All is not lost, when lead goes in the wrong direction

Left sided superior vena cava (SVC) is an uncommon anomaly noted in the general population. It adds complexity to the procedure, when attempting to place pacing or defibrillator devices into the heart. Here we report a case where the leads were placed through the left sided SVC into the right sided chambers giving an interesting X-ray appearance

Squeezing anyons for braiding on small lattices

Adiabatically exchanging anyons gives rise to topologically protected operations on the quantum state of the system, but the desired result is only achieved if the anyons are well separated, which requires a sufficiently large area. Being able to reduce the area needed for the exchange, however, would have several advantages such as enabling a larger number of operations per area and allowing anyon exchange to be studied in smaller systems that are easier to handle. Here, we use optimization techniques to squeeze the charge distribution of Abelian anyons in lattice fractional quantum Hall models, and we show that the squeezed anyons can be exchanged within a smaller area with a close to ideal outcome. We first use a toy model consisting of a modified Laughlin trial state to show that one can shape the anyons without altering the exchange statistics under certain conditions. We then squeeze and braid anyons in the Kapit-Mueller model and an interacting Hofstadter model by adding suitable potentials. We consider a fixed system size, for which the charge distributions of the normal anyons overlap, and we find that the outcome of the exchange process is closer to the ideal value for the squeezed anyons. The time needed for the exchange is also important, and for a particular example we find that the duration needed for the process to be close to the adiabatic limit is about five times longer for the squeezed anyons when the path length is the same. Finally, we show that the exchange outcome is robust with respect to small modifications of the potential away from the optimized value

The operator growth hypothesis in open quantum systems

The operator growth hypothesis (OGH) is a technical conjecture about the behaviour of operators -- specifically, the asymptotic growth of their Lanczos coefficients -- under repeated action by a Liouvillian. It is expected to hold for a sufficiently generic closed many-body system. When it holds, it yields bounds on the high frequency behavior of local correlation functions and measures of chaos (like OTOCs). It also gives a route to numerically estimating response functions. Here we investigate the generalisation of OGH to open quantum systems, where the Liouvillian is replaced by a Lindbladian. For a quantum system with local Hermitian jump operators, we show that the OGH is modified: we define a generalisation of the Lanczos coefficient and show that it initially grows linearly as in the original OGH, but experiences exponentially growing oscillations on scales determined by the dissipation strength. We see this behavior manifested in a semi-analytically solvable model (large-q SYK with dissipation), numerically for an ergodic spin chain, and in a solvable toy model for operator growth in the presence of dissipation (which resembles a non-Hermitian single-particle hopping process). Finally, we show that the modified OGH connects to a fundamental difference between Lindblad and closed systems: at high frequencies, the spectral functions of the former decay algebraically, while in the latter they decay exponentially. This is an experimentally testable statement, which also places limitations on the applicability of Lindbladians to systems in contact with equilibrium environments.Comment: 9 pages, 6 figure

Packaging Problems-Present and Future of Service Rations

Developments of food packaging from the early days of rigid containers up to the modern method of using flexible materials are revealed. Factors involving the selection for packing different types of Service rations are discussed. Future areas of research and development activity are outlined briefly

Quantum many-body scars with chiral topological order in two dimensions and critical properties in one dimension

We construct few-body, interacting, nonlocal Hamiltonians with a quantum scar state in an otherwise thermalizing many-body spectrum. In one dimension, the embedded state is a critical state, and in two dimensions, the embedded state is a chiral topologically ordered state. The models are defined on slightly disordered lattices, and the scar state appears to be independent of the precise realization of the disorder. A parameter allows the scar state to be placed at any position in the spectrum. We show that the level spacing distributions are Wigner-Dyson and that the entanglement entropies of the states in the middle of the spectrum are close to the Page value. Finally, we confirm the topological order in the scar state by showing that one can insert anyons into the state

Disordered Haldane-Shastry model

The Haldane-Shastry model is one of the most studied interacting spin systems. The Yangian symmetry makes it exactly solvable, and the model has semionic excitations. We introduce disorder into the Haldane-Shastry model by allowing the spins to sit at random positions on the unit circle and study the properties of the eigenstates. At weak disorder, the spectrum is similar to the spectrum of the clean Haldane-Shastry model. At strong disorder, the long-range interactions in the model do not decay as a simple power law. The eigenstates in the middle of the spectrum follow a volume law, but the coefficient is small, and the entropy is hence much less than for an ergodic system. In addition, the energy level spacing statistics is neither Poissonian nor of the Wigner-Dyson type. The behavior at strong disorder hence serves as an example of a non-ergodic phase, which is not of the many-body localized kind, in a model with long-range interactions and SU(2) symmetry.Comment: Accepted for publication in PR

Many-body delocalization via symmetry emergence

Many-body localization (MBL) provides a mechanism to avoid thermalization in many-body quantum systems. Here, we show that an {\it emergent} symmetry can protect a state from MBL. Specifically, we propose a $\Z_2$ symmetric model with nonlocal interactions, which has an analytically known, SU(2) invariant, critical ground state. At large disorder strength all states at finite energy density are in a glassy MBL phase, while the lowest energy states are not. These do, however, localize when a perturbation destroys the emergent SU(2) symmetry. The model also provides an example of MBL in the presence of nonlocal, disordered interactions that are more structured than a power law. The presented ideas raise the possibility of an `inverted quantum scar', in which a state that does not exhibit area law entanglement is embedded in an MBL spectrum, which does.Comment: 5 pages, 3 figure