Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States

We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer resources required. This modification is based on a principle of "observing" the system outside the light-cone. We apply this method to study spin relaxation in systems started out of equilibrium with initial conditions that give rise to very rapid entanglement growth. We also show that it is possible to approximate time evolution under a local Hamiltonian by a quantum circuit whose light-cone naturally matches the Lieb-Robinson velocity. Asymptotically, these modified methods allow a doubling of the system size that one can obtain compared to direct simulation. We then consider a different problem of thermal properties of disordered spin chains and use quantum belief propagation to average over different configurations. We test this algorithm on one dimensional systems with mixed ferromagnetic and anti-ferromagnetic bonds, where we can compare to quantum Monte Carlo, and then we apply it to the study of disordered, frustrated spin systems.Comment: 19 pages, 12 figure

Ion collection by oblique surfaces of an object in a transversely-flowing strongly-magnetized plasma

The equations governing a collisionless obliquely-flowing plasma around an ion-absorbing object in a strong magnetic field are shown to have an exact analytic solution even for arbitrary (two-dimensional) object-shape, when temperature is uniform, and diffusive transport can be ignored. The solution has an extremely simple geometric embodiment. It shows that the ion collection flux density to a convex body's surface depends only upon the orientation of the surface, and provides the theoretical justification and calibration of oblique `Mach-probes'. The exponential form of this exact solution helps explain the approximate fit of this function to previous numerical solutions.Comment: Four pages, 2 figures. Submitted to Phys. Rev. Letter

Olfaction Contributes to Pelagic Navigation in a Coastal Shark.

How animals navigate the constantly moving and visually uniform pelagic realm, often along straight paths between distant sites, is an enduring mystery. The mechanisms enabling pelagic navigation in cartilaginous fishes are particularly understudied. We used shoreward navigation by leopard sharks (Triakis semifasciata) as a model system to test whether olfaction contributes to pelagic navigation. Leopard sharks were captured alongshore, transported 9 km offshore, released, and acoustically tracked for approximately 4 h each until the transmitter released. Eleven sharks were rendered anosmic (nares occluded with cotton wool soaked in petroleum jelly); fifteen were sham controls. Mean swimming depth was 28.7 m. On average, tracks of control sharks ended 62.6% closer to shore, following relatively straight paths that were significantly directed over spatial scales exceeding 1600 m. In contrast, tracks of anosmic sharks ended 37.2% closer to shore, following significantly more tortuous paths that approximated correlated random walks. These results held after swimming paths were adjusted for current drift. This is the first study to demonstrate experimentally that olfaction contributes to pelagic navigation in sharks, likely mediated by chemical gradients as has been hypothesized for birds. Given the similarities between the fluid three-dimensional chemical atmosphere and ocean, further research comparing swimming and flying animals may lead to a unifying paradigm explaining their extraordinary navigational abilities

Entropy and Entanglement in Quantum Ground States

We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gapped one-dimensional local Hamiltonians such that the entropy is exponentially large in the correlation length, and we present strong evidence supporting a conjecture that there exist such systems with arbitrarily large entropy. However, we then show that, under an assumption on the density of states which is believed to be satisfied by many physical systems such as the fractional quantum Hall effect, that an efficient matrix product state representation of the ground state exists in any dimension. Finally, we comment on the implications for numerical simulation.Comment: 7 pages, no figure

Critical review of the impacts of grazing intensity on soil organic carbon storage and other soil quality indicators in extensively managed grasslands

Acknowledgements This work contributes to the N-Circle project (grant number BB/N013484/1), and CINAg (BB/N013468/1) Virtual Joint Centres on Agricultural Nitrogen (funded by the Newton Fund via UK BBSRC/NERC), U-GRASS (grant number NE/M016900/1), the Belmont Forum/FACCE-JPI DEVIL project (grant number NE/M021327/1), Soils-R-GGREAT (grant number NE/P019455/1), ADVENT (grant number NE/M019713/1), Sêr Cymru LCEE-NRN project, Climate-Smart Grass and the Scottish Government’s Strategic Research Programme.Peer reviewedPublisher PD

Types and correlates of school non-attendance in students with autism spectrum disorders

School non-attendance in autism spectrum disorders (ASD) has received very little attention to date. The study aimed to provide a comprehensive description of school non-attendance in students with ASD. Through an online survey, parents of 486 children (mean age 11 years) reported on school attendance over one month, and reasons for instances of non-attendance. On average, students missed five days of school of a possible 23 days. Persistent non-attendance (absent on 10%+ of available sessions) occurred among 43% of students. School non-attendance was associated with child older age, not living in a two-parent household, parental unemployment and, especially, attending a mainstream school. School refusal accounted for 43% of non-attendance. School exclusion and school withdrawal each accounted for 9% of absences. Truancy was almost non-existent. Non-problematic absenteeism (mostly related to medical appointments and illness) accounted for 32% of absences. Non-problematic absenteeism was more likely among those with intellectual disability, school refusal was more likely among older students, and school exclusion was more likely among students from single-parent, unemployed, and well educated households. Findings suggest school non-attendance in ASD is a significant issue, and that it is important to capture detail about attendance patterns and reasons for school non-attendance

Entanglement vs. gap for one-dimensional spin systems

We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a one-dimensional system states that for the ground state, the entanglement of any interval is upper-bounded by a constant independent of the size of the interval. However, the possible dependence of the upper bound on the spectral gap Delta is not known, as the best known general upper bound is asymptotically much larger than the largest possible entropy of any model system previously constructed for small Delta. To help resolve this asymptotic behavior, we construct a family of one-dimensional local systems for which some intervals have entanglement entropy which is polynomial in 1/Delta, whereas previously studied systems, such as free fermion systems or systems described by conformal field theory, had the entropy of all intervals bounded by a constant times log(1/Delta).Comment: 16 pages. v2 is final published version with slight clarification

Topology and Phases in Fermionic Systems

There can exist topological obstructions to continuously deforming a gapped Hamiltonian for free fermions into a trivial form without closing the gap. These topological obstructions are closely related to obstructions to the existence of exponentially localized Wannier functions. We show that by taking two copies of a gapped, free fermionic system with complex conjugate Hamiltonians, it is always possible to overcome these obstructions. This allows us to write the ground state in matrix product form using Grassman-valued bond variables, and show insensitivity of the ground state density matrix to boundary conditions.Comment: 4 pages, see also arxiv:0710.329

Simulating adiabatic evolution of gapped spin systems

We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap \Delta E between the ground state and the first excited state is any constant independent of n, the total number of spins, then the ground-state expectation values of local operators, such as correlation functions, can be computed using polynomial space and time resources. Our results also imply that the local ground-state properties of any two spin models in the same quantum phase can be efficiently obtained from each other. A consequence of these results is that adiabatic quantum algorithms can be simulated efficiently if the spectral gap doesn't scale with n. The simulation method we describe takes place in the Heisenberg picture and does not make use of the finitely correlated state/matrix product state formalism.Comment: 13 pages, 2 figures, minor change