Condensed Matter Theory

Abstract:

Since their discovery in 2004, there has been remarkable progress in research on nanomotors, from the elucidation of different propulsion mechanisms to the study of their collective behaviour, culminating in investigations into their applications in biomedicine and environmental remediation. This Perspective reviews this evolution in nanomotor research and discusses the key challenges ahead, including the need for developing advanced characterization techniques, precise motion control, materials innovation, theory and modelling, and translationally feasible in vivo biomedical applications. These challenges highlight the current limitations of synthetic nanomotors and point to exciting future opportunities to revolutionize theranostics and create ‘living’ hybrid systems. We introduce the concept of ‘systems materials’ to encompass interacting functional materials across length scales from molecular to macro. Thus, this Perspective aims to inspire future generations of researchers to advance both fundamental understanding and practical breakthroughs, thereby engineering a paradigm shift in nanomotor research.

Abstract:

Studies of random unitary circuits have shown that the calculation of Rényi entropies of entanglement can be mapped to classical statistical mechanics problems in spacetime. In this paper, we develop an analogous spacetime picture of entanglement generation for random free or weakly interacting fermion systems without conservation laws. We first study a free-fermion model, namely a one-dimensional chain of Majorana modes with nearest-neighbor hoppings, random in both space and time. We analyze the $N\mathrm{th}$ Rényi entropy of entanglement using a replica formalism, and we show that the effective model is equivalent to an $\mathrm{SO}\left(2N\right)$ Heisenberg spin chain evolving in imaginary time. By applying a saddle-point approximation to the coherent states path integral for the $N=2$ case, we arrive at a semiclassical picture for the dynamics of the entanglement purity, in terms of two classical fields in spacetime. The classical solutions involve a smooth domain wall that interpolates between two values, with the width of this smooth domain wall spreading diffusively in time. We then study how adding weak interactions to the free-fermion model modifies this spacetime picture. Interactions reduce the symmetry of the effective continuum description. As a result the width of the entanglement domain wall remains finite, rather than growing diffusively in time. This yields a crossover from diffusive to ballistic spreading of information.

Abstract:

SciPost Submission Detail Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems