Electric fields can spontaneously decay via the Schwinger effect, the nucleation of a charged particle-anti particle pair separated by a critical distance $d$. What happens if the available distance is smaller than $d$? Previous work on this question
has produced contradictory results. Here, we study the quantum evolution of electric fields when the field points in a compact direction with circumference $L < d$ using the massive Schwinger model, quantum electrodynamics in one space dimension with massive charged fermions. We uncover a new and previously unknown set of instantons that result in novel physics that disagrees with all previous estimates. In parameter regimes where the field value can be well-defined in the quantum theory, generic initial fields $E$ are in fact stable and do not decay, while initial values that are quantized in half-integer units of the charge $E = (k/2) g$ with $kin mathbb Z$ oscillate in time from $+(k/2) g$ to $-(k/2) g$, with exponentially small probability of ever taking any other value. We verify our results with four distinct techniques: numerically by measuring the decay directly in Lorentzian time on the lattice, numerically using the spectrum of the Hamiltonian, numerically and semi-analytically using the bosonized description of the Schwinger model, and analytically via our instanton estimate.
We study quantum decoherence numerically in a system consisting of a relativistic quantum field theory coupled to a measuring device that is itself coupled to an environment. The measuring device and environment are treated as quantum, non-relativist
ic particles. We solve the Schrodinger equation for the wave function of this tripartite system using exact diagonalization. Although computational limitations on the size of the Hilbert space prevent us from exploring the regime where the device and environment consist of a truly macroscopic number of degrees of freedom, we nevertheless see clear evidence of decoherence: after tracing out the environment, the density matrix describing the system and measuring device evolves quickly towards a matrix that is close to diagonal in a subspace of pointer states.
We define a large new class of conformal primary operators in the ensemble of Brownian loops in two dimensions known as the ``Brownian loop soup, and compute their correlation functions analytically and in closed form. The loop soup is a conformally
invariant statistical ensemble with central charge $c = 2 lambda$, where $lambda > 0$ is the intensity of the soup. Previous work identified exponentials of the layering operator $e^{i beta N(z)}$ as primary operators. Each Brownian loop was assigned $pm 1$ randomly, and $N(z)$ was defined to be the sum of these numbers over all loops that encircle the point $z$. These exponential operators then have conformal dimension ${frac{lambda}{10}}(1 - cos beta)$. Here we generalize this procedure by assigning a more general random value to each loop. The operator $e^{i beta N(z)}$ remains primary with conformal dimension $frac {lambda}{10}(1 - phi(beta))$, where $phi(beta)$ is the characteristic function of the probability distribution used to assign random values to each loop. Using recent results we compute in closed form the exact two-point functions in the upper half-plane and four-point functions in the full plane of this very general class of operators. These correlation functions depend analytically on the parameters $lambda, beta_i, z_i$, and on the characteristic function $phi(beta)$. They satisfy the conformal Ward identities and are crossing symmetric. As in previous work, the conformal block expansion of the four-point function reveals the existence of additional and as-yet uncharacterized conformal primary operators.
The phase of the wave function of charged matter is sensitive to the value of the electric potential, even when the matter never enters any region with non-vanishing electromagnetic fields. Despite its fundamental character, this archetypal electric
Aharonov-Bohm effect has evidently never been observed. We propose an experiment to detect the electric potential through its coupling to the superconducting order parameter. A potential difference between two superconductors will induce a relative phase shift that is observable via the DC Josephson effect even when no electromagnetic fields ever act on the superconductors, and even if the potential difference is later reduced to zero. This is a type of electromagnetic memory effect, and would directly demonstrate the physical significance of the electric potential.
Gravitational-wave astronomy has the potential to substantially advance our knowledge of the cosmos, from the most powerful astrophysical engines to the initial stages of our universe. Gravitational waves also carry information about the nature of bl
ack holes. Here we investigate the potential of gravitational-wave detectors to test a proposal by Bekenstein and Mukhanov that the area of black hole horizons is quantized in units of the Planck area. Our results indicate that this quantization could have a potentially observable effect on the classical gravitational wave signals received by detectors. In particular, we find distorted gravitational-wave echoes in the post-merger waveform describing the inspiral and merger of two black holes. These echoes have a specific frequency content that is characteristic of black hole horizon area quantization.
We argue that near-future detections of gravitational waves from merging black hole binaries can test a long-standing proposal, originally due Bekenstein and Mukhanov, that the areas of black hole horizons are quantized in integer multiples of the Pl
anck area times an $mathcal O(1)$ dimensionless constant $alpha$. This condition quantizes the frequency of radiation that can be absorbed or emitted by a black hole. If this quantization applies to the ring down gravitational radiation emitted immediately after a black hole merger, a single measurement consistent with the predictions of classical general relativity would rule out most or all (depending on the spin of the hole) of the extant proposals in the literature for the value of $alpha$. A measurement of two such events for final black holes with substantially different spins would rule out the proposal for any $alpha$. If the modification of general relativity is confined to the near-horizon region within the holes light ring and does not affect the initial ring down signal, a detection of echoes with characteristic properties could still confirm the proposal.
A taxonomy is a standardized framework to classify and organize items into categories. Hierarchical taxonomies are ubiquitous, ranging from the classification of organisms to the file system on a computer. Characterizing the typical distribution of i
tems within taxonomic categories is an important question with applications in many disciplines. Ecologists have long sought to account for the patterns observed in species-abundance distributions (the number of individuals per species found in some sample), and computer scientists study the distribution of files per directory. Is there a universal statistical distribution describing how many items are typically found in each category in large taxonomies? Here, we analyze a wide array of large, real-world datasets -- including items lost and found on the New York City transit system, library books, and a bacterial microbiome -- and discover such an underlying commonality. A simple, non-parametric branching model that randomly categorizes items and takes as input only the total number of items and the total number of categories successfully reproduces the abundance distributions in these datasets. This result may shed light on patterns in species-abundance distributions long observed in ecology. The model also predicts the number of taxonomic categories that remain unrepresented in a finite sample.
Current theories of the origin of the Universe, including string theory, predict the existence of a multiverse containing many bubble universes. These bubble universes will generically collide, and collisions with ours produce cosmic wakes that enter
our Hubble volume, appear as unusually symmetric disks in the cosmic microwave background (CMB) and disturb large scale structure (LSS). There is preliminary observational evidence consistent with one or more of these disturbances on our sky. However, other sources can produce similar features in the CMB temperature map and so additional signals are needed to verify their extra-universal origin. Here we find, for the first time, the detailed three-dimensional shape and CMB temperature and polarization signals of the cosmic wake of a bubble collision in the early universe consistent with current observations. The predicted polarization pattern has distinctive features that when correlated with the corresponding temperature pattern are a unique and striking signal of a bubble collision. These features represent the first verifiable prediction of the multiverse paradigm and might be detected by current experiments such as Planck and future CMB polarization missions. A detection of a bubble collision would confirm the existence of the Multiverse, provide compelling evidence for the string theory landscape, and sharpen our picture of the Universe and its origins.
We predict the polarization of cosmic microwave background (CMB) photons that results from a cosmic bubble collision. The polarization is purely E-mode, symmetric around the axis pointing towards the collision bubble, and has several salient features
in its radial dependence that can help distinguish it from a more conventional explanation for unusually cold or hot features in the CMB sky. The anomalous cold spot detected by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite is a candidate for a feature produced by such a collision, and the Planck satellite and other proposed surveys will measure the polarization on it in the near future. The detection of such a collision would provide compelling evidence for the string theory landscape.
We extend our previous work on the cosmology of Coleman-de Luccia bubble collisions. Within a set of approximations we calculate the effects on the cosmic microwave background (CMB) as seen from inside a bubble which has undergone such a collision. W
e find that the effects are always qualitatively similar--an anisotropy that depends only on the angle to the collision direction--but can produce a cold or hot spot of varying size, as well as power asymmetries along the axis determined by the collision. With other parameters held fixed the effects weaken as the amount of inflation which took place inside our bubble grows, but generically survive order 10 efolds past what is required to solve the horizon and flatness problems. In some regions of parameter space the effects can survive arbitrarily long inflation.
