Classical evolution of fractal measures generated by a scalar field on the lattice

We investigate the classical evolution of a $\phi^4$ scalar field theory, using in the initial state random field configurations possessing a fractal measure expressed by a non-integer mass dimension. These configurations resemble the equilibrium state of a critical scalar condensate. The measures of the initial fractal behavior vary in time following the mean field motion. We show that the remnants of the original fractal geometry survive and leave an imprint in the system time averaged observables, even for large times compared to the approximate oscillation period of the mean field, determined by the model parameters. This behavior becomes more transparent in the evolution of a deterministic Cantor-like scalar field configuration. We extend our study to the case of two interacting scalar fields, and we find qualitatively similar results. Therefore, our analysis indicates that the geometrical properties of a critical system initially at equilibrium could sustain for several periods of the field oscillations in the phase of non-equilibrium evolution.Comment: 13 pages, 13 figures, version published at Int. J. Mod. Phys.

Exact Flow Equations and the U(1)-Problem

The effective action of a SU(N)-gauge theory coupled to fermions is evaluated at a large infrared cut-off scale k within the path integral approach. The gauge field measure includes topologically non-trivial configurations (instantons). Due to the explicit infrared regularisation there are no gauge field zero modes. The Dirac operator of instanton configurations shows a zero mode even after the infrared regularisation, which leads to U_A(1)-violating terms in the effective action. These terms are calculated in the limit of large scales k.Comment: 22 pages, latex, no figures, with stylistic changes and some arguments streamlined, typos corrected, References added, to appear in Phys. Rev.

Chronic neural probe for simultaneous recording of single-unit, multi-unit, and local field potential activity from multiple brain sites

Drug resistant focal epilepsy can be treated by resecting the epileptic focus requiring a precise focus localization using stereoelectroencephalography (SEEG) probes. As commercial SEEG probes offer only a limited spatial resolution, probes of higher channel count and design freedom enabling the incorporation of macro and microelectrodes would help increasing spatial resolution and thus open new perspectives for investigating mechanisms underlying focal epilepsy and its treatment. This work describes a new fabrication process for SEEG probes with materials and dimensions similar to clinical probes enabling recording single neuron activity at high spatial resolution. Polyimide is used as a biocompatible flexible substrate into which platinum electrodes and leads are... The resulting probe features match those of clinically approved devices. Tests in saline solution confirmed the probe stability and functionality. Probes were implanted into the brain of one monkey (Macaca mulatta), trained to perform different motor tasks. Suitable configurations including up to 128 electrode sites allow the recording of task-related neuronal signals. Probes with 32 and 64 electrode sites were implanted in the posterior parietal cortex. Local field potentials and multi-unit activity were recorded as early as one hour after implantation. Stable single-unit activity was achieved for up to 26 days after implantation of a 64-channel probe. All recorded signals showed modulation during task execution. With the novel probes it is possible to record stable biologically relevant data over a time span exceeding the usual time needed for epileptic focus localization in human patients. This is the first time that single units are recorded along cylindrical polyimide probes chronically implanted 22 mm deep into the brain of a monkey, which suggests the potential usefulness of this probe for human applications

The beta functions of a scalar theory coupled to gravity

We study a scalar field theory coupled to gravity on a flat background, below Planck's energy. Einstein's theory is treated as an effective field theory. Within the context of Wilson's renormalization group, we compute gravitational corrections to the beta functions and the anomalous dimension of the scalar field, taking into account threshold effects.Comment: 13 pages, plainTe

Multivalued Fields on the Complex Plane and Conformal Field Theories

In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simple $b-c$ systems and scalar fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the conformal blocks can be explicitly solved. Besides of the fact that one obtains in this way an entire class of theories in which the operators obey a nonstandard statistics, these systems are interesting in exploring the connection between statistics and curved space-times, at least in the two dimensional case.Comment: (revised version), 30 pages + one figure (not included), (requires harvmac.tex), LMU-TPW 92-1

Exact and Truncated Dynamics in Nonequilibrium Field Theory

Nonperturbative dynamics of quantum fields out of equilibrium is often described by the time evolution of a hierarchy of correlation functions, using approximation methods such as Hartree, large N, and nPI-effective action techniques. These truncation schemes can be implemented equally well in a classical statistical system, where results can be tested by comparison with the complete nonlinear evolution obtained by numerical methods. For a 1+1 dimensional scalar field we find that the early-time behaviour is reproduced qualitatively by the Hartree dynamics. The inclusion of direct scattering improves this to the quantitative level. We show that the emergence of nonthermal temperature profiles at intermediate times can be understood in terms of the fixed points of the evolution equations in the Hartree approximation. The form of the profile depends explicitly on the initial ensemble. While the truncated evolution equations do not seem to be able to get away from the fixed point, the full nonlinear evolution shows thermalization with a (surprisingly) slow relaxation.Comment: 30 pages with 12 eps figures, minor changes; to appear in Phys.Rev.

Caldera collapse and tectonics along the Main Ethiopian Rift: Reviewing possible relationships

The Main Ethiopian Rift (MER) represents an area where volcanism and tectonics interact to create closely linked volcano-tectonic features. This linkage is paramount in the axial portion of the rift, where magmatic segments localize several large peralkaline eruptive centres. Many of them evolved into caldera collapse (the best preserved of which are younger than ${<}1~\mathrm{Ma}$) generating large ignimbrites and registering the interaction between magmatism and tectonics along the MER. In this work we review the structure of the main collapsed calderas along the axial portion of the MER, to summarize the relationships between volcanism and tectonics proposed in the literature explaining their structural evolution. By doing this, we infer that tectonics had a strong influence in controlling the elongation of the majority of examined calderas. This control was induced by reactivation of inherited crustal fabrics or by stretching of the magma reservoirs under the MER regional stress field

Large N Quantum Time Evolution Beyond Leading Order

For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting classical evolution. Explicit expressions are given for next-to-leading order, and next-to-next-to-leading order time evolution. The large N limit of N-component vector models, and the usual semiclassical limit of point particle quantum mechanics are used as concrete examples. Our formulation directly exploits the appropriate group structure which underlies the construction of suitable coherent states and generates the classical phase space. We discuss the growth of truncation error with time, and argue that truncations of the large-N evolution equations are generically expected to be useful only for times short compared to a ``decoherence'' time which scales like N^{1/2}.Comment: 36 pages, 2 eps figures, latex, uses revtex, epsfig, float