The classical-quantum divergence of complexity in modelling spin chains

The minimal memory required to model a given stochastic process - known as the statistical complexity - is a widely adopted quantifier of structure in complexity science. Here, we ask if quantum mechanics can fundamentally change the qualitative behaviour of this measure. We study this question in the context of the classical Ising spin chain. In this system, the statistical complexity is known to grow monotonically with temperature. We evaluate the spin chain's quantum mechanical statistical complexity by explicitly constructing its provably simplest quantum model, and demonstrate that this measure exhibits drastically different behaviour: it rises to a maximum at some finite temperature then tends back towards zero for higher temperatures. This demonstrates how complexity, as captured by the amount of memory required to model a process, can exhibit radically different behaviour when quantum processing is allowed.Comment: 9 pages, 3 figures, comments are welcom

Surveying structural complexity in quantum many-body systems

Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and entanglement alone. Using tools from complexity science, we characterise such structure. We investigate the structural complexities that can be found within the patterns that manifest from the observational data of these systems. In particular, using two prototypical quantum many-body systems as test cases - the one-dimensional quantum Ising and Bose-Hubbard models - we explore how different information-theoretic measures of complexity are able to identify different features of such patterns. This work furthers the understanding of fully-quantum notions of structure and complexity in quantum systems and dynamics.Comment: 9 pages, 5 figure

Spontaneous Interlayer Charge Transfer near the Magnetic Quantum Limit

Experiments reveal that a confined electron system with two equally-populated layers at zero magnetic field can spontaneously break this symmetry through an interlayer charge transfer near the magnetic quantum limit. New fractional quantum Hall states at unusual total filling factors such as \nu = 11/15 (= 1/3 + 2/5) stabilize as signatures that the system deforms itself, at substantial electrostatic energy cost, in order to gain crucial correlation energy by "locking in" separate incompressible liquid phases at unequal fillings in the two layers (e.g., layered 1/3 and 2/5 states in the case of \nu = 11/15).Comment: 4 pages, 4 figures (1 color) included in text. Related papers at http://www.ee.princeton.edu/~hari/papers.htm

Sequence-based analysis of the genus Ruminococcus resolves its phylogeny and reveals strong host association

It has become increasingly clear that the composition of mammalian gut microbial communities is substantially diet driven. These microbiota form intricate mutualisms with their hosts, which have profound implications on overall health. For example, many gut microbes are involved in the conversion of host-ingested dietary polysaccharides into host-usable nutrients. One group of important gut microbial symbionts are bacteria in the genus Ruminococcus. Originally isolated from the bovine rumen, ruminococci have been found in numerous mammalian hosts, including other ruminants, and non-ruminants such as horses, pigs and humans. All ruminococci require fermentable carbohydrates for growth, and their substrate preferences appear to be based on the diet of their particular host. Most ruminococci that have been studied are those capable of degrading cellulose, much less is known about non-cellulolytic non-ruminant-associated species, and even less is known about the environmental distribution of ruminococci as a whole. Here, we capitalized on the wealth of publicly available 16S rRNA gene sequences, genomes and large-scale microbiota studies to both resolve the phylogenetic placement of described species in the genus Ruminococcus, and further demonstrate that this genus has largely unexplored diversity and a staggering host distribution. We present evidence that ruminococci are predominantly associated with herbivores and omnivores, and our data supports the hypothesis that very few ruminococci are found consistently in non-host-associated environments. This study not only helps to resolve the phylogeny of this important genus, but also provides a framework for understanding its distribution in natural systems

Magnetic-Field-Induced Hybridization of Electron Subbands in a Coupled Double Quantum Well

We employ a magnetocapacitance technique to study the spectrum of the soft two-subband (or double-layer) electron system in a parabolic quantum well with a narrow tunnel barrier in the centre. In this system unbalanced by gate depletion, at temperatures T\agt 30 mK we observe two sets of quantum oscillations: one originates from the upper electron subband in the closer-to-the-gate part of the well and the other indicates the existence of common gaps in the spectrum at integer fillings. For the lowest filling factors $\nu=1$ and $\nu=2$, both the common gap presence down to the point of one- to two-subband transition and their non-trivial magnetic field dependences point to magnetic-field-induced hybridization of electron subbands.Comment: Major changes, added one more figure, the latest version to be published in JETP Let

Evidence for a Goldstone Mode in a Double Layer Quantum Hall System

The tunneling conductance between two parallel 2D electron systems has been measured in a regime of strong interlayer Coulomb correlations. At total Landau level filling $\nu_T=1$ the tunnel spectrum changes qualitatively when the boundary separating the compressible phase from the ferromagnetic quantized Hall state is crossed. A huge resonant enhancement replaces the strongly suppressed equilibrium tunneling characteristic of weakly coupled layers. The possible relationship of this enhancement to the Goldstone mode of the broken symmetry ground state is discussed.Comment: 4 pages, 3 figures, 2 minor typeos fixe

Half-Integral Spin-Singlet Quantum Hall Effect

We provide numerical evidence that the ground state of a short range interaction model at $\nu=1/2$ is incompressible and spin-singlet for a wide range of repulsive interactions. Furthermore it is accurately described by a trial wave function studied earlier. For the Coulomb interaction we find that this wave function provides a good description of the lowest lying spin-singlet state, and propose that fractional quantum Hall effect would occur at $\nu=1/2$ if this state became the global ground state.Comment: Latex 13 pages, 3 figures upon reques

Head-on collision of two black holes: comparison of different approaches

A benchmark problem for numerical relativity has been the head-on collision of two black holes starting from the ``Misner initial data,'' a closed form momentarily stationary solution to the constraint equations with an adjustable closeness parameter \mu_0. We show here how an eclectic mixture of approximation methods can provide both an efficient means of determining the time development of the initial data and a good understanding of the physics of the problem. When the Misner data is chosen to correspond to holes initially very close together, a common horizon surrounds both holes and the geometry exterior to the horizon can be treated as a non-spherical perturbation of a single Schwarzschild hole. When the holes are initially well separated the problem can be treated with a different approximation scheme, ``the particle-membrane method.'' For all initial separations, numerical relativity is in principle applicable, but is costly and of uncertain accuracy. We present here a comparison of the different approaches. We compare waveforms, for \ell=2 and \ell=4 radiation, for different values of \mu_0, from the three different approaches to the problem