non-Hermitian Perturbation Theory Research Articles

Power-law correlation in the homogeneous disordered state of anisotropically self-propelled systems

Self-propelled particles display unique collective phenomena, due to the intrinsic coupling of density and polarity. For instance, the giant number fluctuation appears in the orientationally ordered state, and the motility-induced phase separation appears in systems with repulsion. Effects of strong noise typically lead to a homogeneous disordered state, in which the coupling of density and polarity can still play a significant role. Here we study universal properties of the homogeneous disordered state in two-dimensional systems with uniaxially anisotropic self-propulsion. Using hydrodynamic arguments, we propose that the density correlation and polarity correlation generically exhibit power-law decay with distinct exponents (−2 and −4, respectively) through the coupling of density and polarity. Simulations of self-propelled lattice gas models indeed show the predicted power-law correlations, regardless of whether the interaction type is repulsion or alignment. Further, by mapping the model to a two-component boson system and employing non-Hermitian perturbation theory, we obtain the analytical expression for the structure factors, the Fourier transform of the correlation functions. This reveals that even the first order of the interaction strength induces the power-law correlations. Published by the American Physical Society 2024

Speeding Up Entanglement Generation by Proximity to Higher-Order Exceptional Points.

Entanglement is a key resource for quantum information technologies ranging from quantum sensing to quantum computing. Conventionally, the entanglement between two coupled qubits is established at the timescale of the inverse of the coupling strength. In this Letter, we study two weakly coupled non-Hermitian qubits and observe entanglement generation at a significantly shorter timescale by proximity to a higher-order exceptional point. We establish a non-Hermitian perturbation theory based on constructing a biorthogonal complete basis and further identify the optimal condition to obtain the maximally entangled state. Our study of speeding up entanglement generation in non-Hermitian quantum systems opens new avenues for harnessing coherent nonunitary dissipation for quantum technologies.

Q-Factor Optimization of Modes in Ordered and Disordered Photonic Systems Using Non-Hermitian Perturbation Theory.

The quality factor, Q, of photonic resonators permeates most figures of merit in applications that rely on cavity-enhanced light-matter interaction such as all-optical information processing, high-resolution sensing, or ultralow-threshold lasing. As a consequence, large-scale efforts have been devoted to understanding and efficiently computing and optimizing the Q of optical resonators in the design stage. This has generated large know-how on the relation between physical quantities of the cavity, e.g., Q, and controllable parameters, e.g., hole positions, for engineered cavities in gaped photonic crystals. However, such a correspondence is much less intuitive in the case of modes in disordered photonic media, e.g., Anderson-localized modes. Here, we demonstrate that the theoretical framework of quasinormal modes (QNMs), a non-Hermitian perturbation theory for shifting material boundaries, and a finite-element complex eigensolver provide an ideal toolbox for the automated shape optimization of Q of a single photonic mode in both ordered and disordered environments. We benchmark the non-Hermitian perturbation formula and employ it to optimize the Q-factor of a photonic mode relative to the position of vertically etched holes in a dielectric slab for two different settings: first, for the fundamental mode of L3 cavities with various footprints, demonstrating that the approach simultaneously takes in-plane and out-of-plane losses into account and leads to minor modal structure modifications; and second, for an Anderson-localized mode with an initial Q of 200, which evolves into a completely different mode, displaying a threefold reduction in the mode volume, a different overall spatial location, and, notably, a 3 order of magnitude increase in Q.

Spectral theory of fluctuations in time-average statistical mechanics of reversible and driven systems

We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic stochastic dynamics with continuous or discrete state-space. We derive exact results for the mean, fluctuations and correlations of time average observables from the eigenspectrum of the underlying generator of Fokker-Planck or master equation dynamics, and discuss the results from a physical perspective. Feynman-Kac formulas are re-derived using It\^o calculus and combined with non-Hermitian perturbation theory. The emergence of the universal central limit law in a spectral representation is shown explicitly on large deviation time-scales. For reversible dynamics with equilibrated initial conditions we derive a general upper bound to fluctuations of occupation measures in terms of an integral of the return probability. Simple, exactly solvable examples are analyzed to demonstrate how to apply the theory. As a biophysical example we revisit the Berg-Purcell problem on the precision of concentration measurements by a single receptor. Our results are directly applicable to a diverse range of phenomena underpinned by time-average observables and additive functionals in physical, chemical, biological, and economical systems.

Linking Scalar Elastodynamics and Non-Hermitian Quantum Mechanics

Recent years have seen a fascinating pollination of ideas from quantum theories to elastodynamics---a theory that phenomenologically describes the time-dependent macroscopic response of materials. Here, we open route to transfer additional tools from non-Hermitian quantum mechanics. We begin by identifying the differences and similarities between the one-dimensional elastodynamics equation and the time-independent Schrodinger equation, and finding the condition under which the two are equivalent. Subsequently, we demonstrate the application of the non-Hermitian perturbation theory to determine the response of elastic systems; calculation of leaky modes and energy decay rate in heterogenous solids with open boundaries using a quantum mechanics approach; and construction of degeneracies in the spectrum of these assemblies. The latter result is of technological importance, as it introduces an approach to harness extraordinary wave phenomena associated with non-Hermitian degeneracies for practical devices, by designing them in simple elastic systems. As an example of such application, we demonstrate how an assembly of elastic slabs that is designed with two degenerate shear states according to our scheme, can be used for mass sensing with enhanced sensitivity by exploiting the unique topology near the exceptional point of degeneracy.

Spontaneous emission from nonhermitian perspective: complex scaling of the photon coordinates

ABSTRACTSpontaneous emission (SE) is usually studied within the framework of quantum dissipation theory. In this paper we pursue a different view of SE. Namely, we take advantage of Nonhermitian Quantum Mechanics (NHQM) and interpret SE as the decay of a Feshbach type resonance. Correspondingly, we aim at calculating the SE decay rate Γ (resonance width) and the associated resonance wavefunction via the complex scaling (CS) method. Standard application of CS in NHQM is based on scaling the dissociative coordinates of the system, . In the case of SE, the decay consists in emitting photons. Therefore the CS must be applied on (suitably defined) position coordinates of the photons. Feasibility of such a programme is demonstrated explicitly through choosing the adequate photon coordinates and performing CS of the photon wavefunctions in the position representation. It is anticipated in this way that CS makes the full resonance wavefunction square integrable, and enables thus the calculation of Γ by proceeding in complete analogy with the well established NHQM approaches. As an illustration, the standard Golden Rule formula for Γ is rederived from the CS nonhermitian perturbation theory.

Coupled-cluster methods including noniterative corrections for quadruple excitations

A new method is presented for treating the effects of quadruple excitations in coupled-cluster theory. In the approach, quadruple excitation contributions are computed from a formula based on a non-Hermitian perturbation theory analogous to that used previously to justify the usual noniterative triples correction used in the coupled cluster singles and doubles method with a perturbative treatment of the triple excitations (CCSD(T)). The method discussed in this paper plays a parallel role in improving energies obtained with the full coupled-cluster singles, doubles, and triples method (CCSDT) by adding a perturbative treatment of the quadruple excitations (CCSDT(Q)). The method is tested for an extensive set of examples, and is shown to provide total energies that compare favorably with those obtained with the full singles, doubles, triples, and quadruples (CCSDTQ) method.