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Abstract Mechanical lattices support topological wave phenomena governed by geometric phases. We develop a compact Hilbert-space description for one-dimensional elastic chains, expressing intracell motion as a normalized superposition of orthogonal eigenstates and tracking complex amplitudes as trajectories on a Bloch sphere. For diatomic lattices, this construction makes inversion symmetry protection explicit: the relative phase between in-phase and out-of-phase modes is piecewise locked, and the Zak phase is quantized with band-dependent jumps at symmetry points. Extending the framework to triatomic lattices shows that restoring inversion retains quantization, whereas breaking it dequantizes the geometric phase while leaving the spectrum origin invariant. Viewing norm-preserving transformations of the modal coefficient pair as Bloch-sphere rotations, we demonstrate classical analogs of single-qubit logic gates: a π-phase rotation about a transverse axis swaps the modal poles, and a longitudinal-axis phase flip maps balanced superpositions to their conjugates. These gate-like operations are realized by controlled evolution across wavenumber space and can be driven or reprogramed through spatiotemporal stiffness modulation. Introducing space–time modulation hybridizes carrier and sideband harmonics, producing continuous phase winding and open-path geometric phases accumulated along the Floquet trajectory. Across static and modulated regimes, the framework unifies algebraic and geometric viewpoints, is robust to gauge and basis choices, and operates directly on amplitude-phase data. Results clarify how symmetry, modulation, and topology jointly govern dispersion, modal mixing, and phase accumulation, providing tools to analyze and design vibration and acoustic functionalities in engineered structures. 

Abstract Vibration responses from nonlinear mechanical systems exhibit rich dynamical structure that can be utilized for information encoding and processing. We demonstrate that such structures can be used to encode and manipulate information in a manner analogous to multi-qubit systems. By using a coupled mass and conical spring oscillator, we reveal that distinct harmonic segments of the nonlinear response can be projected onto modal eigenstates to form two-level elastic-bit subsystems, which are analogous to qubits. These bits arise from measurable amplitudes and phase relationships across the Fourier spectrum and evolve deterministically under steady-state excitation. By combining multiple spectral segments within a single oscillator, we achieve two-bit and three-bit states that occupy four- and eight-dimensional Hilbert spaces, respectively. The time dependence of the complex modal coefficients yields intrinsic transformations that act as phase and rotation type gates. The temporal evolution of the complex modal coefficients results in phase accumulation and a rotation-like evolution within this state space. To characterize how the system moves between experimentally observed logical states at different times, we derive a Householder reflection that yields the exact Hermitian and unitary operator connecting these states. This unitary transformation is subsequently decomposed into sequences of analogous quantum gates, providing a representation of the observed modal evolution in terms of familiar multi-qubit logic primitives. This spectral-encoding approach enables scalable state construction within a single mechanical platform, establishing a pathway toward room-temperature mechanical computation based on deterministic nonlinear dynamics. 

Abstract Wave reflection and refraction at a time interface follow different conservation laws compared to conventional scattering at a spatial interface. This study presents the experimental demonstration of refraction and reflection of flexural waves across a temporal boundary in a continuum-based mechanical metabeam, and unveils opportunities that emerge by tailoring temporal scattering phenomena for phononic applications. We observe these phenomena in an elastic beam attached to an array of piezoelectric patches that can vary in time the effective elastic properties of the beam. Frequency conversion and phase conjugation are observed upon a single temporal interface. These results are consistent with the temporal Snell’s law and Fresnel equations for temporal interfaces. Further, we illustrate the manipulation of amplitude and frequency spectra of flexural wave temporal refraction and reflection through multi-stepped temporal interfaces. Finally, by implementing a smooth time variation of wave impedance, we numerically and experimentally demonstrate the capabilities of the temporal metabeam to realize waveform morphing and information coding. Our findings enable precise control over wave amplitude and frequency through temporally modulated mechanical systems, providing a concrete framework for designing time-mechanical metamaterials and time-phononic crystals. 

Abstract This study demonstrates a novel nondestructive evaluation (NDE) method that combines geometric phase sensing with cross-correlation processed acoustical responses, enabling the detection of structural anomalies even when the acoustic excitation is stochastic and the source characteristics are variable. Traditional ultrasonic techniques, which depend on impulse responses from known source locations to capture wave transmission behavior, often fail under stochastic excitations due to incoherent phase alignment and unpredictable wave paths. The proposed method applies cross-correlation between a fixed reference site and other sensor locations to refine the acoustic field representation, enabling physically meaningful geometric phase extraction through the dot product of two state vectors representative of the acoustic field in a high-dimensional complex Hilbert space. This allows detection of both excitation-induced field asymmetries and subtle nonlinearities. Experimental validation using laser Doppler vibrometry on a circular IN625 plate demonstrates that this approach preserves excitation-induced field asymmetries while remaining sensitive to structural perturbations such as mass defects. The cross-correlation geometric phase change (CC-Δφ) spectra reveal modal differences across excitation conditions, even under white noise, where geometric phase without cross-correlation (Δφ) remains centered near 90 deg, obscuring structural insights. The method also detects mass-induced effects, showing increased average CC-Δφ compared to the no-mass case under the same excitation condition. These results establish a foundation for a robust, non-contact, source-independent NDE technique, suitable for operation under variable and uncontrolled excitation scenarios. 

Abstract We leverage ambient seismic noise to implement a novel geometric phase sensing method for investigating the effects of environmental conditions on near‐surface ground properties. The geometric phase, derived from topological acoustics, characterizes the geometry of a wavefield by incorporating cross‐correlation information between seismic sensors. Changes in geometric phase, , are expressed as changes in vectorial orientation, describing the wavefield evolution over time. To demonstrate the method, we designed an end‐to‐end workflow by applying an open access temporal high‐resolution data from a seismic array in southwest Iceland and measured over a 2‐year period. We observe that the seasonal fluctuations of are highly correlated with surface air temperature, reflecting changes in ground properties during the freeze‐thaw cycle. We assess the seasonal stability of the noise source distribution and conduct a numerical test to verify that the seasonal pattern in is minimally affected by shifts in noise source direction. Several advantages of geometric phase measurements, including the elimination of lag window selection and reduced computational costs, suggest their strong effectiveness in monitoring changes in ground properties with time. We suggest that the geometric phase can play a significant role in the future of environmental monitoring. 

Abstract Optoelectronics are crucial for developing energy‐efficient chip technology, with phase‐change materials (PCMs) emerging as promising candidates for reconfigurable components in photonic integrated circuits, such as nonvolatile phase shifters. Antimony sulfide (Sb₂S₃) stands out due to its low optical loss and considerable phase‐shifting properties, along with the non‐volatility of both phases. This study demonstrates that the crystallization kinetics of Sb₂S₃can be switched from growth‐driven to nucleation‐driven by altering the sample dimension from bulk to film. This tuning of the crystallization process is critical for optical switching applications requiring control over partial crystallization. Calorimetric measurements with heating rates spanning over six orders of magnitude, reveal that, unlike conventional PCMs that crystallize below the glass transition, Sb₂S₃exhibits a measurable glass transition prior to crystallization from the undercooled liquid (UCL) phase. The investigation of isothermal crystallization kinetics provides insights into nucleation rates and crystal growth velocities while confirming the shift to nucleation‐driven behavior at reduced film thicknesses—an essential aspect for effective device engineering. A fundamental difference in chemical bonding mechanisms was identified between Sb₂S₃, which exhibits covalent bonding in both material phases, and other PCMs, such as GeTe and Ge₂Sb₂Te₅, which demonstrate pronounced bonding alterations upon crystallization. 

Abstract A newly developed nonlinear ultrasonic (NLU) technique called sideband band peak count-index (or SPC-I) measures the degree of nonlinearity associated with the inspected specimen – larger SPC-I values indicate higher nonlinearity. In various published papers, the SPC-I technique has shown its effectiveness and superiority in comparison to other techniques for nondestructive testing (NDT) and structural health monitoring (SHM) applications. In this work, the performance of SPC-I in non-homogeneous specimens having different topographies is investigated using peridynamics based periultrasound modeling. Three types of topographies – “X” topography, “Y” topography and “XY” topography are introduced by adding thin strips made up of a second material and thus converting the homogeneous plate into a heterogeneous structure. It is observed that “X” and “XY” topographies can help to hide the crack growth, thus making cracks undetectable to the nonlinear SPC-I based monitoring technique. In addition to the SPC-I technique, we investigate the applicability of the emerging method of topological acoustic sensing. This method monitors the changes in the geometric phase; a measure of the changes in linear or nonlinear wave’s spatial behavior during its propagation in plate structures having various topographies. The computed results show that the magnitudes of jumps in geometric phase change plots can be good indicators to distinguish cracks with different thicknesses although these cracks can remain hidden in some topographies during the single point inspection based on the nonlinear SPC-I based monitoring technique.