Undecidability of the Spectral Gap (full version)

We show that the spectral gap problem is undecidable. Specifically, we construct families of translationally-invariant, nearest-neighbour Hamiltonians on a 2D square lattice of d-level quantum systems (d constant), for which determining whether the system is gapped or gapless is an undecidable problem. This is true even with the promise that each Hamiltonian is either gapped or gapless in the strongest sense: it is promised to either have continuous spectrum above the ground state in the thermodynamic limit, or its spectral gap is lower-bounded by a constant in the thermodynamic limit. Moreover, this constant can be taken equal to the local interaction strength of the Hamiltonian.Comment: v1: 146 pages, 56 theorems etc., 15 figures. See shorter companion paper arXiv:1502.04135 (same title and authors) for a short version omitting technical details. v2: Small but important fix to wording of abstract. v3: Simplified and shortened some parts of the proof; minor fixes to other parts. Now only 127 pages, 55 theorems etc., 10 figures. v4: Minor updates to introductio

The Complexity of Relating Quantum Channels to Master Equations

Completely positive, trace preserving (CPT) maps and Lindblad master equations are both widely used to describe the dynamics of open quantum systems. The connection between these two descriptions is a classic topic in mathematical physics. One direction was solved by the now famous result due to Lindblad, Kossakowski Gorini and Sudarshan, who gave a complete characterisation of the master equations that generate completely positive semi-groups. However, the other direction has remained open: given a CPT map, is there a Lindblad master equation that generates it (and if so, can we find it's form)? This is sometimes known as the Markovianity problem. Physically, it is asking how one can deduce underlying physical processes from experimental observations. We give a complexity theoretic answer to this problem: it is NP-hard. We also give an explicit algorithm that reduces the problem to integer semi-definite programming, a well-known NP problem. Together, these results imply that resolving the question of which CPT maps can be generated by master equations is tantamount to solving P=NP: any efficiently computable criterion for Markovianity would imply P=NP; whereas a proof that P=NP would imply that our algorithm already gives an efficiently computable criterion. Thus, unless P does equal NP, there cannot exist any simple criterion for determining when a CPT map has a master equation description. However, we also show that if the system dimension is fixed (relevant for current quantum process tomography experiments), then our algorithm scales efficiently in the required precision, allowing an underlying Lindblad master equation to be determined efficiently from even a single snapshot in this case. Our work also leads to similar complexity-theoretic answers to a related long-standing open problem in probability theory.Comment: V1: 43 pages, single column, 8 figures. V2: titled changed; added proof-overview and accompanying figure; 50 pages, single column, 9 figure

Black hole thermodynamics from simulations of lattice Yang-Mills theory

We report on lattice simulations of 16 supercharge SU(N) Yang-Mills quantum mechanics in the 't Hooft limit. Maldacena duality conjectures that in this limit the theory is dual to IIA string theory, and in particular that the behavior of the thermal theory at low temperature is equivalent to that of certain black holes in IIA supergravity. Our simulations probe the low temperature regime for N <= 5 and the intermediate and high temperature regimes for N <= 12. We observe 't Hooft scaling and at low temperatures our results are consistent with the dual black hole prediction. The intermediate temperature range is dual to the Horowitz-Polchinski correspondence region, and our results are consistent with smooth behavior there. We include the Pfaffian phase arising from the fermions in our calculations where appropriate.Comment: 4 pages, 4 figure

Integrating effects of species composition and soil properties to predict shifts in montane forest carbon-water relations.

This study was designed to address a major source of uncertainty pertaining to coupled carbon-water cycles in montane forest ecosystems. The Sierra Nevada of California was used as a model system to investigate connections between the physiological performance of trees and landscape patterns of forest carbon and water use. The intrinsic water-use efficiency (iWUE)-an index of CO2 fixed per unit of potential water lost via transpiration-of nine dominant species was determined in replicated transects along an ∼1,500-m elevation gradient, spanning a broad range of climatic conditions and soils derived from three different parent materials. Stable isotope ratios of carbon and oxygen measured at the leaf level were combined with field-based and remotely sensed metrics of stand productivity, revealing that variation in iWUE depends primarily on leaf traits (∼24% of the variability), followed by stand productivity (∼16% of the variability), climatic regime (∼13% of the variability), and soil development (∼12% of the variability). Significant interactions between species composition and soil properties proved useful to predict changes in forest carbon-water relations. On the basis of observed shifts in tree species composition, ongoing since the 1950s and intensified in recent years, an increase in water loss through transpiration (ranging from 10 to 60% depending on parent material) is now expected in mixed conifer forests throughout the region

Evaluation of Three Trap Types and Five Lures for Monitoring \u3ci\u3eHylurgus Ligniperda\u3c/i\u3e (Coleoptera: Scolytidae) and Other Local Scolytids in New York

Hylurgus ligniperda (Coleoptera: Scolytidae) is a pine (Pinus spp.) pest native to Eurasia and northern Africa. In December 2000, an established population of H. ligniperda was discovered in Monroe County, New York. When surveys were initiated to determine the distribution of H. ligniperda, questions arose regarding the most effective trap and lure for survey purposes. We conducted a study in April-May 2001 to compare the effectiveness of commercially available scolytid traps and lures for attracting and capturing H. ligniperda. Traps tested included: 1) 12-unit Lindgren funnel trap, 2) Intercept panel trap, and 3) Theysohn slot-trap. Lures tested included: 1) α-pinene high release (750 mg/day) and ethanol (280 mg/ day), 2) α-pinene low release (300 mg/day) and ethanol, 3) β-pinene high release (2000 mg/day) and ethanol, 4) α-pinene low release, and 5) the “exotic bark beetle lure” [ipsdienol (0.15 mg/day), cis-verbenol (0.35 mg/day), and methylbutenol (10 mg/day)]. All three trap designs captured H. ligniperda, however, the Lindgren funnel trap caught significantly higher numbers. Capture rates of Tomicus piniperda (Coleoptera: Scolytidae) and Hylastes opacus were highest in Lindgren funnel traps; whereas Orthotomicus caelatus collections were highest in Theysohn traps. Capture rates of Ips grandicollis and Xyleborinus saxeseni did not vary significantly among trap types. Behavioral differences among scolytid species such as visual stimuli, flight and landing behavior, and host selection may explain some of these differences. Lures containing α-pinene or β-pinene and ethanol were most attractive to H. ligniperda adults, with ethanol and high-release α-pinene attracting the highest numbers in absolute terms. The exotic bark beetle lure was the least attractive lure to H. ligniperda. Attractiveness of the lures tested varied significantly for other Scolytidae, including Dendroctonus valens, H. opacus, Ips calligraphus, I. grandicollis, I. pini, O. caelatus, T. piniperda, and X. saxeseni. These differences likely were due to variation in lure release rates, host preferences, and/or species-specific pheromone attraction

Diel variation in vertical distribution of an offshore ichthyoplankton community off the Oregon coast

We examined the diel ver-tical distribution, concentration, and community structure of ichthyoplank-ton from a single station 69 km off the central Oregon coast in the northeast Pacific Ocean. The 74 depth-stratified samples yielded 1571 fish larvae from 20 taxa, representing 11 families, and 128 fish eggs from 11 taxa within nine families. Dominant larval taxa were Sebastes spp. (rockfishes), Stenobra-chius leucopsarus (northern lampfish), Tarletonbeania crenularis (blue lan-ternfish), and Lyopsetta exilis (slender sole), and the dominant egg taxa were Sardinops sagax (Pacific sardine), Icichthys lockingtoni (medusafish), and Chauliodus macouni (Pacific viperfish). Larval concentrations generally increased from the surface to 50 m, then decreased with depth. Larval concentrations were higher at night than during the day, and there was evidence of larval diel vertical migration. Depth stratum was the most important factor explaining variability in larval and egg concentrations