Markov quantum fields on a manifold

We study scalar quantum field theory on a compact manifold. The free theory is defined in terms of functional integrals. For positive mass it is shown to have the Markov property in the sense of Nelson. This property is used to establish a reflection positivity result when the manifold has a reflection symmetry. In dimension d=2 we use the Markov property to establish a sewing operation for manifolds with boundary circles. Also in d=2 the Markov property is proved for interacting fields.Comment: 14 pages, 1 figure, Late

Wilson Line Picture of Levin-Wen Partition Functions

Levin and Wen [Phys. Rev. B 71, 045110 (2005)] have recently given a lattice Hamiltonian description of doubled Chern-Simons theories. We relate the partition function of these theories to an expectation of Wilson loops that form a link in 2+1 dimensional spacetime known in the mathematical literature as Chain-Mail. This geometric construction gives physical interpretation of the Levin-Wen Hilbert space and Hamiltonian, its topological invariance, exactness under coarse-graining, and how two opposite chirality sectors of the doubled theory arise.Comment: Final published version; Appendix adde

Stimulus-invariant processing and spectrotemporal reverse correlation in primary auditory cortex

The spectrotemporal receptive field (STRF) provides a versatile and integrated, spectral and temporal, functional characterization of single cells in primary auditory cortex (AI). In this paper, we explore the origin of, and relationship between, different ways of measuring and analyzing an STRF. We demonstrate that STRFs measured using a spectrotemporally diverse array of broadband stimuli -- such as dynamic ripples, spectrotemporally white noise, and temporally orthogonal ripple combinations (TORCs) -- are very similar, confirming earlier findings that the STRF is a robust linear descriptor of the cell. We also present a new deterministic analysis framework that employs the Fourier series to describe the spectrotemporal modulations contained in the stimuli and responses. Additional insights into the STRF measurements, including the nature and interpretation of measurement errors, is presented using the Fourier transform, coupled to singular-value decomposition (SVD), and variability analyses including bootstrap. The results promote the utility of the STRF as a core functional descriptor of neurons in AI.Comment: 42 pages, 8 Figures; to appear in Journal of Computational Neuroscienc

Variation of Molecular Line Ratios and Cloud Properties in the Arp 299 Galaxy Merger

High resolution observations of 12CO (2.''3), 13CO (3.''9), and HCN (5.''4) J=1--0 in the galaxy merger Arp 299 (IC 694 and NGC 3690) show the line ratios vary dramatically across the system. The 12CO/13CO ratio is unusually large, 60 +- 15, at the IC 694 nucleus, where 12CO emission is very strong, and much smaller, 10 +- 3, in the southern extended disk of that galaxy. Elsewhere, the 12CO/13CO line ratio is 5-20, typical of spiral galaxies. The line ratio variation in the overlap between the two galaxies is smaller, ranging from 10 +- 3 in the east to 20 +- 4 in the west. The 12CO/HCN line ratio also varies across Arp 299, although to a lesser degree. HCN emission is bright towards each galaxy nucleus and in the extranuclear region of active star formation; it was not detected in the IC 694 disk, or the eastern part of the overlap region, leading to lower limits of 25 and 20 respectively. By contrast, at the nuclei of IC 694 and NGC 3690 the ratios are 9 +- 1 and 14 +- 3 respectively. In the western part of the overlap region it is 11 +- 3.Comment: 16 pages, 4 postscript figures, to appear in ApJ Letter

Identification of criticality in neuronal avalanches: II. A theoretical and empirical investigation of the Driven case

The observation of apparent power laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a separation of timescales is thought to be crucial for the observation of power-law dynamics and computational models are often constructed with this property. However, this is not necessarily a characteristic of physiological neural networks—external input does not only occur when the network is at rest/a steady state. In this paper we study a simple neuronal network model driven by a continuous external input (i.e. the model does not have an explicit separation of timescales from seeding the system only when in the quiescent state) and analytically tuned to operate in the region of a critical state (it reaches the critical regime exactly in the absence of input—the case studied in the companion paper to this article). The system displays avalanche dynamics in the form of cascades of neuronal firing separated by periods of silence. We observe partial scale-free behaviour in the distribution of avalanche size for low levels of external input. We analytically derive the distributions of waiting times and investigate their temporal behaviour in relation to different levels of external input, showing that the system’s dynamics can exhibit partial long-range temporal correlations. We further show that as the system approaches the critical state by two alternative ‘routes’, different markers of criticality (partial scale-free behaviour and long-range temporal correlations) are displayed. This suggests that signatures of criticality exhibited by a particular system in close proximity to a critical state are dependent on the region in parameter space at which the system (currently) resides

Crossover from Conserving to Lossy Transport in Circular Random Matrix Ensembles

In a quantum dot with three leads the transmission matrix t_{12} between two of these leads is a truncation of a unitary scattering matrix S, which we treat as random. As the number of channels in the third lead is increased, the constraints from the symmetry of S become less stringent and t_{12} becomes closer to a matrix of complex Gaussian random numbers with no constraints. We consider the distribution of the singular values of t_{12}, which is related to a number of physical quantities. Changing the number of channels in the third lead corresponds to increasing the amount of loss in the system (and is distinct from prior uses of a third lead to model dephasing)

Identification of criticality in neuronal avalanches: I. A theoretical investigation of the non-driven case

In this paper, we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate how they should perform in a finite-size system. By calculating the exact distribution of avalanche sizes, we are able to show that, over a limited range of avalanche sizes which we precisely identify, the distribution has scale free properties but is not a power law. This suggests that it would be inappropriate to dismiss a system as not being critical purely based on an inability to rigorously fit a power law distribution as has been recently advocated. In assessing whether a system, especially a finite-size one, is critical it is thus important to consider other possible markers. We illustrate one of these by showing the divergence of susceptibility as the critical point of the system is approached. Finally, we provide evidence that power laws may underlie other observables of the system that may be more amenable to robust experimental assessment

Quantization of the scalar field in a static quantum metric

We investigate the Hamiltonian formulation of quantum scalar fields in a static quantum metric. We derive a functional integral formula for the propagator. We show that the quantum metric substantially changes the behaviour of the scalar propagator and the effective Yukawa potential.Comment: Latex, 12 page

Multiwavelength Studies of PSR J1420-6048, a Young Pulsar in the Kookaburra

We present X-ray, radio, and infrared observations of the 68 ms pulsar PSR J1420-6048 and its surrounding nebula, a possible counterpart of the gamma-ray source GeV J1417-6100/3EG J1420-6038. Pulsed X-ray emission at the radio period is marginally detected by ASCA from a source embedded in the hard spectrum X-ray nebula AX J1420.1-6049. At radio wavelengths, the pulsar is found to be strongly linearly and circularly polarized, and the polarization sweep is measured. A comparison of high resolution ATCA radio imaging of the Kookaburra's upper wing (G313.6+0.3), which contains the pulsar and the X-ray nebula, with infrared images suggests the radio emission is partly non-thermal.Comment: 8 pages, 4 figures, to appear in Astrophysical Journal Letter