A driven Kerr oscillator with two-fold degeneracies for qubit protection.

We present the experimental finding of multiple simultaneous two-fold degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing drive resulting from a three-wave mixing process, in combination with the Kerr interaction, creates an effective static two-well potential in the phase space rotating at half the frequency of the sinusoidal drive generating the squeezing. Remarkably, these degeneracies can be turned on-and-off on demand, as well as their number by simply adjusting the frequency of the squeezing drive. We find that when the detuning Δ between the frequency of the oscillator and the second subharmonic of the drive equals an even multiple of the Kerr coefficient K, [Formula: see text], the oscillator displays [Formula: see text] exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. These degeneracies can be explained by the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime, thus creating a protected cat qubit in the ground state manifold of our oscillator. Our results illustrate the relationship between degeneracies and noise protection in a driven quantum system.

Emergence of threefold symmetric helical photocurrents in epitaxial low twinned Bi2Se3.

We present evidence of a strong circular photon drag effect (PDE) in topological insulators (TIs) through the observation of helicity-dependent topological photocurrents with threefold rotational symmetry using THz spectroscopy in epitaxially-grown Bi2Se3 with reduced crystallographic twinning. We establish how twinned domains introduce competing nonlinear optical (NLO) responses inherent to the crystal structure that obscure geometry-sensitive optical processes through the introduction of a spurious mirror symmetry. Minimizing the twinning defect reveals strong NLO response currents whose magnitude and direction depend on the alignment of the excitation to the crystal axes and follow the threefold rotational symmetry of the crystal. Notably, photocurrents arising from helical light reverse direction for left/right circular polarizations and maintain a strong azimuthal dependence-a result uniquely attributable to the circular PDE, where the photon momentum acts as an applied in-plane field stationary in the laboratory frame. Our results demonstrate new levels of control over the magnitude and direction of photocurrents in TIs and that the study of single-domain films is crucial to reveal hidden phenomena that couple topological order and crystal symmetries.

Simulating molecular polaritons in the collective regime using few-molecule models.

The study of molecular polaritons beyond simple quantum emitter ensemble models (e.g., Tavis-Cummings) is challenging due to the large dimensionality of these systems and the complex interplay of molecular electronic and nuclear degrees of freedom. This complexity constrains existing models to either coarse-grain the rich physics and chemistry of the molecular degrees of freedom or artificially limit the description to a small number of molecules. In this work, we exploit permutational symmetries to drastically reduce the computational cost of ab initio quantum dynamics simulations for large N. Furthermore, we discover an emergent hierarchy of timescales present in these systems, that justifies the use of an effective single molecule to approximately capture the dynamics of the entire ensemble, an approximation that becomes exact as N → ∞. We also systematically derive finite N corrections to the dynamics and show that addition of k extra effective molecules is enough to account for phenomena whose rates scale as 𝒪(N-k). Based on this result, we discuss how to seamlessly modify existing single-molecule strong coupling models to describe the dynamics of the corresponding ensemble. We call this approach collective dynamics using truncated equations (CUT-E), benchmark it against well-known results of polariton relaxation rates, and apply it to describe a universal cavity-assisted energy funneling mechanism between different molecular species. Beyond being a computationally efficient tool, this formalism provides an intuitive picture for understanding the role of bright and dark states in chemical reactivity, necessary to generate robust strategies for polariton chemistry.

Opportunities for fundamental physics research with radioactive molecules.

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

Revisiting the observability and identifiability properties of a popular HIV model.

This paper revisits the observability and identifiability properties of a popular ODE model commonly adopted to characterize the HIV dynamics in HIV-infected patients with antiretroviral treatment. These properties are determined by using the general analytical solution of the unknown input observability problem, introduced very recently in Martinelli (2022). This solution provides the systematic procedures able to determine the state observability and the parameter identifiability of any ODE model, in particular, even in the presence of time varying parameters. Four variants of the HIV model are investigated. They differ because some of their parameters are considered constant or time varying. Fundamental new properties, which also highlight an error in the scientific literature, are automatically determined and discussed. Additionally, for each variant, the paper provides a quantitative answer to the following practical question: What is the minimal external information (external to the available measurements of the system outputs) required to make observable the state and identifiable all the model parameters? The answer to this fundamental question is obtained by exploiting the concept of continuous symmetry, recently introduced in Martinelli (2019). This concept allows us to determine a first preliminary general result which is then applied to the HIV model. Finally, for each variant, the paper concludes by providing a redefinition of the state and of the parameters in order to obtain a full description of the system only in terms of a state which is observable and a set of parameters which are identifiable (both constant and time varying).

Calculation of asymptotic charges at the critical sets of null infinity.

The asymptotic structure of null and spatial infinities of asymptotically flat spacetimes plays an essential role in discussing gravitational radiation, gravitational memory effect, and conserved quantities in General Relativity (GR). Bondi, Metzner and Sachs (BMS) established that the asymptotic symmetry group for asymptotically simple spacetimes is the infinite-dimensional BMS group. Given that null infinity is divided into two sets: past null infinity [Formula: see text] and future null infinity [Formula: see text], one can identify two independent symmetry groups: [Formula: see text] at [Formula: see text] and [Formula: see text] at [Formula: see text]. Associated with these symmetries are the so-called BMS charges. A recent conjecture by Strominger suggests that the generators of [Formula: see text] and [Formula: see text] and their associated charges are related via an antipodal reflection map near spatial infinity. To verify this matching, an analysis of the gravitational field near spatial infinity is required. This task is complicated due to the singular nature of spatial infinity for spacetimes with non-vanishing ADM mass. Different frameworks have been introduced in the literature to address this singularity, e.g. Friedrich's cylinder, Ashtekar-Hansen's hyperboloid and Ashtekar-Romano's asymptote at spatial infinity. This paper reviews the role of Friedrich's formulation of spatial infinity in the investigation of the matching of the spin-2 charges on Minkowski spacetime and in the full GR setting. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.

Γ valley transition metal dichalcogenide moiré bands.

The valence band maxima of most group VI transition metal dichalcogenide thin films remain at the Γ point all of the way from bulk to bilayer. In this paper, we develop a continuum theory of the moiré minibands that are formed in the valence bands of Γ-valley homobilayers by a small relative twist. Our effective theory is benchmarked against large-scale ab initio electronic structure calculations that account for lattice relaxation. As a consequence of an emergent [Formula: see text] symmetry, we find that low-energy Γ-valley moiré holes differ qualitatively from their K-valley counterparts addressed previously; in energetic order, the first three bands realize 1) a single-orbital model on a honeycomb lattice, 2) a two-orbital model on a honeycomb lattice, and 3) a single-orbital model on a kagome lattice.

Flavor's Delight.

Discrete flavor symmetries provide a promising approach to understand the flavor sector of the standard model of particle physics. Top-down (TD) explanations from string theory reveal two different types of such flavor symmetries: traditional and modular flavor symmetries that combine to the eclectic flavor group. There have been many bottom-up (BU) constructions to fit experimental data within this scheme. We compare TD and BU constructions to identify the most promising groups and try to give a unified description. Although there is some progress in joining BU and TD approaches, we point out some gaps that have to be closed with future model building.

Quantum Nonlocality: How Does Nature Do It?

In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space-time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality, Einstein -causality and global symmetries. Bell tests allow only rejecting probabilistic coupling provided by a local hidden variable model, but they do not justify metaphysical speculations about quantum nonlocality and objects which know about each other's state, even when separated by large distances. The violation of Bell inequalities in physics and in cognitive science can be explained using the notion of Bohr- contextuality. If contextual variables, describing varying experimental contexts, are correctly incorporated into a probabilistic model, then the Bell-CHSH inequalities cannot be proven and nonlocal correlations may be explained in an intuitive way. We also elucidate the meaning of statistical independence assumption incorrectly called free choice, measurement independence or no- conspiracy. Since correlation does not imply causation, the violation of statistical independence should be called contextuality; it does not restrict the experimenter's freedom of choice. Therefore, contrary to what is believed, closing the freedom-of choice loophole does not close the contextuality loophole.

Lung Cancer Gene Regulatory Network of Transcription Factors Related to the Hallmarks of Cancer.

The transcriptomic analysis of microarray and RNA-Seq datasets followed our own bioinformatic pipeline to identify a transcriptional regulatory network of lung cancer. Twenty-six transcription factors are dysregulated and co-expressed in most of the lung cancer and pulmonary arterial hypertension datasets, which makes them the most frequently dysregulated transcription factors. Co-expression, gene regulatory, coregulatory, and transcriptional regulatory networks, along with fibration symmetries, were constructed to identify common connection patterns, alignments, main regulators, and target genes in order to analyze transcription factor complex formation, as well as its synchronized co-expression patterns in every type of lung cancer. The regulatory function of the most frequently dysregulated transcription factors over lung cancer deregulated genes was validated with ChEA3 enrichment analysis. A Kaplan-Meier plotter analysis linked the dysregulation of the top transcription factors with lung cancer patients' survival. Our results indicate that lung cancer has unique and common deregulated genes and transcription factors with pulmonary arterial hypertension, co-expressed and regulated in a coordinated and cooperative manner by the transcriptional regulatory network that might be associated with critical biological processes and signaling pathways related to the acquisition of the hallmarks of cancer, making them potentially relevant tumor biomarkers for lung cancer early diagnosis and targets for the development of personalized therapies against lung cancer.

DNA sequence symmetries from randomness: the origin of the Chargaff's second parity rule.

Most living organisms rely on double-stranded DNA (dsDNA) to store their genetic information and perpetuate themselves. This biological information has been considered as the main target of evolution. However, here we show that symmetries and patterns in the dsDNA sequence can emerge from the physical peculiarities of the dsDNA molecule itself and the maximum entropy principle alone, rather than from biological or environmental evolutionary pressure. The randomness justifies the human codon biases and context-dependent mutation patterns in human populations. Thus, the DNA 'exceptional symmetries,' emerged from the randomness, have to be taken into account when looking for the DNA encoded information. Our results suggest that the double helix energy constraints and, more generally, the physical properties of the dsDNA are the hard drivers of the overall DNA sequence architecture, whereas the selective biological processes act as soft drivers, which only under extraordinary circumstances overtake the overall entropy content of the genome.

Glide symmetry breaking and Ising criticality in the quasi-1D magnet CoNb2O6.

We construct a microscopic spin-exchange Hamiltonian for the quasi-one-dimensional (1D) Ising magnet [Formula: see text] that captures detailed and hitherto-unexplained aspects of its dynamic spin structure factor. We perform a symmetry analysis that recalls that an individual Ising chain in this material is buckled, with two sites in each unit cell related by a glide symmetry. Combining this with numerical simulations benchmarked against neutron scattering experiments, we argue that the single-chain Hamiltonian contains a staggered spin-exchange term. We further argue that the transverse-field-tuned quantum critical point in [Formula: see text] corresponds to breaking this glide symmetry, rather than an on-site Ising symmetry as previously believed. This gives a unified microscopic explanation of the dispersion of confined states in the ordered phase and quasiparticle breakdown in the polarized phase at high transverse field.

Quantum Fourier analysis.

Quantum Fourier analysis is a subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum symmetry. We establish bounds on the quantum Fourier transform F, as a map between suitably defined [Formula: see text] spaces, leading to an uncertainty principle for relative entropy. We cite several applications of quantum Fourier analysis in subfactor theory, in category theory, and in quantum information. We suggest a topological inequality, and we outline several open problems.

Pattern-induced local symmetry breaking in active-matter systems.

The emergence of macroscopic order and patterns is a central paradigm in systems of (self-)propelled agents and a key component in the structuring of many biological systems. The relationships between the ordering process and the underlying microscopic interactions have been extensively explored both experimentally and theoretically. While emerging patterns often show one specific symmetry (e.g., nematic lane patterns or polarized traveling flocks), depending on the symmetry of the alignment interactions patterns with different symmetries can apparently coexist. Indeed, recent experiments with an actomysin motility assay suggest that polar and nematic patterns of actin filaments can interact and dynamically transform into each other. However, theoretical understanding of the mechanism responsible remains elusive. Here, we present a kinetic approach complemented by a hydrodynamic theory for agents with mixed alignment symmetries, which captures the experimentally observed phenomenology and provides a theoretical explanation for the coexistence and interaction of patterns with different symmetries. We show that local, pattern-induced symmetry breaking can account for dynamically coexisting patterns with different symmetries. Specifically, in a regime with moderate densities and a weak polar bias in the alignment interaction, nematic bands show a local symmetry-breaking instability within their high-density core region, which induces the formation of polar waves along the bands. These instabilities eventually result in a self-organized system of nematic bands and polar waves that dynamically transform into each other. Our study reveals a mutual feedback mechanism between pattern formation and local symmetry breaking in active matter that has interesting consequences for structure formation in biological systems.

The metaphysics of fibre bundles.

Recently, Dewar (2019) has suggested that one can apply the strategy of 'sophistication'-as exemplified by sophisticated substantivalism as a response to the diffeomorphism invariance of General Relativity-to gauge theories such as electrodynamics. This requires a shift to the formalism of fibre bundles. In this paper, I develop and defend this suggestion. Where my approach differs from previous discussions is that I focus on the metaphysical picture underlying the fibre bundle formalism. In particular, I aim to affirm the physical reality of gauge properties. I argue that this allows for a local and separable explanation of the Aharonov-Bohm effect. Its puzzling features are explained by a form of holism inherent to fibre bundles.

Hidden scale invariance in Navier-Stokes intermittency.

We expose a hidden scaling symmetry of the Navier-Stokes equations in the limit of vanishing viscosity, which stems from dynamical space-time rescaling around suitably defined Lagrangian scaling centres. At a dynamical level, the hidden symmetry projects solutions which differ up to Galilean invariance and global temporal scaling onto the same representative flow. At a statistical level, this projection repairs the scale invariance, which is broken by intermittency in the original formulation. Following previous work by the first author, we here postulate and substantiate with numerics that hidden symmetry statistically holds in the inertial interval of fully developed turbulence. We show that this symmetry accounts for the scale-invariance of a certain class of observables, in particular, the Kolmogorov multipliers. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.

On the role of continuous symmetries in the solution of the three-dimensional Euler fluid equations and related models.

We review and apply the continuous symmetry approach to find the solution of the three-dimensional Euler fluid equations in several instances of interest, via the construction of constants of motion and infinitesimal symmetries, without recourse to Noether's theorem. We show that the vorticity field is a symmetry of the flow, so if the flow admits another symmetry then a Lie algebra of new symmetries can be constructed. For steady Euler flows this leads directly to the distinction of (non-)Beltrami flows: an example is given where the topology of the spatial manifold determines whether extra symmetries can be constructed. Next, we study the stagnation-point-type exact solution of the three-dimensional Euler fluid equations introduced by Gibbon et al. (Gibbon et al. 1999 Physica D 132, 497-510. (doi:10.1016/S0167-2789(99)00067-6)) along with a one-parameter generalization of it introduced by Mulungye et al. (Mulungye et al. 2015 J. Fluid Mech. 771, 468-502. (doi:10.1017/jfm.2015.194)). Applying the symmetry approach to these models allows for the explicit integration of the fields along pathlines, revealing a fine structure of blowup for the vorticity, its stretching rate and the back-to-labels map, depending on the value of the free parameter and on the initial conditions. Finally, we produce explicit blowup exponents and prefactors for a generic type of initial conditions. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

R. J. Boscovich on physical symmetries.

R. J. Boscovich (1711-1787) is best known for his unified theory of natural phenomena of 1758, based on the notion of centrally interacting point-particles. While addressing contemporaneous scientific questions, his natural philosophy also systematically integrated many methodological and metaphysical ideas related to the pursuits of natural philosophy. One such excursion is Boscovich's treatment of what we today consider physical symmetries. In this paper I suggest a comprehensive interpretation of his comments on physical symmetries. I give special emphasis to Boscovich's notable inclusion of a re-scaling transformation among better known symmetries of Newtonian physics and show that it instantiates a generalization of standard dynamical symmetries. My interpretation shows that Boscovich's position results not only from his theory of matter (or basic ontology) but also from his explicit metaphysics and epistemology of space and time and his views on nomological possibility.

Identification of approximate symmetries in biological development.

Virtually all forms of life, from single-cell eukaryotes to complex, highly differentiated multicellular organisms, exhibit a property referred to as symmetry. However, precise measures of symmetry are often difficult to formulate and apply in a meaningful way to biological systems, where symmetries and asymmetries can be dynamic and transient, or be visually apparent but not reliably quantifiable using standard measures from mathematics and physics. Here, we present and illustrate a novel measure that draws on concepts from information theory to quantify the degree of symmetry, enabling the identification of approximate symmetries that may be present in a pattern or a biological image. We apply the measure to rotation, reflection and translation symmetries in patterns produced by a Turing model, as well as natural objects (algae, flowers and leaves). This method of symmetry quantification is unbiased and rigorous, and requires minimal manual processing compared to alternative measures. The proposed method is therefore a useful tool for comparison and identification of symmetries in biological systems, with potential future applications to symmetries that arise during development, as observed in vivo or as produced by mathematical models. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Study of Forward and Backward Modes in Double-Sided Dielectric-Filled Corrugated Waveguides.

This work studies the propagation characteristics of a rectangular waveguide with aligned/misaligned double-sided dielectric-filled metallic corrugations. Two modes are found to propagate in the proposed double-sided configuration below the hollow-waveguide cutoff frequency: a quasi-resonant mode and a backward mode. This is in contrast to the single-sided configuration, which only allows for backward propagation. Moreover, the double-sided configuration can be of interest for waveguide miniaturization on account of the broader band of its backward mode. The width of the stopband between the quasi-resonant and backward modes can be controlled by the misalignment of the top and bottom corrugations, being null for the glide-symmetric case. The previous study is complemented with numerical results showing the impact of the height of the corrugations, as well as the filling dielectric permittivity, on the bandwidth and location of the appearing negative-effective-permeability band. The multi-modal transmission-matrix method has also been employed to estimate the rejection level and material losses in the structure and to determine which port modes are associated with the quasi-resonant and backward modes. Finally, it is shown that glide symmetry can advantageously be used to reduce the dispersion and broadens the operating band of the modes.