Mott, Floquet, and the response of periodically driven Anderson insulators

We consider periodically driven Anderson insulators. The short time behavior for weak, monochromatic, uniform electric fields is given by linear response theory and was famously derived by Mott. We go beyond this to consider both long times---which is the physics of Floquet late time states---and strong electric fields. This results in a `phase diagram' in the frequency-field strength plane, in which we identify four distinct regimes. These are: a linear response regime dominated by pre-existing Mott resonances, which exists provided Floquet saturation is not reached within a period; a non-linear perturbative regime, which exhibits multiphoton-absorption in response to the field; a near-adiabatic regime, which exhibits a primarily reactive response spread over the entire sample and is insensitive to pre-existing resonances; and finally an enhanced dissipative regime.Comment: 15 pages, 9 figure

D3 branes in a Melvin universe: a new realm for gravitational holography

The decoupling limit of a certain configuration of D3 branes in a Melvin universe defines a sector of string theory known as Puff Field Theory (PFT) - a theory with non-local dynamics but without gravity. In this work, we present a systematic analysis of the non-local states of strongly coupled PFT using gravitational holography. And we are led to a remarkable new holographic dictionary. We show that the theory admits states that may be viewed as brane protrusions from the D3 brane worldvolume. The footprint of a protrusion has finite size - the scale of non-locality in the PFT - and corresponds to an operator insertion in the PFT. We compute correlators of these states, and we demonstrate that only part of the holographic bulk is explored by this computation. We then show that the remaining space holographically encodes the dynamics of the D3 brane tentacles. The two sectors are coupled: in this holographic description, this is realized via quantum entanglement across a holographic screen - a throat in the geometry - that splits the bulk into the two regions in question. We then propose a description of PFT through a direct product of two Fock spaces - akin to other non-local settings that employ quantum group structures.Comment: 44 pages, 13 figures; v2: minor corrections, citations added; v3: typos corrected in section on local operators, some asymptotic expansions improved and made more consistent with rest of paper in section on non-local operator

Floquet Prethermalization in a Bose-Hubbard System

Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system -- leading to long-lived 'prethermal' regimes. In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model. By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude. The tunability of the lattice potentials allows us to explore one- and two-dimensional systems in a range of different interacting regimes. Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension. Our results show experimental evidence of the phenomenon of Floquet prethermalization, and provide insight into the characterization of heating for driven bosonic systems

Phenomenology of the Prethermal Many-Body Localized Regime

The dynamical phase diagram of interacting disordered systems has seen substantial revision over the past few years. Theory must now account for a large prethermal many-body localized (MBL) regime in which thermalization is extremely slow, but not completely arrested. We derive a quantitative description of these dynamics in short-ranged one-dimensional systems using a model of successive many-body resonances. The model explains the decay timescale of mean autocorrelators, the functional form of the decay - a stretched exponential - and relates the value of the stretch exponent to the broad distribution of resonance timescales. The Jacobi method of matrix diagonalization provides numerical access to this distribution, as well as a conceptual framework for our analysis. The resonance model correctly predicts the stretch exponents for several models in the literature. Successive resonances may also underlie slow thermalization in strongly disordered systems in higher dimensions, or with long-range interactions.Comment: 7 pages, 3 figures + 9 pages, 9 figures; (v2) additional appendix on the absence of rare region effects, new numerical data for Heisenberg model autocorrelation functions and Floquet model decimated element distributions, other clarifications and correction

Entanglement phase transitions in measurement-only dynamics

Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone. This motivates us to introduce \emph{measurement-only models}, in which the "scrambling" and "un-scrambling" effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes. This represents a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits. We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models. We find that the principle driving the EPTs in these models is \emph{frustration}, or mutual incompatibility, of the measurements. Suprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local ($\gtrsim 3$-body) operators. We identify a class of exceptions to this behavior ("bipartite ensembles") which cannot sustain an entangling phase, but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points. Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light-cone, despite the non-locality inherent to quantum measurements.Comment: 14 pages + bibliography and appendices, 10 figures. v2: added section on quantum code properties, added references. v3: substantial changes to the structure of the paper, improved clarit

Characterization of the bias between oxygen saturation measured by pulse oximetry and calculated by an arterial blood gas analyzer in critically ill neonates

Continuous monitoring of oxygenation with pulse oximetry is the standard of care for critically ill neonates. A better understanding of its measurement bias compared to arterial oxygen saturation could be helpful both for the clinician and researcher. Towards that end, we examined the electronic database from a large neonatal ICU. From a 24-month period we identified 23,032 paired SpO2-SaO2 measurements from 1,007 infants who were receiving supplemental oxygen during mechanical ventilation. We found that SpO2 was consistently higher than SaO2. The size of the bias was fairly constant when SpO2 was between 75-93%, above which it dropped steadily. The median size of this bias was 1% SpO2 during hyperoxemia (SpO2 97-100%) with a median variation of 1.3% above and below. During periods of hypoxemia (SpO2 75-85%) and normoxemia (SpO2 89-93%) the bias was approximately 5% SpO2, with a median variation of 5% above and below

Observation of discrete time-crystalline order in a disordered dipolar many-body system

Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic "time-crystalline" phases, which spontaneously break the discrete time-translation symmetry of the underlying drive. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of $\sim 10^6$ dipolar spin impurities in diamond at room-temperature. We observe long-lived temporal correlations at integer multiples of the fundamental driving period, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions; this order is remarkably stable against perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.Comment: 6 + 3 pages, 4 figure

Predicting Body Height in a Pediatric Intensive Care Unit Using Ulnar Length

Objective: To determine if ulnar length obtained by the bedside nurse can be used to estimate patient length. To compare our findings to previous predictive equations of height and ulnar length. To evaluate the performance of predictive equations for height and ulnar length on patients with syndromes that affect height.Design: Retrospective observational study of prospectively collected data.Settings: Multidisciplinary Pediatric Intensive Care Unit in a university teaching hospital.Patients: 1,177 patients, ages 1 month to 23 years. Mean age was 79.7 months (1,3 IQR 19.5, 164.5 months) and 55.4% male.Measurements: Ulnar length was obtained using digital calipers by bedside nurses in PICU as well as height and weight. The electronic health care record was used to extract patient information.Main Results: The predictive equation for height for the entire group is: height (cm) = 0.59*ulnar length (mm) + 13.1 (r2 = 0.93). Bland Altman analysis of the derivation formula applied to the testing group did not show any systematic bias.Conclusions: Our study shows that ulnar length measurements can be used to predict height with a simple linear formula in a PICU setting. Not having specific individuals or specific training for ulnar measurement did not seem to alter the accuracy (r2 = 0.93). The robust nature of the measurement and ease of use may make this an unconventional but reasonable alternative to obtaining height when that cannot be measured directly