On null singularities in general relativity
Mihalis Dafermos Princeton University
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Our Lopsided Universe
Marina Cortes Institute for Astrophysics and Space Sciences
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Bosonic particle-correlated states
Zhang Jiang University of New Mexico
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The National Ignition Facility (NIF):Pathway to Energy Security and Physics of the Cosmos
Edward Moses Lawrence Livermore National Laboratory
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Cosmological constraints on complex scalar-field dark matter
Tanja Rindler-Daller University of Michigan–Ann Arbor
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Time, Dynamics, Chaos, and the Brain
Dean Buonomano University of California, Los Angeles
PIRSA:13010117 -
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On null singularities in general relativity
Mihalis Dafermos Princeton University
This talk will discuss the formation, structure and interaction of null singularities for
the Einstein equations, as well as what this all means for the singular boundary
of generic space times within black hole regions. -
Applications of Information Theory in Direct Sum and Direct Product Problems
A fundamental question in complexity theory is how much resource is needed to solve k independent instances of a problem compared to the resource required to solve one instance. Suppose solving one instance of a problem with probability of correctness p, we require c units of some resource in a given model of computation. A direct sum theorem states that in order to compute k independent instances of a problem, it requires k times units of the resource needed to compute one instance. A strong direct product theorem states that, with o(k • c) units of the resource, one can only compute all the k instances correctly with probability exponentially small in k. In this talk, I am going to present some of recent progress on direct sum and direct product theorems in the model of communication complexity and two-prover one-round games with information-theoretic approach. The talk is based on parts of my doctoral work. -
Our Lopsided Universe
Marina Cortes Institute for Astrophysics and Space Sciences
After a short introduction to open inflation and the observed large-scale cosmic microwave anomalies, which have been confirmed by the Planck satellite, I'll argue that the anomalies are naturally explained in the context of a marginally-open, negatively curved universe. I'll look in particular at the dipole power asymmetry, and motivate that this asymmetry can happen if our universe has bubble nucleated in a phase transition during a period of early inflation, and, as a result, has open geometry. Open inflation models, which are motivated by the string landscape and can excite `super-curvature' perturbation modes, can explain the presence of a very-large-scale perturbation, like the one we observe, which leads to a dipole modulation of the power spectrum. I'll provide a specific implementation of the scenario which is compatible with all existing constraints. -
Bosonic particle-correlated states
Zhang Jiang University of New Mexico
Quantum many-body problems are notorious hard. This is partly because the Hilbert space becomes exponentially big with the particle number N. While exact solutions are often considered intractable, numerous approaches have been proposed using approximations. A common trait of these approaches is to use an ansatz such that the number of parameters either does not depend on N or is proportional to N, e.g., the matrix-product state for spin lattices, the BCS wave function for superconductivity, the Laughlin wave function for fractional quantum Hall effects, and the Gross-Pitaecskii theory for BECs. Among them the product ansatz for BECs has precisely predicted many useful properties of Bose gases at ultra-low temperature. As particle-particle correlation becomes important, however, it begins to fail. To capture the quantum correlations, we propose a new
set of states, which constitute a natural generalization of the product-state ansatz. Our state of N=d& times;n identical particles is derived by symmetrizing the n-fold product of a d-particle quantum state. For fixed d, the parameter space of our state does not grow with N. Numerically, we show that our ansatz gives the right description for the ground state and time evolution of the two-site Bose-Hubbard model. -
The Radius of Neutron Stars and the Dense Matter Equation of State
Robert Rutledge McGill University
The equation of state of matter at and above nuclear densities remains a major theoretically uncertain prediction of QCD. Observations of the mass-radius relationship of neutron stars constrain, and can directly measure, the dense matter equation of state. I will discuss how measurements of neutron star radii have already constrained the dEOS, and how future work will directly measure the dEOS, providing an important constraint on models of the strong force. -
The National Ignition Facility (NIF):Pathway to Energy Security and Physics of the Cosmos
Edward Moses Lawrence Livermore National Laboratory
NIF is the world's most energetic laser system capable of producing over 1.8 MJ and 500 TW of ultraviolet light, about 100 times more than any other operating laser of its kind. This talk describes the unprecedented experimental capabilities of NIF, its role in fundamental science, the pathway to achieving fusion ignition and energy security missions, and the status of progress in these areas. -
Towards a 1/c Expansion in 2d Conformal Field Theory
I will describe progress in deriving 3d gravity directly from 2d conformal field theory at large central charge 'c'. In a large class of CFTs, using general arguments like modular invariance, crossing symmetry, and the OPE expansion, the spectrum, the entanglement entropy, and certain partition functions can be computed to leading order in a 1/c expansion. The results agree with universal features of 3d gravity required by black hole thermodynamics and the Ryu-Takayanagi formula; furthermore, the relevant 3d geometries appear automatically from CFT calculations in this regime. -
Cosmological constraints on complex scalar-field dark matter
Tanja Rindler-Daller University of Michigan–Ann Arbor
The nature of dark matter is a fundamental problem in cosmology and particle physics. Many particle candidates have been devised over the course of the last decades, and are still at stake to be soon discovered or rejected. However, astronomical observations, in conjunction with the phenomenological efforts in astrophysical modeling, as well as in particle theories to explain them, have helped to pin down several key properties which any successful candidate has to have. In this talk, I will explore the possibility that dark matter is described by a complex scalar field (SFDM), while the other cosmic components are treated in the usual way, assuming a cosmological constant for the dark energy. We will see that the background evolution of a Universe with SFDM and a cosmological constant (LSFDM) complies with the concordance LCDM model, if the model parameters of the SFDM Lagrangian, mass and repulsive 2-particle self-interaction coupling strength, are properly constrained by observations of the cosmic microwave background and Big Bang nucleosynthesis (BBN). However, not only does LSFDM lead to non-standard expansion histories prior to BBN, it also exemplifies differences at small scales, which could help to resolve the discrepancies found between LCDM and certain galaxy observations. I will highlight the differences between complex SFDM and dark matter described by real fields, as for instance axion-like particles. If time permits, I will also talk about possible implementations of SFDM in the very early Universe, in the wake of its inflationary phase. -
Black hole entropy and the case for self-dual loop quantum gravity
By focusing on aspects of black hole thermodynamics, I will present some evidences supporting the unexpected role of the complex self-dual variables in quantum gravity. This will also be the occasion of revisiting some aspects of three-dimensional gravity, and in particular the link between the BTZ black hole and the Turaev-Viro state sum model. Also the information on the website for next week needs to be modified: We will not have a seminar on Thursday (as Thursday is PI day). Instead, we will have the seminar on Wednesday, but actually would prefer a different time, namely 3.30 pm. -
Time, Dynamics, Chaos, and the Brain
Dean Buonomano University of California, Los Angeles
PIRSA:13010117Time poses a fundamental problem in neuroscience, in part, because at its core the brain is a prediction machine: the brain evolved to allow animals to anticipate, adapt, and prepare for future events. To accomplish this function the brain tells time on scales spanning 12 orders of magnitude. In contrast to most man made clocks that share a very simply underlying principle-counting the "tics" of an oscillator-evolution has devised many different solutions to the problem of telling time. On the scale of milliseconds and seconds experimental and computational evidence suggests that the brain relies on neural dynamics to tell time. For this strategy to work two conditions have to be met: the states of the neural network must evolve in a nonrepeating pattern over the relevant interval, and the sequence of states must be reproducible every time the system is reengaged. Recurrently connected networks of neurons can generate rich dynamics, but a long standing challenge is that the regimes that create computationally powerful dynamics are chaotic-and thus cannot generate reproducible patterns. We have recently demonstrated that by tuning the weights (the coupling coefficients) between the units of artificial neural networks it is possible to generate locally stable trajectories embedded within chaotic attractors. These stable patterns function as "dynamic attractors" and can be used to encode and tell time. They also exhibit a novel feature characteristic of biological systems: the ability to autonomously "return" to the pattern being generated in the face of perturbations. -
Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
Carlo Meneghelli University of Oxford
In arXiv:0908.4052, Nekrasov and Shatashvili pointed out that the N=2 instanton partition function in a special limit of the Omega-deformation parameters is characterized by certain thermodynamic Bethe ansatz (TBA) like equations.In this talk I will present an explicit derivation of this fact as well as generalizations to quiver gauge theories. The TBA equations derived entirely within gauge theory have been proposed to encode the spectrum of a large class of quantum integrable systems. I will conclude with some remarks on this correspondence. -
New light on 21cm intensity fluctuations from the dark ages
Fluctuations of the 21 cm brightness temperature before the formation of the first stars hold the promise of becoming a high-precision cosmological probe in the future. The growth of over densities is very well described by perturbation theory at that epoch and the signal can in principle be predicted to arbitrary accuracy for given cosmological parameters. Recently, Tseliakhovich and Hirata pointed out a previously neglected and important physical effect, due to the fact that baryons and cold dark matter (CDM) have supersonic relative velocities after recombination. This relative velocity suppresses the growth of matter fluctuations on scales k∼10−10^3 Mpc^−1. In addition, the amplitude of the small-scale power spectrum is modulated on the large scales over which the relative velocity varies, corresponding to k∼0.005−1 Mpc^−1. In this talk, I will describe the effect of the relative velocity on 21 cm brightness temperature fluctuations from redshifts z≥30. I will show that the 21 cm power spectrum is affected on most scales. On small scales, the signal is typically suppressed several tens of percent, except for extremely small scales (k≳2000 Mpc−1) for which the fluctuations are boosted by resonant excitation of acoustic waves. On large scales, 21 cm fluctuations are enhanced due to the non-linear dependence of the brightness temperature on the underlying gas density and temperature. The enhancement of the 21 cm power spectrum is of a few percent at k∼0.1 Mpc−1 and up to tens of percent at k≲0.005 Mpc−1, for standard ΛCDM cosmology. In principle this effect allows to probe the small-scale matter power spectrum not only through a measurement of small angular scales but also through its effect on large angular scales.