Nonreciprocal Systems Research Articles

Self-Organized Patterns in Non-Reciprocal Active Droplet Systems.

Non-equilibrium patterns are widespread in nature and often arise from the self-organization of constituents through nonreciprocal chemotactic interactions. In this study, we demonstrate how active oil-in-water droplet mixtures with predator-prey interactions can result in a variety of self-organized patterns. By manipulating physical parameters, the droplet diameter ratio and number ratio, we identify distinct classes of patterns within a binary droplet system, rationalize the pattern formation, and quantify motilities. Experimental results are recapitulated in numerical simulations using a minimal computational model that solely incorporates chemotactic interactions and steric repulsion among the constituents. The time evolution of the patterns is investigated and chemically explained. We also investigate how patterns vary with differing interaction strength by altering surfactant composition. Leveraging insights from the binary droplet system, the framework is extended to a ternary droplet mixture composed of multiple chasing droplet pairs to create chemically directed hierarchical organization. Our findings demonstrate how rationalizable, self-organized patterns can be programmed in a chemically minimal system and provide the basis for exploration of emergent organization and higher order complexity in active colloids.

Rosen–Zener transition in a nonlinear nonreciprocal two-level system

The dynamics of the Rosen–Zener transition (RZT) in interacting two-level systems within nonreciprocal systems is examined, where nonreciprocity stems from asymmetric couplings between energy levels. For the linear case, an analytical expression for the RZT probability is derived. In the nonlinear scenario, numerical experiments are utilized to investigate the impact of various initial states and scanning periods on transition probabilities under adiabatic conditions. Additionally, an equivalent classical Hamiltonian is formulated to elucidate the origin of transition asymmetry under different initial state conditions. The influence of energy level detuning on the RZT is explored, leading to the suggestion of new applications for studying parameters of two-level systems related to nonlinearity and nonreciprocity. This opens avenues for potential Rosen–Zener–Stückelberg interferometry implementations.

Observation of dynamic non-Hermitian skin effects

Non-Hermitian physics has emerged as a new paradigm that profoundly changes our understanding of non-equilibrium systems, introducing novel concepts such as exceptional points, spectral topology, and non-Hermitian skin effects (NHSEs). Most existing studies focus on non-Hermitian eigenstates, whereas dynamic properties have been discussed only recently, and the dynamic NHSEs are not yet confirmed in experiments. Here, we report the experimental observation of non-Hermitian skin dynamics using tunable one-dimensional nonreciprocal double-chain mechanical systems with glide-time symmetry. Remarkably, dynamic NHSEs are observed with various behaviors in different dynamic phases, which can be understood via the generalized Brillouin zone and the related concepts. Moreover, the observed dynamic NHSEs, amplifications, bulk unidirectional wave propagation, and boundary wave trapping provide promising ways to manipulate waves in a controllable and robust way. Our findings open a new pathway toward non-Hermitian dynamics, which will fertilize the study of non-equilibrium phases of matter.

Magneto-optical chiral metasurfaces for achieving polarization-independent nonreciprocal transmission.

Nonreciprocal transmission, resulting from the breaking of Lorentz reciprocity, plays a pivotal role in nonreciprocal communication systems by enabling asymmetric forward and backward propagations. Metasurfaces endowed with nonreciprocity represent a compact and facile platform for manipulating electromagnetic waves in an unprecedented manner. However, most passive metasurfaces that achieve nonreciprocal transmissions are polarization dependent. While incorporation of active elements or nonlinear materials can achieve polarization-independent nonreciprocal metasurfaces, the complicated configurations limit their practical applications. To address this issue, we propose and demonstrate a passive and linear metasurface that combines magneto-optical and chiral effects, enabling polarization-independent isolation. The designed metasurface achieves a transmittance of up to 80%, with a high contrast between forward and backward propagations. Our work introduces a novel mechanism for nonreciprocal transmission and lays the foundation for the development of compact, polarization-insensitive nonreciprocal devices.

Nonreciprocal interactions in crowd dynamics: Investigating the impact of moving threats on pedestrian speed preferences

Nonreciprocal interaction crowd systems, such as human–human, human–vehicle, and human–robot systems, often have serious impacts on pedestrian safety and social order. A more comprehensive understanding of these systems is needed to optimize system stability and efficiency. Despite the importance of these interactions, empirical research in this area remains limited. Thus, in our study we explore this underresearched area, focusing on scenarios where nonreciprocity plays a critical role, such as mass stabbings, which pose a substantial risk to public safety. We conducted the first experiments on this system and analysed high-accuracy data obtained from these experiments. Specifically, we conduct laboratory experiments on three scenarios: single exits, dual exits, and obscured chases. Then, we introduce an equation to describe the mechanism behind a direct threat zone, which significantly affects pedestrian behaviour. The extent of the direct threat zone is determined by the speed of the moving threat and the radius of danger occurrence. The equation can provide insights for different nonreciprocal interaction crowd systems, where the subjects of the nonreciprocal interactions can be a pedestrian, an autonomous robot or a vehicle. We further categorize potential threats into direct, adjacent, and rear-view zones, quantifying the level of threat for pedestrians. Our study revealed that a pedestrian’s desired velocity correlated positively with potential threat intensity, increasing until near the direct threat zone. An emerging steady state is observed when escape routes are blocked by moving threats. This deviation affects the density–velocity relationship, making it distinct from the general relationship. This deviation signifies unique pedestrian behaviour in the presence of moving threats. Additionally, the rate of change in the angle for pedestrian motion in various desired directions is synchronized. This indicates the emergence of collective intelligence in nonreciprocal interaction crowd systems. As a result, our study may constitute a pioneering step towards understanding nonreciprocal interactions in crowd systems through laboratory experiments. These findings may enhance pedestrian safety and inform not only government crowd management strategies but also individual self-protection measures.

Topological phases and non-Hermitian topology in tunable nonreciprocal cyclic three-mode optical systems

We propose a method for simulating a 1D non-Hermitian Su-Schrieffer-Heeger model with modulated nonreciprocal hopping using a cyclic three-mode optical system. The current system exhibits different localization of topologically nontrivial phases, which can be characterized by the winding number. We find that the eigenenergies of such a system undergo a real-complex transition as the nonreciprocal hopping changes, accompanied by a non-Bloch parity-time symmetry breaking. We explain this phase transition by considering the evolution of saddle points on the complex energy plan and the ratio of complex eigenenergies. Additionally, we demonstrate that the skin states resulting from the non-Hermitian skin effect possess higher-order exceptional points under the critical point of the non-Bloch parity-time phase transition. Furthermore, we investigate the non-Hermitian skin phase transition by the directional mean inverse participation ratio and the generalized Brillouin zone. This work provides an alternative way to investigate the novel topological and non-Hermitian effects in nonreciprocal optical systems.

Stress guides in generic static mechanical metamaterials.

The confinement of waves within a waveguide can enable directional transmission of signals, which has found wide applications in communication, imaging, and signal isolation. Extending this concept to static systems, where material deformation is piled up along a spatial trajectory, remains elusive due to the sensitivity of localized deformation to structural defects and impurities. Here, we propose a general framework to characterize localized static deformation responses in two-dimensional generic static mechanical metamaterials, by exploiting the duality between space in static systems and time in one-dimensional non-reciprocal wave systems. An internal time-reverse symmetry is developed by the space-time duality. Upon breaking this symmetry, quasi-static load-induced deformation can be guided to travel along a designated path, thereby realizing a stress guide. A combination of time-reverse and inversion symmetries discloses the parity-time symmetry inherent in static systems, which can be leveraged to achieve directional deformation shielding. The tailorable stress guides can find applications in various scenarios, ranging from stress shielding and energy harvesting in structural tasks to information processing in mechanical computing devices.

Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity.

We investigate the impact of nonreciprocity on universality and critical phenomena in open quantum interacting many-body systems. Nonreciprocal open quantum systems often have an exotic spectral sensitivity to boundary conditions, known as the Liouvillian skin effect (LSE). By considering an open quantum XXZ spin chain that exhibits LSE, we demonstrate the existence of a universal scaling regime that is not affected by the presence of the LSE. We resolve the critical exponents, which differ from those of free fermions, via tensor network methods and demonstrate that observables exhibit a universal scaling collapse, irrespective of the reciprocity. We find that the LSE only becomes relevant when a healing length scale ξ_{heal} at the system's edge (which is different from the localization length of the eigenstate of the Liouvillian) exceeds the system size, allowing edge properties to dominate the physics. We expect this result to be a generic feature of nonreciprocal models in the vicinity of a critical point. The driven-dissipative quantum criticality we observe has no classical analog and stems from the existence of multiple dark states.

Exact analog of the Hatano-Nelson model in one-dimensional continuous nonreciprocal systems

Non-Hermitian topology offers a promising avenue toward an enhanced control of waves, and many of the underlying interesting phenomena are studied through the paradigmatic Hatano-Nelson (HN) model, which remains unexplored in continuous wave systems. Herein, we propose a framework to map one-dimensional continuous nonreciprocal systems onto the HN model. Our approach, based on the properties of transfer matrices, is applicable across various physical domains. We experimentally apply our method in audible acoustics using active elements, where we not only observe the predicted skin effect but also access the spectrum topology using stable configurations and observe its subsequent boundary sensitivity. By establishing a connection between continuous wave systems and the discrete HN model, our results significantly broaden the potential application of nonreciprocal topological phenomena. Published by the American Physical Society 2024

Collective non-Hermitian skin effect: point-gap topology and the doublon-holon excitations in non-reciprocal many-body systems

Open quantum systems provide a plethora of exotic topological phases of matter that have no Hermitian counterpart. Non-Hermitian skin effect, macroscopic collapse of bulk states to the boundary, has been extensively studied in various experimental platforms. However, it remains an open question whether such topological phases persist in the presence of many-body interactions. Previous studies have shown that the Pauli exclusion principle suppresses the skin effect. In this study, we present a counterexample by demonstrating the presence of the skin effect in doublon-holon excitations. While the ground state of the spin-half Hatano-Nelson model shows no skin effect, the doublon-holon pairs, as its collective excitations, display the many-body skin effect even in strong coupling limit. We establish the robustness of this effect by revealing a bulk-boundary correspondence mediated by the point gap topology within the many-body energy spectrum. Our findings underscore the existence of non-Hermitian topological phases in collective excitations of many-body interacting systems.

Noise performance analysis of PT-symmetric non-reciprocal transmission systems

Non-reciprocity is a crucial concept in the field of signal transmission and processing as it protects sensitive elements from the effects of feedback signal. The non-reciprocal components based on ferrite materials are bound to show shortcomings due to incompatibility with chip-level ICs. In recent years, parity-time (PT)-symmetric non-reciprocal transmission in electronic systems has been proposed and analyzed. Here, we propose the simplified noise analysis model based on a PT-symmetric non-reciprocal transmission system. And we verify the theoretical noise model by simulation analysis and experimental demonstrations. The experimental result shows that the noise figure of the proposed PT-symmetric non-reciprocal transmission device is 7.5 dB because of the employment of the active amplifier. This work establishes a noise performance analysis framework, providing guidance for the development of lossless and miniaturized applications of non-reciprocal components.

Characteristic Modes of Nonreciprocal Systems

Characteristic Modes of Nonreciprocal Systems

Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice.

Recent studies of non-Hermitian periodic lattices unveiled the non-Hermitian skin effect (NHSE), in which the bulk modes under the periodic boundary conditions (PBC) become skin modes under open boundary conditions. The NHSE is a topological effect owing to the nontrivial spectral winding, and such spectral behaviors appear naturally in nonreciprocal systems. Hence prevailing approaches rely on nonreciprocity to achieve the NHSE. Here, we report the experimental realization of the geometry-dependent skin effect in a two-dimensional reciprocal system, in which the skin effect occurs only at boundaries whose macroscopic symmetry mismatches with the lattice symmetry. The role of spectral reciprocity and symmetry is revealed by connecting reflective channels at given boundaries with the spectral topology of the PBC spectrum. Our work highlights the vital role of reciprocity, symmetry, and macroscopic geometry on the NHSE in dimensionality larger than one and opens new routes for wave structuring using non-Hermitian effects.

A predictive approach for the compositional and temperature representation of thermal conductivity in multicomponent molten salt systems for advanced energy applications

This study presents a theoretical model, based on kinetic theory, for accurately predicting thermal conductivity in molten salt mixtures, a vital factor in designing advanced energy systems such as concentrating solar power, thermal energy storage, and advanced nuclear reactors. Applicable to non-complex, non-reciprocal systems, the model represents thermal conductivity with respect to composition and temperature. We evaluated the model using molecular dynamics simulations on binary systems from fluoride, chloride, bromide, iodide salt families. The model predictions were also compared against existing experimental datasets for those families as well as binary nitrates and carbonates. The model demonstrated an improvement in predictive accuracy over the ideal linear estimation and showed reasonable agreement with the reliable experimental data. Deviations from ideal conductivity, analyzed using the Redlich-Kister method, pointed to the molecular weight and thermal conductivity of individual compounds as primary influencing factors. When applied to predict the thermal conductivity of higher order eutectic salt mixtures relevant to energy applications, the model showed predictive accuracy comparable to empirical methods. The model was further applied to generate compositional mapping to quantify deviations from ideality over the compositional space. This advance enhances new molten salt mixtures evaluation efficiency and extends the model to complex mixtures.

Wave analysis of rotors with longitudinal periodicity

The dynamics of rotating systems plays an important role in the efficiency and reliability of such machines. For this reason, understanding their dynamics is essential to predict and mitigate the resultant vibrations that can occur in such machines. Considering that vibration is essentially the propagation of waves in a continuous medium, methods of wave analysis can also be employed to investigate the dynamics of rotating systems, especially when the system presents some sort of periodicity. The difficulty lies in the fact that rotating systems are non-reciprocal systems due to the gyroscopic effects, which create forward and backward whirl motions with associated mode waves. The conventional wave methods usually do not tackle this problem. This work presents a methodology for analyzing rotating systems with wave methods based on the combination of conventional modal analysis, Bloch wave propagation theory, and directional frequency response functions. In this case, it is possible to separate the forward and backward modes, thus allowing the analysis of forward and backward wavenumbers separately. Consequently, one can draw separate dispersion diagrams for the wave modes associated with the forward and backward motions of the rotor. The numerical results show the feasibility of the method, and the methodology is applied experimentally to a rotating system in the laboratory.

Prethermalization in periodically driven nonreciprocal many-body spin systems

Prethermalization in periodically driven nonreciprocal many-body spin systems

Mechanical nonreciprocity in a uniform composite material.

Mechanical nonreciprocity, or the asymmetric transmission of mechanical quantities between two points in space, is crucial for developing systems that can guide, damp, and control mechanical energy. We report a uniform composite hydrogel that displays substantial mechanical nonreciprocity, owing to direction-dependent buckling of embedded nanofillers. This material exhibits an elastic modulus more than 60 times higher when sheared in one direction compared with the opposite direction. Consequently, it can transform symmetric vibrations into asymmetric ones that are applicable for mass transport and energy harvest. Furthermore, it exhibits an asymmetric deformation when subjected to local interactions, which can induce directional motion of various objects, including macroscopic objects and even small living creatures. This material could promote the development of nonreciprocal systems for practical applications such as energy conversion and biological manipulation.

Electromagnetic Doppler effect in non-reciprocal medium

Reflected light from a moving object, such as a mirror, is frequency-shifted via the Doppler effect. This well-known phenomenon is used to determine the speed and direction of an object due to the red or blue shifting of the received electromagnetic radiation frequency. To date, the Doppler theory has focused on the propagation of electromagnetic radiation through reciprocal media where the transiting photons have the same speed, regardless of direction. However, optical birefringence exists in solid-state, liquid, and gas media, which results in spatially dependent, and vector field-dependent, propagation velocities. When combined with the Faraday effect, which is employed routinely in laboratory setups and present at galactic scales, non-reciprocal Doppler effects may occur. A non-reciprocal Doppler effect theory is derived showing frequency shift dependencies on the object velocity and the directional speed of light in the medium. This general Doppler theory is shown to simplify the canonical relations for the Doppler effect in systems without a directional dependence on light. In non-reciprocal systems, when the mirror velocity is much less than the speed of light, the general frequency shift relation simplifies to a dependency on the roundtrip average speed of light. This theory provides a basis for the application of the Doppler effect to estimate the velocity of moving objects in non-reciprocal systems.

Transport effects in non-Hermitian nonreciprocal systems: General approach

In this paper, we present a unifying analytical framework for identifying conditions for transport effects such as reflectionless and transparent transport, lasing, and coherent perfect absorption in non-Hermitian nonreciprocal systems using a generalized transfer matrix method. This provides a universal approach to studying the transport of tight-binding platforms, including higher-dimensional models and those with an internal degree of freedom going beyond the previously studied case of one-dimensional chains with nearest-neighbor couplings. For a specific class of tight-binding models, the relevant transport conditions and their signatures of non-Hermitian, nonreciprocal, and topological behavior are analytically tractable from a general perspective. We investigate this class and illustrate our formalism in a paradigmatic ladder model where the system's parameters can be tuned to adjust the transport effect and topological phases.

Onsager’s Variational Principle for Nonreciprocal Systems with Odd Elasticity

Using Onsager's variational principle, we derive dynamical equations for a nonequilibrium active system with odd elasticity. The elimination of the extra variable that is coupled to the nonequilibrium driving force leads to the nonreciprocal set of equations for the material coordinates. The obtained nonreciprocal equations manifest the physical origin of the odd elastic constants that are proportional to the nonequilibrium force and the friction coefficients. Our approach offers a systematic and consistent way to derive nonreciprocal equations for active matter in which the time-reversal symmetry is broken.