Condensed Matter Theory

Abstract:

We use numerical simulations and linear stability analysis to study an active nematic layer where the director is allowed to point out of the plane. Our results highlight the difference between extensile and contractile systems. Contractile stress suppresses the flows perpendicular to the layer and favours in-plane orientations of the director. By contrast, extensile stress promotes instabilities that can turn the director out of the plane, leaving behind a population of distinct, in-plane regions that continually elongate and divide. This supports extensile forces as a mechanism for the initial stages of layer formation in living systems, and we show that a planar drop with extensile (contractile) activity grows into three dimensions (remains in two dimensions). The results also explain the propensity of disclination lines in three dimensional active nematics to be of twist-type in extensile or wedge-type in contractile materials.

Abstract:

We consider the spectral statistics of the Floquet operator for disordered, periodically driven spin chains in their quantum chaotic and many-body localized (MBL) phases. The spectral statistics are characterized by the traces of powers t of the Floquet operator, and our approach hinges on the fact that for integer t in systems with local interactions, these traces can be re-expressed in terms of products of dual transfer matrices, each representing a spatial slice of the system. We focus on properties of the dual transfer matrix products as represented by a spectrum of Lyapunov exponents, which we call spectral Lyapunov exponents. In particular, we examine the features of this spectrum that distinguish chaotic and MBL phases. The transfer matrices can be block diagonalized using time-translation symmetry, and so the spectral Lyapunov exponents are classified according to a momentum in the time direction. For large t we argue that the leading Lyapunov exponents in each momentum sector tend to zero in the chaotic phase, while they remain finite in the MBL phase. These conclusions are based on results from three complementary types of calculation. We find exact results for the chaotic phase by considering a Floquet random quantum circuit with on-site Hilbert space dimension q in the large-q limit. In the MBL phase, we show that the spectral Lyapunov exponents remain finite by systematically analyzing models of noninteracting systems, weakly coupled systems, and local integrals of motion. Numerically, we compute the Lyapunov exponents for a Floquet random quantum circuit and for the kicked Ising model in the two phases. As an additional result, we calculate exactly the higher-point spectral form factors (hpSFFs) in the large-q limit and show that the generalized Thouless time scales logarithmically in system size for all hpSFFs in the large-q chaotic phase.