Classical GR as a topological theory with linear constraints

We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints. Our analysis clarifies how the discrete constructions of spin foam models are related to a continuum theory with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010 (ERE2010, Granada, Spain

Classical GR as a topological theory with linear constraints

We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints. Our analysis clarifies how the discrete constructions of spin foam models are related to a continuum theory with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010 (ERE2010, Granada, Spain

Classical GR as a topological theory with linear constraints

We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints. Our analysis clarifies how the discrete constructions of spin foam models are related to a continuum theory with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010 (ERE2010, Granada, Spain

Cosmological evolution as squeezing: a toy model for group field cosmology

We present a simple model of quantum cosmology based on the group field theory (GFT) approach to quantum gravity. The model is formulated on a subspace of the GFT Fock space for the quanta of geometry, with a fixed volume per quantum. In this Hilbert space, cosmological expansion corresponds to the generation of new quanta. Our main insight is that the evolution of a flat Friedmann–Lemaître–Robertson–Walker universe with a massless scalar field can be described on this Hilbert space as squeezing, familiar from quantum optics. As in GFT cosmology, we find that the three-volume satisfies an effective Friedmann equation similar to the one of loop quantum cosmology, connecting the classical contracting and expanding solutions by a quantum bounce. The only free parameter in the model is identified with Newton’s constant. We also comment on the possible topological interpretation of our squeezed states. This paper can serve as an introduction into the main ideas of GFT cosmology without requiring the full GFT formalism; our results can also motivate new developments in GFT and its cosmological application

Time-encoding analog-to-digital converters : bridging the analog gap to advanced digital CMOS? Part 2: architectures and circuits

The scaling of CMOS technology deep into the nanometer range has created challenges for the design of highperformance analog ICs: they remain large in area and power consumption in spite of process scaling. Analog circuits based on time encoding [1], [2], where the signal information is encoded in the waveform transitions instead of its amplitude, have been developed to overcome these issues. While part one of this overview article [3] presented the basic principles of time encoding, this follow-up article describes and compares the main time-encoding architectures for analog-to-digital converters (ADCs) and discusses the corresponding design challenges of the circuit blocks. The focus is on structures that avoid, as much as possible, the use of traditional analog blocks like operational amplifiers (opamps) or comparators but instead use digital circuitry, ring oscillators, flip-flops, counters, an so on. Our overview of the state of the art will show that these circuits can achieve excellent performance. The obvious benefit of this highly digital approach to realizing analog functionality is that the resulting circuits are small in area and more compatible with CMOS process scaling. The approach also allows for the easy integration of these analog functions in systems on chip operating at "digital" supply voltages as low as 1V and lower. A large part of the design process can also be embedded in a standard digital synthesis flow

Time-encoding analog-to-digital converters : bridging the analog gap to advanced digital CMOS : part 1: basic principles

The scaling of CMOS technology deep into the nanometer range has created challenges for the design of highperformance analog ICs. The shrinking supply voltage and presence of mismatch and noise restrain the dynamic range, causing analog circuits to be large in area and have a high power consumption in spite of the process scaling. Analog circuits based on time encoding [1], [2] and hybrid analog/digital signal processing [3] have been developed to overcome these issues. Realizing analog circuit functionality with highly digital circuits results in more scalable design solutions that can achieve excellent performance. This article reviews the basic principles of time encoding applied, in particular, to analog-to-digital converters (ADCs) based on voltage-controlled oscillators (VCOs), one of the most successful time-encoding techniques to date

Efficient offline outer/inner DAC mismatch calibration in wideband ΔΣ ADCs

Distortion due to feedback DAC mismatch is a key limitation in Delta Sigma ADCs for wideband wireless communications. This article presents an efficient frequency-domain mask-based offline mismatch calibration method of both the outer DAC and the inner DACs in a Delta Sigma ADC. The test stimulus for the calibration is a two-tone signal near the band edge. To avoid the need for high-performance signal generation, a frequency mask is applied to void the stimulus signal and its phase noise. In this way, the method is robust against distortion and jitter in the stimulus signal, which therefore could be combined from two low-quality signal generators. The two-tone band-edge signal has the additional benefit that the number of needed samples of the excitation signal is very modest because as many intermodulations as possible contribute to the calculation of the mismatch errors of the DACs. Experimental results confirming the calibration method are obtained from a prototype chip, designed for an 85MHz signal bandwidth in 28nm CMOS technology. A two-tone stimulus around 78 MHz is applied to calculate the mismatch of the outer DAC and the inner DAC with only 68K samples. With the DACs calibrated, an SFDR improvement of 28.1 dB is achieved for a single-tone input at 5 MHz, while for a two-tone input around 71 MHz, the IM3 is improved from -63.6 dBc to below the noise floor (<-94.1 dBc). This illustrates the effectiveness of the approach

Carbonaceous molecules in the oxygen-rich circumstellar environment of binary post-AGB stars: C_{60} fullerenes and polycyclic aromatic hydrocarbons

Context. The circumstellar environment of evolved stars is generally rich in molecular gas and dust. Typically, the entire environment is either oxygen-rich or carbon-rich, depending on the evolution of the central star. Aims. In this paper we discuss three evolved disc sources with evidence of atypical emission lines in their infrared spectra. The stars were taken from a larger sample of post-AGB binaries for which we have Spitzer infrared spectra, characterised by the presence of a stable oxygen-rich circumbinary disc. Our previous studies have shown that the infrared spectra of post-AGB disc sources are dominated by silicate dust emission, often with an extremely high crystallinity fraction. However, the three sources described here are selected because they show a peculiar molecular chemistry. Methods. Using Spitzer infrared spectroscopy, we study in detail the peculiar mineralogy of the three sample stars. Using the observed emission features, we identify the different observed dust, molecular and gas species. Results. The infrared spectra show emission features due to various oxygen-rich dust components, as well as CO2 gas. All three sources show the strong infrared bands generally ascribed to polycyclic aromatic hydrocarbons. Furthermore, two sample sources show C60 fullerene bands. Conclusions. Even though the majority of post-AGB disc sources are dominated by silicate dust in their circumstellar environment, we do find evidence that, for some sources at least, additional processing must occur to explain the presence of large carbonaceous molecules. There is evidence that some of these sources are still oxygen-rich, which makes the detection of these molecules even more surprising.Comment: Accepted for publication in Astronomy and Astrophysics, 10 pages, 7 figure