ABSTRACT
Quantum many-body systems display rich phase structure in their low-temperature equilibrium states1. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases2-8 that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC)7,9-15. Concretely, dynamical phases can be defined in periodically driven many-body-localized (MBL) systems via the concept of eigenstate order7,16,17. In eigenstate-ordered MBL phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, or from regimes in which the dynamics of a few select states can mask typical behaviour. Here we implement tunable controlled-phase (CPHASE) gates on an array of superconducting qubits to experimentally observe an MBL-DTC and demonstrate its characteristic spatiotemporal response for generic initial states7,9,10. Our work employs a time-reversal protocol to quantify the impact of external decoherence, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. Furthermore, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to studying non-equilibrium phases of matter on quantum processors.
Subject(s)
Cold Temperature , Phase Transition , ThermodynamicsABSTRACT
Thrombin and thrombin peptides play a role in initiating tissue repair. The potential safety and efficacy of TP508 (Chrysalin) treatment of diabetic foot ulcers was evaluated in a 60-subject, prospective, randomized, double-blind, placebo-controlled phase I/II clinical trial. Chrysalin in saline or saline alone was applied topically, twice weekly, to diabetic ulcers with standardized care and offloading. A dose-dependent effect was seen in the per-protocol population where 1 and 10 mug Chrysalin treatment resulted in 45 and 72% more subjects with complete healing than placebo treatment. Chrysalin treatment of foot ulcers more than doubled the incidence of complete healing (p<0.05), increased mean closure rate approximately 80% (p<0.05), and decreased the median time to 100% closure by approximately 40% (p<0.05). Chrysalin treatment of heel ulcers within this population resulted in mean closure rates 165% higher than placebos (p<0.02) and complete healing in 86% (6/7) of ulcers compared with 0% (0/5) of placebo ulcers (p<0.03). Local wound reactions and adverse events (AEs) were equal between groups with no reported drug-related changes in laboratory tests or serious AEs. These results indicate the potential safety and efficacy of Chrysalin for treatment of diabetic foot ulcers.
