False Minima Research Articles

Thermal curvature perturbations in thermal inflation

We compute the power spectrum of super-horizon curvature perturbations generated during a late period of thermal inflation, taking into account fluctuation-dissipation effects resulting from the scalar flaton field's interactions with the ambient radiation bath. We find that, at the onset of thermal inflation, the flaton field may reach an equilibrium with the radiation bath even for relatively small coupling constants, maintaining a spectrum of thermal fluctuations until the critical temperature T c, below which thermal effects stop holding the field at the false potential minimum. This enhances the field variance compared to purely quantum fluctuations, therefore increasing the average energy density during thermal inflation and damping the induced curvature perturbations. In particular, we find that this inhibits the later formation of primordial black holes, at least on scales that leave the horizon for T > T c. The larger thermal field variance also reduces the duration of a period of fast-roll inflation below T c, as the field rolls to the true potential minimum, which should also affect the generation of (large) curvature perturbations on even smaller scales.

Fate of false vacuum in non-perturbative regimes

We use some exact results in scalar field theory to revise the analysis by Coleman and Callan about false vacuum decay and propose a simple non-perturbative formalism. We introduce an exact Green’s function which incorporates non-perturbative corrections in the strong coupling regimes of the theory. The solution of the scalar field theory involves the Jacobi elliptical function and has been used to calculate the effective potential for any arbitrary coupling values. We demonstrate the use of this formalism in a simple λ ϕ 4 theory, and show that the effective potential exhibits a false minimum at the origin. We then calculate the false vacuum decay rate in the thin wall approximation, and suggest simple analytic formulae that may be useful for the analysis for the first-order phase transition beyond the perturbative regime. In our methodology, we show that the standard results obtained in perturbation theory are reproduced by making the coupling values very small.

Incommensurate magnetic structure of CrAs at low temperatures and high pressures.

The magnetic structure of chromium arsenide CrAs is studied with neutron powder diffraction at ambient pressure in the temperature range 1.5-300 K as well as with neutron single-crystal diffraction at 2 K and 0.12 GPa. The material undergoes an anti-isostructural phase transition at TN = 267 K and atmospheric conditions, in which both orthorhombic phases have the same space-group symmetry (Pnma, Z = 4) but different distortions of the parent hexagonal structure of the NiAs type (P63/mmc, Z = 2). The magnetic structure below TN is incommensurate with the propagation vector k = (0, 0, kc). At ambient pressure, the component kc decreases from kc = 0.3807 (7) at 260 K to kc = 0.3531 (6) at 50 K. Below this temperature, it is basically constant. With increasing pressure at 2 K, kc is also constant within standard uncertainties [kc = 0.353 (2)]. For the analysis of the magnetic structure, a group-theoretical approach based on the space group of the nuclear structure and its subgroups is used. To avoid falling into false minima in the refinements, a random search for magnetic moments in the models is implemented. In the literature, the magnetic structure has been determined on the basis of powder diffraction data as a double helix propagating along the c axis. Although this double-helical model leads to satisfactory agreement factors for our powder data, it does not reproduce the intensities of the magnetic satellite reflections measured on single-crystal data in a satisfactory way and can therefore be discarded. Instead, several other models are found that lead to better agreement. Each of them is spiral-like with directional components in all three directions and with no spin-density wave character that would cause a non-constant magnetic moment. In all these models, the ordering of the spins is neither a pure helix nor a pure cycloid. Instead, the unit vectors of the spin rotation planes make an angle α, 0° < α < 90°, with respect to the c* direction. The model in superspace group P21.1'(α0γ)0s yields the best agreement factors in the refinements of the neutron single-crystal and powder diffraction data. This model is unique as it is the only one in which all the magnetic moments rotate with the same chirality.

Quantum-inspired tempering for ground state approximation using artificial neural networks

A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update or train the ANN parameters can get trapped in local minima, especially for frustrated systems and even if the representation is sufficiently expressive. We propose a parallel tempering method that facilitates escape from such local minima. This methods involves training multiple ANNs independently, with each simulation governed by a Hamiltonian with a different "driver" strength, in analogy to quantum parallel tempering, and it incorporates an update step into the training that allows for the exchange of neighboring ANN configurations. We study instances from two classes of Hamiltonians to demonstrate the utility of our approach using Restricted Boltzmann Machines as our parameterized ANN. The first instance is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it increasingly to a false local minimum. The second instance is four hydrogen atoms arranged in a rectangle, which is an instance of the second quantized electronic structure Hamiltonian discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem’s small size. We show that augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of these problem instances.

Quantum optimization of complex systems with a quantum annealer

We perform an in-depth comparison of quantum annealing with several classical optimisation techniques, namely thermal annealing, Nelder-Mead, and gradient descent. We begin with a direct study of the 2D Ising model on a quantum annealer, and compare its properties directly with those of the thermal 2D Ising model. These properties include an Ising-like phase transition that can be induced by either a change in 'quantum-ness' of the theory, or by a scaling the Ising couplings up or down. This behaviour is in accord with what is expected from the physical understanding of the quantum system. We then go on to demonstrate the efficacy of the quantum annealer at minimising several increasingly hard two dimensional potentials. For all the potentials we find the general behaviour that Nelder-Mead and gradient descent methods are very susceptible to becoming trapped in false minima, while the thermal anneal method is somewhat better at discovering the true minimum. However, and despite current limitations on its size, the quantum annealer performs a minimisation very markedly better than any of these classical techniques. A quantum anneal can be designed so that the system almost never gets trapped in a false minimum, and rapidly and successfully minimises the potentials.

AGN X-ray spectroscopy with neural networks

ABSTRACT We explore the possibility of using machine learning to estimate physical parameters directly from active galactic nucleus (AGN) X-ray spectra without needing computationally expensive spectral fitting. Specifically, we consider survey quality data, rather than long pointed observations, to ensure that this approach works in the regime where it is most likely to be applied. We simulate Athena Wide Field Imager spectra of AGN with warm absorbers, and train simple neural networks to estimate the ionization and column density of the absorbers. We find that this approach can give comparable accuracy to spectral fitting, without the risk of outliers caused by the fit sticking in a false minimum, and with an improvement of around three orders of magnitude in speed. We also demonstrate that using principal component analysis to reduce the dimensionality of the data prior to inputting it into the neural net can significantly increase the accuracy of the parameter estimation for negligible computational cost, while also allowing a simpler network architecture to be used.

Gravitino dark matter, nonthermal leptogenesis, and low reheating temperature in no-scale Higgs inflation

We revisit Higgs inflation in the framework of a minimal extension of the Standard Model gauge symmetry by a $U(1)_{B-L}$ factor. Various aspects are taken into account with particular focus on the role of the supersymmetry breaking (SUSY) scale and the cosmological constraints associated with the gravitino. The scalar potential of the model is considered in the context of no-scale supergravity consisting of the F-part constructed from the K\"ahler function, the D-terms and soft SUSY contributions. We investigate several limiting cases and by varying the SUSY scale from a few TeV up to intermediate energies, for a spectral index around $n_s\sim 0.9655$ and reheating temperature $T_r\le 10^{9}$ GeV we find that the value of the tensor-to-scalar ratio ranges from $r\approx 10^{-3}$ to $10^{-2}$. Furthermore, it is shown that for certain regions of the parameter space the gravitino can live sufficiently long and as such is a potential candidate for a dark matter component. In general, the inflationary scenario is naturally implemented and it is consistent with non-thermal leptogenesis whereas the dominant decay channel of the inflaton yields right-handed neutrinos. Other aspects of cosmology and particle physics phenomenology are briefly discussed. Finally, we investigate the case where the inflaton is initially relaxed in a false minimum and estimate its probability to decay to the true vacuum.

Experimental test of search range in quantum annealing

We construct an Ising Hamiltonian with an engineered energy landscape such that it has a local energy minimum which is near the true global minimum solution and further away from a false minimum. Using a technique established in previous experiments, we design our experiment such that (at least on timescales relevant to our study) the false minimum is reached preferentially in forward annealing due to high levels of quantum fluctuations. This allows us to demonstrate the key principle of reverse annealing, that the solution space can be searched locally, preferentially finding nearby solutions, even in the presence of a false minimum. The techniques used here are distinct from previously used experimental techniques and allow us to probe the fundamental search range of the device in an alternative way. We perform these experiments on two flux qubit quantum annealers, one with higher noise levels than the other. We find evidence that the lower noise device is more likely to find the more distant energy minimum (the false minimum in this case), suggesting that reducing noise fundamentally increases the range over which flux qubit quantum annealers are able to search. Our work explains why reducing the noise leads to improved performance on these quantum annealers. This supports the idea that these devices may be able to search over broad regions of the solution space quickly, one of the core reasons why quantum annealers are viewed as a potential avenue for a quantum computational advantage.

Unconventional quantum annealing methods for difficult trial problems

We consider a range of unconventional modifications to Quantum Annealing (QA), applied to an artificial trial problem with continuously tunable difficulty. In this problem, inspired by "transverse field chaos" in larger systems, classical and quantum methods are steered toward a false local minimum. To go from this local minimum to the global minimum, all N spins must flip, making this problem exponentially difficult to solve. We numerically study this problem by using a variety of new methods from the literature: inhomogeneous driving, adding transverse couplers, and other types of coherent oscillations in the transverse field terms (collectively known as RFQA). We show that all of these methods improve the scaling of the time to solution (relative to the standard uniform sweep evolution) in at least some regimes. Comparison of these methods could help identify promising paths towards a demonstrable quantum speedup over classical algorithms in solving some realistic problems with near-term quantum annealing hardware.

High-fidelity pixel-super-resolved complex field reconstruction via adaptive smoothing.

Pixel super-resolution (PSR) techniques have been developed to overcome the sampling limit in lensless digital holographic imaging. However, the inherent non-convexity of the PSR phase retrieval problem can potentially degrade reconstruction quality by causing the iterations to tend toward a false local minimum. Furthermore, the ill posedness of the up-sampling procedure renders PSR algorithms highly susceptible to noise. In this Letter, we propose a heuristic PSR algorithm with adaptive smoothing (AS-PSR) to achieve high-fidelity reconstruction. By automatically adjusting the intensity constraints on the estimated field, the algorithm can effectively locate the optimal solution and converge with high reconstruction quality, pushing the resolution toward the diffraction limit. The proposed method is verified experimentally within a coherent modulation phase retrieval framework, achieving a twofold improvement in resolution. The AS-PSR algorithm can be further applied to other phase retrieval methods based on alternating projection.

Real-Time Performance of the PLUM Earthquake Early Warning Method during the 2019 M 6.4 and 7.1 Ridgecrest, California, Earthquakes

ABSTRACTWe evaluate the timeliness and accuracy of ground-motion-based earthquake early warning (EEW) during the July 2019 M 6.4 and 7.1 Ridgecrest earthquakes. In 2018, we began retrospective and internal real-time testing of the propagation of local undamped motion (PLUM) method for earthquake warning in California, Oregon, and Washington, with the potential that PLUM might one day be included in the ShakeAlert EEW system. A real-time version of PLUM was running on one of the ShakeAlert EEW system’s development servers at the time of the 2019 Ridgecrest sequence, allowing us to evaluate the timeliness and accuracy of PLUM’s warnings for the M 6.4 and 7.1 mainshocks in real time with the actual data availability and latencies of the operational ShakeAlert EEW system. The latter is especially important because high-data latencies during the M 7.1 earthquake degraded ShakeAlert’s performance. PLUM proved to be largely immune to these latencies. In this article, we present a retrospective analysis of PLUM performance and explore three potential regional alerting strategies ranging from spatially large regions (counties), to moderate-size regions (National Weather Service public forecast zones), to high-spatial specificity (50 km regular geographic grid). PLUM generated initial shaking forecasts for the two mainshocks 5 and 6 s after their respective origin times, and faster than the ShakeAlert system’s first alerts. PLUM was also able to accurately forecast shaking across southern California for all three alerting strategies studied. As would be expected, a cost-benefit analysis of each approach illustrates trade-offs between increasing warning time and minimizing the area receiving unneeded alerts. Choosing an optimal alerting strategy requires knowledge of users’ false alarm tolerance and minimum required warning time for taking protective action, as well as the time required to distribute alerts to users.

Об ангармонических колебаниях двухатомной молекулы и атомарного димера

According to modern concepts, the interaction potential as a function of the interatomic distance has a single minimum, has no other extremum points, and does not have inflection points, where its derivative is zero. Usually, to take into account harmonic vibrations and the effect of anharmonic effects on these vibrations, the interaction potential is expanded in the Taylor series and a quadratic term is taken into account, which takes into account harmonic vibrations, and third and fourth order corrections for deviations of the interatomic distance from its equilibrium value, taking into account anharmonic effects. These three members of the Taylor series constitute an approximate interaction potential. To take into account the anharmonic effects in the partition function of the diatomic molecule in the Boltzmann factor, an exponential factor is selected that takes into account the anharmonic part of the above approximate potential, and this factor is expanded in the Taylor series, the integration limits are changed to plus and minus infinity, the integration is carried out and the first few members of the power series are left on return temperature. Obviously, the approximate potential, like the initial potential, should not have other extremum points, except for a single minimum, and inflection points, where its derivative is equal to zero. In this paper, it is shown that: if the coefficient in front of the fourth-order term in the approximate potential is negative, then the approximate potential has two false maxima; if it is zero, then there is one false maximum; if it is positive, then the potential can have one false minimum and one false maximum or one inflection point where the derivative of the potential is equal to zero. The conditions imposed on the interaction potential are found when the anharmonic effects in the vibrations of a diatomic molecule can be approximately taken into account by corrections of the third and fourth orders to the quadratic harmonic potential. It is shown that this approximation can be used in the case of the interaction of atoms of a diatomic molecule by means of the Mie-Grüneisen and Lennard-Jones potential.

HotSpotAnnotations-a database for hotspot mutations and annotations in cancer.

Hotspots, recurrently mutated DNA positions in cancer, are thought to be oncogenic drivers because random chance is unlikely and the knowledge of clear examples of oncogenic hotspots in genes like BRAF, IDH1, KRAS and NRAS among many other genes. Hotspots are attractive because provide opportunities for biomedical research and novel treatments. Nevertheless, recent evidence, such as DNA hairpins for APOBEC3A, suggests that a considerable fraction of hotspots seem to be passengers rather than drivers. To document hotspots, the database HotSpotsAnnotations is proposed. For this, a statistical model was implemented to detect putative hotspots, which was applied to TCGA cancer datasets covering 33 cancer types, 10 182 patients and 3 175 929 mutations. Then, genes and hotspots were annotated by two published methods (APOBEC3A hairpins and dN/dS ratio) that may inform and warn researchers about possible false functional hotspots. Moreover, manual annotation from users can be added and shared. From the 23 198 detected as possible hotspots, 4435 were selected after false discovery rate correction and minimum mutation count. From these, 305 were annotated as likely for APOBEC3A whereas 442 were annotated as unlikely. To date, this is the first database dedicated to annotating hotspots for possible false functional hotspots.

Primordial black hole formation with non-Gaussian curvature perturbations

In the context of transient constant-roll inflation near a local maximum, we derive the non-perturbative field redefinition that relates a Gaussian random field with the true non-Gaussian curvature perturbation. Our analysis shows the emergence of a new critical amplitude ζ*, corresponding to perturbations that prevent the inflaton from overshooting the local maximum, thus becoming trapped in the false minimum of the potential. For potentials with a mild curvature at the local maximum (and thus small non-Gaussianity), we recover the known perturbative field redefinition. We apply these results to the formation of primordial black holes, and discuss the cases for which ζ* is smaller or of the same order than the critical value for collapse of spherically symmetric overdensities. In the latter case, we present a simple potential for which the power spectrum needs an amplitude 10 times smaller that in the Gaussian case for producing a sizeable amount of primordial black holes.

Probing Trans-Electroweak First Order Phase Transitions from Gravitational Waves

We propose direct tests of very high energy first-order phase transitions, which are elusive to collider physics, deploying the gravitational waves’ measurements. We show that first-order phase transitions lying in a large window of critical temperatures, which is considerably larger than the electroweak energy scale, can be tested from advanced LIGO (aLIGO) and the Einstein Telescope. This provides the possibility to probe several inflationary mechanisms ending with the inflaton in a false minimum and high-energy first order phase transitions that are due to new scalar bosons, beyond the Standard Model of particle physics. As an important example, we consider the axion monodromy inflationary scenario and analyze the potential for its experimental verification, deploying the gravitational wave interferometers.

Computational multiqubit tunnelling in programmable quantum annealers.

Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive.

WE-AB-BRA-12: Virtual Endoscope Tracking for Endoscopy-CT Image Registration

Purpose: The use of endoscopy in radiotherapy will remain limited until we can register endoscopic video to CT using standard clinical equipment. In this phantom study we tested a registration method using virtual endoscopy to measure CT-space positions from endoscopic video. Methods: Our phantom is a contorted clay cylinder with 2-mm-diameter markers in the luminal surface. These markers are visible on both CT and endoscopic video. Virtual endoscope images were rendered from a polygonal mesh created by segmenting the phantom's luminal surface on CT. We tested registration accuracy by tracking the endoscope's 6-degree-of-freedom coordinates frame-to-frame in a video recorded as it moved through the phantom, and using these coordinates to measure CT-space positions of markers visible in the final frame. To track the endoscope we used the Nelder-Mead method to search for coordinates that render the virtual frame most similar to the next recorded frame. We measured the endoscope's initial-frame coordinates using a set of visible markers, and for image similarity we used a combination of mutual information and gradient alignment. CT-space marker positions were measured by projecting their final-frame pixel addresses through the virtual endoscope to intersect with the mesh. Registration error was quantified as the distance between this intersection and the marker's manually-selected CT-space position. Results: Tracking succeeded for 6 of 8 videos, for which the mean registration error was 4.8±3.5mm (24 measurements total). The mean error in the axial direction (3.1±3.3mm) was larger than in the sagittal or coronal directions (2.0±2.3mm, 1.7±1.6mm). In the other 2 videos, the virtual endoscope got stuck in a false minimum. Conclusion: Our method can successfully track the position and orientation of an endoscope, and it provides accurate spatial mapping from endoscopic video to CT. This method will serve as a foundation for an endoscopy-CT registration framework that is clinically valuable and requires no specialized equipment.

Gravitational wave background and Higgs false vacuum inflation

For a narrow band of values of the top quark and Higgs boson masses, the standard model Higgs potential develops a shallow local minimum at energies of about ${10}^{16}\text{ }\mathrm{GeV}$, where primordial inflation could have started in a cold metastable state. For each point of that band, the highness of the Higgs potential at the false minimum is calculable, and there is an associated prediction for the inflationary gravitational wave background, namely, for the tensor to scalar ratio $r$. We show that the recent measurement of $r$ by the BICEP2 collaboration, $r=0.1{6}_{\ensuremath{-}0.05}^{+0.06}$ at $1\ensuremath{\sigma}$, combined with the most up-to-date measurements of the top quark and Higgs boson masses, reveals that the hypothesis that a standard model shallow false minimum was the source of inflation in the early Universe is viable.

Applications of the Infrared Measurement Analyzer: Hydrogenated LWIR HgCdTe Detectors

Low-cost silicon-based alternative substrates are an attractive choice for next-generation large-area high-resolution multicolor infrared (IR) detector arrays. However, the high density of dislocations formed during molecular-beam epitaxy growth of HgCdTe/CdTe/Si limits the performance of IR arrays, especially in the long-wavelength infrared (LWIR) region. Atomic hydrogen introduced by inductively coupled plasma (ICP) into HgCdTe is expected to passivate dislocations, bulk and surface defects, removing their contributions to dark current. Passivation using ICP hydrogenation can have different effects on HgCdTe photodiode performance, depending on which class of defects is being passivated. The infrared measurement analyzer (IRMA) was used to deconvolute the effects of hydrogenation on LWIR HgCdTe photodiodes through a reverse-modeling fit of the current–voltage (I–V) characteristic. This approach results in a fit with fewer false minima, low parameter error and bias, and high confidence in extracted device parameters. A description of this tool and its application to hydrogenated HgCdTe LWIR detectors is presented. Lower dark currents have been observed after hydrogenation of fully fabricated devices. Model-fits performed on a wide variety of LWIR HgCdTe photodiodes suggest that hydrogenation provides both surface and bulk quality improvements. These benefits of ICP hydrogenation have been retained over several months.

Confidence Regions in Models of Ordered Data

As a particular structure in reliability, a sequential k-out-of-n system fails if more than of its n components fail, where the failure of some component may affect the residual lifetimes of the remaining components of the system. Sequential order statistics serve as a model for the (ordered) lifetimes of the components and the system, respectively. When dealing with the conditional proportional hazard rate model with pre-fixed baseline distribution, the model parameters are usually unknown and have to be estimated from data. Confidence intervals for single model parameters as well as multidimensional confidence regions for respective vectors are proposed, and desirable properties including optimality in the sense of minimum coverage probabilities of false parameters and minimum (expected) volume are also obtained. The confidence sets are illustrated and compared in terms of a simulation study indicating further properties.