Bounds on Information Propagation in Disordered Quantum Spin Chains

We investigate the propagation of information through the disordered XY model. We find, with a probability that increases with the size of the system, that all correlations, both classical and quantum, are suppressed outside of an effective lightcone whose radius grows at most polylogarithmically with |t|.Comment: 4 pages, pdflatex, 1 pdf figure. Corrected the bound for the localised propagator and quantified the probability it bound occur

Nonlinear states and dynamics in a synthetic frequency dimension

Recent advances in the study of synthetic dimensions revealed a possibility to employ the frequency space as an additional degree of freedom which allows for investigating and exploiting higher-dimensional phenomena in a priori low-dimensional systems. However, the influence of nonlinear effects on the synthetic frequency dimensions was studied only under significant restrictions. In the present paper, we develop a generalized mean-field model for the optical field envelope inside a single driven-dissipative resonator with quadratic and cubic nonlinearities, whose frequencies are coupled via an electro-optical resonant temporal modulation. The leading order equation takes the form of driven Gross-Pitaevskii equation with a cosine potential. We numerically investigate the nonlinear dynamics in such microring resonator with a synthetic frequency dimension in the regime where parametric frequency conversion occurs. In the case of anomalous dispersion, we find that the presence of electro-optical mode coupling confines and stabilizes the chaotic modulation instability region. This leads to the appearance of a novel type of stable coherent structures which emerge in the synthetic space with restored translational symmetry, in a region of parameters where conventionally only chaotic modulation instability states exist. This structure appears in the center of the synthetic band and, therefore, is referred to as Band Soliton. Finally, we extend our results to the case of multiple modulation frequencies with controllable relative phases creating synthetic lattices with nontrivial geometry. We show that an asymmetric synthetic band leads to the coexistence of chaotic and coherent states of the electromagnetic field inside the cavity i.e. dynamics that can be interpreted as chimera-like states. Recently developed $\chi^{(2)}$ microresonators can open the way to experimentally explore our findings.Comment: 12 pages, 5 figures; figure 4 and typos correcte

Astrophysical Fluid Dynamics via Direct Statistical Simulation

In this paper we introduce the concept of Direct Statistical Simulation (DSS) for astrophysical flows. This technique may be appropriate for problems in astrophysical fluids where the instantaneous dynamics of the flows are of secondary importance to their statistical properties. We give examples of such problems including mixing and transport in planets, stars and disks. The method is described for a general set of evolution equations, before we consider the specific case of a spectral method optimised for problems on a spherical surface. The method is illustrated for the simplest non-trivial example of hydrodynamics and MHD on a rotating spherical surface. We then discuss possible extensions of the method both in terms of computational methods and the range of astrophysical problems that are of interest.Comment: 26 pages, 11 figures, added clarifying remarks and references, and corrected typos. This version is accepted for publication in The Astrophysical Journa

Entanglement Witnesses for Graph States: General Theory and Examples

We present a general theory for the construction of witnesses that detect genuine multipartite entanglement in graph states. First, we present explicit witnesses for all graph states of up to six qubits which are better than all criteria so far. Therefore, lower fidelities are required in experiments that aim at the preparation of graph states. Building on these results, we develop analytical methods to construct two different types of entanglement witnesses for general graph states. For many classes of states, these operators exhibit white noise tolerances that converge to one when increasing the number of particles. We illustrate our approach for states such as the linear and the 2D cluster state. Finally, we study an entanglement monotone motivated by our approach for graph states.Comment: 12 pages + appendix, 7 figure

Bacteriophage and their potential roles in the human oral cavity.

The human oral cavity provides the perfect portal of entry for viruses and bacteria in the environment to access new hosts. Hence, the oral cavity is one of the most densely populated habitats of the human body containing some 6 billion bacteria and potentially 35 times that many viruses. The role of these viral communities remains unclear; however, many are bacteriophage that may have active roles in shaping the ecology of oral bacterial communities. Other implications for the presence of such vast oral phage communities include accelerating the molecular diversity of their bacterial hosts as both host and phage mutate to gain evolutionary advantages. Additional roles include the acquisitions of new gene functions through lysogenic conversions that may provide selective advantages to host bacteria in response to antibiotics or other types of disturbances, and protection of the human host from invading pathogens by binding to and preventing pathogens from crossing oral mucosal barriers. Recent evidence suggests that phage may be more involved in periodontal diseases than were previously thought, as their compositions in the subgingival crevice in moderate to severe periodontitis are known to be significantly altered. However, it is unclear to what extent they contribute to dysbiosis or the transition of the microbial community into a state promoting oral disease. Bacteriophage communities are distinct in saliva compared to sub- and supragingival areas, suggesting that different oral biogeographic niches have unique phage ecology shaping their bacterial biota. In this review, we summarize what is known about phage communities in the oral cavity, the possible contributions of phage in shaping oral bacterial ecology, and the risks to public health oral phage may pose through their potential to spread antibiotic resistance gene functions to close contacts

Approximate locality for quantum systems on graphs

In this Letter we make progress on a longstanding open problem of Aaronson and Ambainis [Theory of Computing 1, 47 (2005)]: we show that if A is the adjacency matrix of a sufficiently sparse low-dimensional graph then the unitary operator e^{itA} can be approximated by a unitary operator U(t) whose sparsity pattern is exactly that of a low-dimensional graph which gets more dense as |t| increases. Secondly, we show that if U is a sparse unitary operator with a gap \Delta in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/\Delta increases. These two results can be interpreted as a way to convert between local continuous-time and local discrete-time processes. As an example we show that the discrete-time coined quantum walk can be realised as an approximately local continuous-time quantum walk. Finally, we use our construction to provide a definition for a fractional quantum fourier transform.Comment: 5 pages, 2 figures, corrected typ

Transcriptome analysis of bacteriophage communities in periodontal health and disease.

BackgroundThe role of viruses as members of the human microbiome has gained broader attention with the discovery that human body surfaces are inhabited by sizeable viral communities. The majority of the viruses identified in these communities have been bacteriophages that predate upon cellular microbiota rather than the human host. Phages have the capacity to lyse their hosts or provide them with selective advantages through lysogenic conversion, which could help determine the structure of co-existing bacterial communities. Because conditions such as periodontitis are associated with altered bacterial biota, phage mediated perturbations of bacterial communities have been hypothesized to play a role in promoting periodontal disease. Oral phage communities also differ significantly between periodontal health and disease, but the gene expression of oral phage communities has not been previously examined.ResultsHere, we provide the first report of gene expression profiles from the oral bacteriophage community using RNA sequencing, and find that oral phages are more highly expressed in subjects with relative periodontal health. While lysins were highly expressed, the high proportion of integrases expressed suggests that prophages may account for a considerable proportion of oral phage gene expression. Many of the transcriptome reads matched phages found in the oral cavities of the subjects studied, indicating that phages may account for a substantial proportion of oral gene expression. Reads homologous to siphoviruses that infect Firmicutes were amongst the most prevalent transcriptome reads identified in both periodontal health and disease. Some genes from the phage lytic module were significantly more highly expressed in subjects with periodontal disease, suggesting that periodontitis may favor the expression of some lytic phages.ConclusionsAs we explore the contributions of viruses to the human microbiome, the data presented here suggest varying expression of bacteriophage communities in oral health and disease

On single-photon quantum key distribution in the presence of loss

We investigate two-way and one-way single-photon quantum key distribution (QKD) protocols in the presence of loss introduced by the quantum channel. Our analysis is based on a simple precondition for secure QKD in each case. In particular, the legitimate users need to prove that there exists no separable state (in the case of two-way QKD), or that there exists no quantum state having a symmetric extension (one-way QKD), that is compatible with the available measurements results. We show that both criteria can be formulated as a convex optimisation problem known as a semidefinite program, which can be efficiently solved. Moreover, we prove that the solution to the dual optimisation corresponds to the evaluation of an optimal witness operator that belongs to the minimal verification set of them for the given two-way (or one-way) QKD protocol. A positive expectation value of this optimal witness operator states that no secret key can be distilled from the available measurements results. We apply such analysis to several well-known single-photon QKD protocols under losses.Comment: 14 pages, 6 figure

A Multiscale Dynamo Model Driven by Quasi-geostrophic Convection

A convection-driven multiscale dynamo model is developed in the limit of low Rossby number for the plane layer geometry in which the gravity and rotation vectors are aligned. The small-scale fluctuating dynamics are described by a magnetically-modified quasi-geostrophic equation set, and the large-scale mean dynamics are governed by a diagnostic thermal wind balance. The model utilizes three timescales that respectively characterize the convective timescale, the large-scale magnetic evolution timescale, and the large-scale thermal evolution timescale. Distinct equations are derived for the cases of order one and low magnetic Prandtl number. It is shown that the low magnetic Prandtl number model is characterized by a magnetic to kinetic energy ratio that is asymptotically large, with ohmic dissipation dominating viscous dissipation on the large-scales. For the order one magnetic Prandtl number model the magnetic and kinetic energies are equipartitioned and both ohmic and viscous dissipation are weak on the large-scales; large-scale ohmic dissipation occurs in thin magnetic boundary layers adjacent to the horizontal boundaries. For both magnetic Prandtl number cases the Elsasser number is small since the Lorentz force does not enter the leading order force balance. The new models can be considered fully nonlinear, generalized versions of the dynamo model originally developed by Childress and Soward [Phys. Rev. Lett., 29, p.837, 1972], and provide a new theoretical framework for understanding the dynamics of convection-driven dynamos in regimes that are only just becoming accessible to direct numerical simulations