Topologically quantized macroscopic attractor states in hydrated DNA

Abstract

Driven dissipative systems at ambient conditions typically exhibit continuous responses shaped by fluctuations and relaxation, with discrete macroscopic states arising only under specific dynamical constraints. Here, we report the emergence of discrete attractor states in a quasi-two-dimensional hydrated DNA sample under magnetic excitation. The transverse polarization voltage Vxy displays telegraph switching between well-defined levels, indicating stochastic transitions between metastable macroscopic states. Statistical analysis of the voltage time series reveals bimodal distributions and strong Bayesian model selection in favor of multiple coexisting states. These observations can be consistently interpreted within a phase-field framework in which a collective U(1) polarization phase organizes into integer-labeled winding sectors, with transitions mediated by phase-slip events. This framework gives rise to discrete voltage levels reflecting topologically distinct attractors of the driven system. The results suggest that macroscopic quantization can emerge in a classical system at ambient conditions as a consequence of dissipative dynamics constrained by phase topology.

Figures (15)

• Figure 1: Transverse voltage $V_{xy}$ measured during a magnetic-field sweep in hydrated DNA (500 ng µL$^{-1}$, 5 µL) at ambient temperature ($T=21.9^{\circ}$C). The magnetic field was adjusted manually and increased monotonically during the measurement. The plateaus are not synchronized with individual field adjustments but correspond to intrinsic metastable attractors stabilized under sufficiently quiet magnetic conditions. Small cyclic fluctuations accompany field variation, while strong telegraph-switching events occur rarely and are confined to plateau boundaries. A pronounced threshold appears near $B \approx 0.25$--0.27 T, marking a transition from a weakly varying response to a regime characterized by strong nonlinearity and the emergence of discrete voltage structures. The full dataset (approximately $10^5$ points) is available on Zenodo 10.5281/zenodo.14716955.
• Figure 2: Zoomed view of the post-threshold transverse voltage response $V_{xy}(B)$ from Fig. \ref{['fig:threshold']}, focusing on the magnetic-field range $B \gtrsim 0.27$ T. In this regime, the signal organizes into a sequence of discrete, metastable voltage plateaus separated by fluctuation-dominated transition regions. Horizontal line segments indicate representative plateau levels, determined from the local $V_{xy}$ values between successive extrema in the field derivative. The finite magnetic-field extent of each segment reflects the limited stability range of the corresponding metastable state. Inset: field derivative $dV_{xy}/dB$, highlighting sharp transition events and intermittent telegraph-like switching between neighboring plateaus.
• Figure 3: Dwell-density map of the transverse voltage $V_{xy}$ as a function of magnetic field $B$ for the DNA--water system (500 ng $\mu$L$^{-1}$, $T=21.9^{\circ}$C), constructed as a two-dimensional histogram of the time-ordered data in the post-threshold regime ($B \gtrsim 0.25$ T). Color encodes $\log_{10}(\mathrm{counts}+1)$ and highlights the most frequently occupied voltage levels. The appearance of narrow, ridge-like bands indicates a discrete set of preferred metastable polarization states persisting over finite magnetic-field intervals. Broadening and fragmentation of the ridges near their boundaries reflect enhanced fluctuations and telegraph-like switching associated with transitions between neighboring states.
• Figure 4: Statistical signature of attractor competition in the transverse voltage response. Left: within a stable plateau, the voltage distribution is unimodal and well described by a single Gaussian probability density, indicating residence near a single metastable attractor. Right: near a plateau boundary, the distribution becomes bimodal and is accurately captured by a two-Gaussian mixture, reflecting noise-assisted switching between two coexisting attractors. Model selection using the Bayesian information criterion confirms a transition from unimodal to bimodal voltage distributions near plateau boundaries. The quantitative Bayesian model selection underlying this bimodality is presented in the Supplementary Information.
• Figure S1: Schematic illustration of noise-induced switching between neighboring metastable phase attractors in a compact polarization phase landscape. Two coexisting attractors, labeled by indices $n$ and $n+1$, are separated by an effective barrier in the phase potential $U(\theta;B)$. Thermal and environmental fluctuations enable stochastic hopping between these attractors, resulting in random telegraph switching between two discrete transverse voltage levels. In the overdamped regime relevant here, the dynamics are governed by Eqs. (\ref{['eq:SI_full_langevin']})--(\ref{['eq:washboard']}), with phase slips corresponding to $2\pi$ changes of the global phase winding. This schematic illustrates the physical origin of bimodal voltage distributions and intermittent switching observed experimentally near plateau boundaries, where neighboring attractors coexist.