loss, gain, and momentum-resolved DOS are organized in isotropy-broken electromagnetic materials. Full article

Symmetry transformations are defined by operators in quantum mechanics that preserve the modulus of the scalar product between Hilbert space vectors. According to Wigner’s theorem, any such transformation is represented by either a unitary linear operator or an antiunitary (isometric conjugate-linear) operator. Although antiunitary symmetries—most notably time reversal and charge conjugation—are encountered less frequently than unitary ones, they are fundamental to the description of non-conservative and reversible systems. The most frequently treated antiunitary operators are the involutive ones, called conjugations. Any antiunitary operator can be written as a product of a conjugation and a unitary operator. Considering general scattering problems defined by a scattering potential and separating conjugation from the symmetry operator, one can find the role of complex symmetric (in other words self-transpose) unitary operators in physical problems. This approach provides a robust framework for analyzing the role of non-Hermitian symmetries in wave scattering and dissipative dynamics. To demonstrate the practical applicability of these theoretical concepts, we analyze the case of polarized neutron reflectometry (PNR). We show that the scattering potential in PNR, comprising nuclear and magnetic terms, can satisfy the condition of being unitarily equivalent to its transpose, thereby guaranteeing reciprocity under specific orientations of the magnetic field. Full article

Eddy-current inspection of anisotropic composites, such as aeronautical CFRP, demands models that ensure mathematical rigor, tensorial consistency, and clear energetic interpretation. This work presents a novel unified variational framework with a multiplicative tensor perturbation for the time-harmonic eddy-current problem in anisotropic media with defective regions. The formulation is posed in the natural spaces $H(\mathrm{curl};\Omega )\times H^1\left({\Omega }_c\right)$, and the well-posedness is established via the Lax–Milgram theorem under physically consistent assumptions on permeability and conductivity. The sesquilinear form admits a Hermitian decomposition that separates dissipative and reactive contributions, revealing the energetic structure of the weak formulation. Defects are modeled through multiplicative modifications of the baseline anisotropic conductivity tensor. This congruence-based approach preserves symmetry and positive definiteness, ensuring non-negative Joule losses and structural stability, allowing a modular representation of subsurface delamination, fiber breakage, conductive inclusions, and distributed porosity within a single tensorial framework. A central result of the present formulation is the reconstruction of the complex power functional from the evaluation of the weak form at the solution, showing that the active dissipated power and the magnetic reactive power arise directly from the same integral terms. Through the complex Poynting theorem, the quadratic form is linked to the internal complex power, establishing a direct connection between the variational formulation and measurable quantities such as probe impedance variations. Simulations of realistic layered CFRP configurations, including single- and multi-defect scenarios, confirm that, compared with additive perturbations, the multiplicative model provides enhanced energetic contrast, particularly in strongly anisotropic and interacting defect conditions. Agreement with experimental measurements, supported by a quantitative comparison of dissipated power variations obtained from controlled EC experiments, corroborates the physical relevance and robustness of the proposed complex power functional. Full article

A conceptually consistent understanding is sought for the interactions sampled by the imaginary cubic oscillator with potential $V^{\left(ICO\right)}\left(x\right)=\mathrm{i}{x}^3$, which is by itself not acceptable as a meaningful quantum model due to a combination of its non-Hermiticity, unboundedness, and most of all the Riesz-basis non-diagonalizability of the Hamiltonian, known as its intrinsic exceptional point (IEP) feature. For the purposes of a perturbation-theory-based simulation of the emergence of such a singular system, a simplified (though not too strictly related) toy-model Hamiltonian is proposed. It combines an $N-$point discretization of the real line of coordinates with an ad hoc interaction in a two-parametric N-by-N-matrix Hamiltonian $H=H^{\left(N\right)}(A,B)$. After such a simplification, one can still encounter a somewhat weaker form of non-diagonalizability at the conventional Kato’s exceptional-point (EP) limit of parameters $(A,B)\to (A^{\left(EP\right)},B^{\left(EP\right)})$. The IEP-non-diagonalizability phenomenon itself appears mimicked by the less enigmatic EP degeneracy of the discrete toy model, especially at large $N\gg 1$. What we gain is that, in contrast to the IEP case, the regularization of the simplified toy model in vicinity to the black conventional EP becomes feasible. Full article

The conventional time-dependent perturbation theory in quantum mechanics is established within the framework of Hermitian Hamiltonians, applicable for describing quantum transitions and associated energy level responses in such systems. However, this theory has fundamental limitations when applied to non-Hermitian systems. Consequently, researchers have systematically extended time-dependent perturbation theory to non-Hermitian systems, establishing a corresponding mature framework. Building on this foundation, this study extends the theory to investigate the transition dynamics induced by non-Hermitian interactions in non-Hermitian Hamiltonian systems. We employ a biorthogonal basis representation for a three-level non-Hermitian system. This work investigates a system comprising an unperturbed static non-Hermitian Hamiltonian and a periodically driven time-dependent perturbation Hamiltonian. Taking the three-level system as a concrete example, we combine analytical methods with numerical simulations to solve and analyze its dynamical evolution equations. These complementary approaches reveal that when system parameters complete a full cycle around an exceptional point, the transitional behavior exhibits specific evolutionary patterns. In this system, quantum transition probabilities exhibit significant asymmetry and non-conservation that depend on the initial and final states, revealing inherent directional characteristics in the dynamical process. Furthermore, for a three-level, periodically driven non-Hermitian system with time-dependent perturbations, this asymmetry is even more pronounced, manifesting as a distinct disparity between forward and reverse transition probabilities. The periodic driving actively amplifies the asymmetry in the transition process. By designing the perturbation spectrum, selective manipulation of specific quantum states can be achieved. Moreover, transition probabilities can be significantly enhanced under resonance conditions, while non-Hermiticity further breaks the system’s inherent symmetry, leading to substantial amplification of transitions in a single direction. By precisely tuning the drive frequency, interactions between specific coupling channels can be selectively enhanced or suppressed. The amplification of channel asymmetry by non-Hermitian properties provides a novel mechanism for directional control of quantum states and opens new pathways for realizing related quantum technologies. Full article

We present an analytical solution for the complex spectrum of a Creutz ladder subject to an imaginary Stark potential. By mapping the system to a momentum-space differential equation, we derive the closed-form solution for the momentum-space wavefunctions. We identify a distinct cross-shaped spectrum consisting of discrete localized sectors and a continuous branch of asymptotically real states. Our derivation reveals that the discrete sectors arise from a global phase winding condition, whereas the asymptotically real branch emerges when the energy magnitude is smaller than the inter-cell hopping strength, a regime in which the momentum-space wavefunction develops singularities. We demonstrate that these singularities prevent standard quantization; instead, the open boundary conditions are satisfied via a size-dependent imaginary energy component that regulates the wavefunction decay. To investigate the properties of this branch in the thermodynamic limit, we perform large-scale finite-size scaling analysis up to system sizes $L\sim {10}^9$. The numerical results confirm the power-law decay of the residual imaginary energy, supporting the asymptotic reality of these states. Furthermore, scaling of the inverse participation ratio and fractal dimension indicates that these states, while exhibiting size-dependent localization in finite systems, evolve into an extended phase in the thermodynamic limit. Our results establish a theoretical framework for understanding spectral transitions in systems with imaginary Stark potentials, with potential realizations in photonic frequency synthetic dimensions. Full article

Phase transition in quantum mechanics is interpreted as an evolution, at the end of which, typically, a parameter-dependent and Hermitizable Hamiltonian $H\left(g\right)$ loses its observability. In the language of mathematics, such a “quantum catastrophe” occurs at an exceptional point of order N (EPN). Although the Hamiltonian $H\left(g\right)$ itself becomes unphysical in the limit of $g\to g^{EPN}$, it is shown that it can play the role of an unperturbed operator in an innovative perturbation-approximation analysis of the vicinity of the EPN singularity. As long as such an analysis is elementary at $N\le 3$ and purely numerical at $N\ge 5$, we pick up $N=4$ and demonstrate that for an arbitrary quantum system, the specific (i.e., already sufficiently phenomenologically rich) EP4 degeneracy becomes accessible via a unitary evolution process. This process is shown realizable inside a parametric domain ${\mathcal{D}}_{\mathrm{physical}}$, the boundaries of which are determined, near $g^{EP4}$, non-numerically. Possible relevance of such a mathematical result in the context of non-Hermitian photonics is emphasized. Full article

The giant atom paradigm, where a single quantum emitter couples to a continuum at multiple discrete points, has enabled unprecedented control over light-matter interactions, including decoherence-free subspaces and chiral emission. However, realizing these non-local effects beyond the microwave regime remains a significant challenge due to the diffraction limit. Here, we theoretically propose a photonic analog of giant atoms operating at optical frequencies, utilizing a quantum emitter resonantly coupled to a pair of spatially separated single-mode cavities interacting with a common 1D photonic continuum. By rigorously deriving the effective non-Hermitian Hamiltonian and integrating out the bath degrees of freedom, we demonstrate that the interference between cavity-mediated emission pathways leads to the formation of robust Bound States in the Continuum (BICs). These interference-induced dark states allow for the infinite trapping of excitation within the emitter-cavity subsystem, effectively shielding it from radiative decay. Our results extend the giant atom toolbox to the optical domain, offering a scalable architecture for integrated quantum photonics and quantum interconnects. Full article

In quasi-Hermitian quantum mechanics (QHQM) of unitary systems, an optimal, calculation-friendly form of Hamiltonian is generally non-Hermitian, $H\ne H^{†}$. This makes its physical interpretation ambiguous. Without altering H, this ambiguity can be resolved either via a transformation of H into its isospectral Hermitian form via a so-called Dyson map $\mathrm{\Omega }:H\to \mathfrak{h}$, or via a (formally equivalent) specification of a nontrivial physical inner-product metric $\mathrm{\Theta }$ in Hilbert space. Here, we focus on the former strategy. Our present construction of the Hermitian isospectral twins $\mathfrak{h}$ of H is exhaustive. As a byproduct, it not only restores the conventional correspondence principle between quantum and classical physics, but it also provides a framework for a systematic classification of all of the admissible probabilistic interpretations of quantum systems using a preselected H in QHQM framework. Full article

Owing to its substantial implications for black hole spectroscopy, spectral instability has attracted considerable attention in the literature. While the emergence of such instability is attributed to the non-Hermitian nature of the gravitational system, it remains sensitive to various factors. In this work, we conduct a focused analysis of black hole spectral instability using the Pöschl–Teller potential as a toy model. We investigate the dependence of the resulting spectral instability on the magnitude, spatial scale, and localization of deterministic and random perturbations in the effective potential of the wave equation, and discuss the underlying physical interpretations. It is observed that small perturbations in the potential initially have a limited impact on the less damped black hole quasinormal modes, with deviations typically around their unperturbed values, a phenomenon first derived by Skakala and Visser in a more restrictive context. In the higher-overtone region, the deviation propagates, amplifies, and eventually gives rise to spectral instability and, inclusively, bifurcation in the quasinormal mode spectrum. While deterministic perturbations give rise to a deformed but well-defined quasinormal spectrum, random perturbations lead to uncertainties in the resulting spectrum. Nonetheless, the primary trend of the spectral instability remains consistent, being sensitive to both the strength and location of the perturbation. However, we demonstrate that the observed spectral instability might be suppressed for perturbations that are physically appropriate. Full article

We investigate a non-Hermitian two-spin XY model driven by alternating real and imaginary transverse fields and derive an explicit analytic formula for the ground-state entanglement negativity. This provides a systematic analytic characterization of how ground-state entanglement behaves across PT-symmetry breaking in a non-Hermitian spin dimer. In the PT-symmetric regime, the anisotropy $\gamma$ enhances entanglement, whereas the real field h₀ suppresses it; in the PT-broken regime dominated by $\left|{\phi }_3\right.⟩$, the negativity decreases monotonically with the imaginary field ${\eta }_0$. Moreover, the first derivative of the negativity exhibits a cusp-type non-analyticity at the exceptional point (EP), consistent with the ground-state phase boundary and revealing a direct correspondence between entanglement transitions and exceptional-point physics. To facilitate implementation in integrated quantum photonics, we map $\left(h_0,{\eta }_0,\gamma \right)$ onto the device parameters $\left(\Delta \beta ,g,\kappa \right)$ of a PT-symmetric directional coupler and propose a two-qubit quantum state tomography readout based on local Pauli measurements, thereby offering a concrete entanglement-based probe of exceptional-point signatures in a realistic photonic platform. Within this model, we identify parameter regimes for observing this signature: a cusp feature is expected near $\Delta \beta \approx 0$ and $g\approx \kappa ,$ which remains observable under small detuning and moderate loss mismatch. These results offer a testable avenue for entanglement-based probing of PT-symmetry breaking and may inform device characterization and quantitative assessment in integrated quantum photonics. These combined advances provide both analytical insight into non-Hermitian entanglement structure and a feasible route toward experimentally diagnosing PT-symmetry breaking using entanglement. Full article

Fresnel wave surfaces, or isofrequency light shells, provide a powerful framework for describing electromagnetic wave propagation in anisotropic media, yet their applicability is restricted to reciprocal, lossless materials and far-field radiation. This paper extends the concept by incorporating near-field effects and non-Hermitian responses arising in media with loss, gain, or non-reciprocity. Using the Om-potential approach to macroscopic electromagnetism, we reinterpret near fields as off-shell electromagnetic modes, in analogy with off-shell states in quantum field theory. Formally, both QFT off-shell states and electromagnetic near-field modes lie away from the dispersion shell; physically, however, wavefunctions of fundamental particles admit no external sources (virtual contributions live only inside propagators), whereas macroscopic electromagnetic near-fields are intrinsically source-generated by charges, currents, and boundaries and are therefore directly measurable—for example via near-field probes and momentum-resolved imaging—making “off-shell” language more natural and operational in our setting. We show that photonic density of states (PDOS) distributions near Fresnel surfaces acquire Lorentzian broadening in non-reciprocal media, directly linking this effect to the Beer–Bouguer–Lambert law of exponential attenuation or amplification. Furthermore, we demonstrate how Abraham and Minkowski momenta, locked to light shells in the far field, naturally shift to characterize source structures in the near-field regime. This unified treatment bridges the gap between sources and radiation, on-shell and off-shell modes, and reciprocal and non-reciprocal responses. The framework provides both fundamental insight into structured light and practical tools for the design of emitters and metamaterial platforms relevant to emerging technologies such as 6G communications, photonic density-of-states engineering, and non-Hermitian photonics. Full article

The exceptional surface (ES) in non-Hermitian physics has attracted much attention due to its strong robustness and enhanced frequency splitting in the sensing field. However, the detection limit of the ES-based sensing structure is still limited by the mode linewidth in the optical microcavity. In this paper, we demonstrate that Sagnac–Fizeau shift in a microcavity based on an ES separates the dark mode from the bright mode, further enhancing the frequency splitting in the transmission spectrum. Moreover, a strategy for manipulating spectral line shape is realized by the phase in the reflection loop. Compared with the traditional ES-based sensing structure, the proposed nanoparticle sensing mechanism significantly reduces the detection limit for weak perturbations. This work will contribute to the development of high-precision nanoparticle sensors. Full article