Universe, Volume 10, Issue 1 (January 2024) – 52 articles

As a consequence of the spacetime structure, defined by the tetrad field instead of the metric tensor alone, $f\left(T\right)$ gravity seems to harbor its own chronology protection agency. When Gott’s pair of moving cosmic strings is considered, it is shown that the requirement of having a global parallelization—i.e., a global smooth field of tetrads– drastically restricts the form of the tetrads on the junction surface between the two strings. The junction conditions on the tetrad field are satisfied only if the corresponding boosts needed to put the strings in motion are null on the matching surface. This seems to throw overboard Gott’s construction from the outset without the need for analyzing the divergence of the expectation value of the energy–momentum tensor on the Cauchy horizon, evading in this way bothersome quarrels concerning the choice of vacuum. Full article

The angular distributions of the elastic and inelastic scattering of α-particles on ¹⁰B nuclei were measured at an energy of 29 MeV (with excitation of the 0.718 MeV (1⁺) state). The data obtained by us, together with the angular distributions of the elastic scattering measured earlier in a wide range of energies from 24 to 90 MeV, were described using an optical model, the coupled-channel method, and parameterized phase analysis. The optimal parameters of optical potentials were found, and a good description of the experimental data in the specified energy range of α-particles was achieved. By taking into account the contribution of the elastic transfer mechanism of the ⁶Li cluster, it was possible to correctly reproduce the rise of the cross section at the backward angles in the elastic channel. The value of the quadrupole deformation parameter was extracted from the analysis of inelastic scattering using the coupled-channel method. The geometric parameters of the interaction potentials were determined using parameterized phase analysis. The radii of the ¹⁰B nuclei in the high-energy region (30 MeV and above) obtained by PPA are in good agreement with the radii calculated in the framework of the optical model. Full article

In the PMNS matrix, the relation $|U_{\mu i}| = |U_{\tau i}|$ (with $i=1,2,3$) is experimentally favored at the present stage. The possible implications of this relation on some hidden flavor symmetry has attracted a lot of interest in the neutrino community. In this paper, we analyze the implications of $|U_{\mu i}| = |U_{\tau i}|$ (with $i=1,2,3$) in the context of the canonical seesaw mechanism. We also show that the minimal $\mu -\tau$ symmetry proposed in JHEP 06 (2022) 034 is a possible but not necessary reason for the above-mentioned relation. Full article

Cumulants up to the sixth-order of the net-particle multiplicity distributions were measured at RHIC for the Beam Energy Scan and fixed-target program, from which we obtained some interesting hints on the phase structure of the QCD matter. In this article, we present recent experimental results on (net-)proton cumulants and discuss current interpretations on the QCD critical point and the nature of the phase transition. We will also report recent results for measurements of the bayron-strangeness correlations, which were measured with the newly developed analysis technique to remove the effect from the combinatorial backgrounds for hyperon reconstruction. Full article

Cosmological parameters are constrained by a wide variety of observations. We examine the concordance diagram for modern measurements of the Hubble constant, the shape parameter from the large-scale structure, the cluster baryon fraction, and the age of the universe, all from non-CMB data. There is good agreement for $H_0=73.24\pm 0.38\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ and ${\Omega }_m=0.237\pm 0.015$. This concordance value is indistinguishable from the WMAP3 cosmology but is not consistent with that of Planck: there is a tension in ${\Omega }_m$ as well as $H_0$. These tensions have emerged as progressively higher multipoles have been incorporated into CMB fits. This temporal evolution is suggestive of a systematic effect in the analysis of CMB data at fine angular scales and may be related to the observation of unexpectedly massive galaxies at high redshift. These are overabundant relative to $\Lambda$CDM predictions by an order of magnitude at $z>7$. Such massive objects are anomalous and could cause gravitational lensing of the surface of last scattering in excess of the standard calculation made in CMB fits, potentially skewing the best-fit cosmological parameters and contributing to the Hubble tension. Full article

Superdeterminism—where the Measurement Independence assumption in Bell’s Theorem is violated—is frequently assumed to imply implausibly conspiratorial correlations between properties $\lambda$ of particles being measured and measurement settings x and y. But it does not have to be so: a superdeterministic but non-conspiratorial locally causal model is developed where each pair of entangled particles has unique $\lambda$. The model is based on a specific but arbitrarily fine discretisation of complex Hilbert space, where $\lambda$ defines the information, over and above the freely chosen nominal settings x and y, which fixes the exact measurement settings X and Y of a run of a Bell experiment. Pearlean interventions, needed to assess whether x and y are Bell-type free variables, are shown to be inconsistent with rational-number constraints on the discretised Hilbert states. These constraints limit the post-hoc freedom to vary x keeping $\lambda$ and y fixed but disappear with any coarse-graining of $\lambda$, X, and Y, rendering so-called drug-trial conspiracies irrelevant. Points in the discretised space can be realised as ensembles of symbolically labelled deterministic trajectories on an ‘all-at-once’ fractal attractor. It is shown how quantum mechanics might be ‘gloriously explained and derived’ as the singular continuum limit of the discretisation of Hilbert space. It is argued that the real message behind Bell’s Theorem has less to do with locality, realism, or freedom to choose, and more to do with the need to develop more explicitly holistic theories when attempting to synthesise quantum and gravitational physics. Full article

The discovery of collective effects in small collision systems has spurred a renewed interest in hadronization models, and is also a source for collective effects all the way to large collision systems, where they are usually ascribed to the creation of a Quark–Gluon Plasma. In this topical mini-review, the microscopic model for string interactions, based on the Lund string hadronization model, developed with exactly this aim in mind is reviewed, and some prospects for the future are presented. Full article

From a recently found family of analytic, finite and accelerating 1+1-dimensional solutions to perfect fluid relativistic hydrodynamics, we derive simple and powerful formulae to describe the rapidity and pseudorapidity density distributions. By introducing a new scaling function, we notice that the rapidity distribution data of the different experiments all collapse into a single curve. This data-collapsing (or -scaling) behaviour in the rapidity distributions suggests that high-energy $p+p$ collisions may be described as collective systems. Full article

A viable radiation-dominated era in the early universe is best described by the standard (FLRW) model of cosmology. In this short review, we demonstrate reconstruction of the forms of $F\left(R\right)$ in the modified theory of gravity and the metric compatible $F\left(\mathrm{T}\right)$ together with the symmetric $F\left(Q\right)$ in alternative teleparallel theories of gravity, from different perspectives, primarily rendering emphasis on a viable FLRW radiation era. Inflation has also been studied for a particular choice of the scalar potential. The inflationary parameters are found to agree appreciably with the recently released observational data. Full article

In recent decades, extensive research has led to the understanding that Mars once hosted substantial liquid-water reserves. While the current Martian landscape boasts significant water-ice deposits at its North and South poles, the elusive presence of liquid-water bodies has remained undetected. A breakthrough occurred with the identification of radar-echo reflections at the base of the Martian South Pole, using MARSIS (Mars Advanced Radar for Subsurface and Ionospheric Sounding) in 2018. These radar echoes strongly suggest the presence of a highly concentrated liquid-water body. However, a counter-narrative has emerged, contending that the subterranean conditions beneath the ice cap, encompassing factors like temperature and pressure, may be inhospitable to liquid water. Consequently, alternative hypotheses posit that the observed bright echoes could be attributed to conductive minerals or water-absorbing clay-like materials. The ongoing discourse regarding the presence of liquid water beneath the southern polar ice cap is a hot topic in the realm of Martian exploration. The primary focus of this paper is to provide a comprehensive overview of Martian radar detection, the recent controversies regarding liquid water’s existence in the Martian South Pole, and the implications regarding the potential existence of Martian life forms in the water on Mars. The revelation of liquid water on Mars fundamentally suggests an environment conducive to the viability of Martian life, consequently furnishing invaluable insights for future exploratory endeavors in the pursuit of Martian biospheres. In addition, this paper anticipates the forthcoming research dedicated to Martian liquid water and potential life forms, while also underscoring the profound significance of identifying liquid water on Mars in propelling the field of astrobiology forward. Full article

We present a detailed analysis of a partial eruption of a sigmoid filament lying along the polarity inversion line (PIL) of the small active region (AR) NOAA 12734 (with an area of 1.44 $\times {10}^3$ square megameters). The active filament was rooted in a dipole sunspot of the AR. The eruption was associated with a C1.3 flare and subsequent large-scale coronal disturbances. During its solar disk passage before the flare, the AR had the following characteristics: (1) Most of the time, the magnetic field lines in the AR showed a sigmoidal structure (‘L1’) in the low corona and arc-shaped loops (i.e., ‘L2’) in the upper atmosphere. (2) An ‘X’-shaped structure was formed between the original ‘S’-shaped magnetic loop (‘L1’) and the newly rising one (‘L3’) between the main positive and negative magnetic polarities of the sunspots, and the intersection point of flux ropes ‘L1’ and ‘L3’ corresponds well with the area where the initial extreme-ultraviolet (EUV) 1600 Å brightening of the flare occurred. (3) The AR disobeyed the hemispherical helicity rule and had magnetic twist and writhe of the same signs, i.e., its magnetic helicity/current helicity were positive in the northern hemisphere. (4) Sustained magnetic emergence and cancellation occurred before the flare. Therefore, the magnetic reconnection of highly twisted helical flux ropes under the confinement of the overlying magnetic fields is probably responsible for the partial eruption of the filament. Full article

We imagine spherically symmetric configurations made of both dark matter and dark energy in the halo of spiral galaxies. Adopting a polytropic equation of state for dark matter and the Extended Chaplygin gas equation of state for dark energy, we model the same object with three different dark matter–dark energy compositions. We compute the frequencies and the corresponding eigenfunctions of the ten lowest modes, integrating the equations for the radial perturbations by imposing the appropriate boundary conditions at the center and the surface of the object. Also, a comparison between the different models is made. Full article

Using data from the MESSENGER spacecraft magnetometer that describes the magnetopause and the bow shock crossing points of the Mercury’s magnetosphere, we have calculated the parameters of the paraboloids of revolution approximating the obtained points. For each spacecraft orbit, the subsolar magnetopause and bow shock standoff distances were obtained, based on the paraboloid parameters for each crossing point. The dependences of the magnetopause and bow shock subsolar standoff distances on the Mercury’s position relative to the Sun have been obtained. These profiles agree with decreases of the solar wind plasma dynamic pressure and the interplanetary magnetic field strength with heliocentric distance. The variations of the interplanetary and magnetosheath magnetic field were investigated. The average subsolar magnetosheath thickness and the value of the magnetic field jump at the bow shock during the transition from the upstream interplanetary magnetic field region to the magnetosheath were obtained. Full article

We study the second-order scalar and density perturbations generated by Gaussian curvature perturbations and primordial gravitational waves in the radiation-dominated era. After presenting all the possible second-order source terms, we obtain the explicit expressions of the kernel functions and the power spectra of the second-order scalar perturbations. We show that the primordial gravitational waves might affect second-order energy density perturbation ${\delta }^{\left(2\right)}=\delta {\rho }^{\left(2\right)}/{\rho }^{\left(0\right)}$ significantly. The effects of primordial gravitational waves are studied in terms of different kinds of primordial power spectra. Full article

The chromomagnetic vacuum of SU(2) gluodynamics is considered in the background of a finite radius flux tube (center vortex) with a homogeneous field inside and a zero field outside. In this background, there are tachyonic modes. These modes cause an instability. It is assumed that the self-interaction of these modes stops the creation of gluons, and it is assumed that a condensate will be formed. For constant condensates, the minimum of the effective potential is found at the tree level. In the background of these condensates, all tachyonic modes acquire non-zero real masses, which will result in a real effective potential of this system. Considering only the tachyonic modes and adding the energy of the background field, the total energy is found to have a minimum at some value of the background field, which depends on the coupling of the initial SU(2) model. For small coupling, this dependence is polynomial in distinction from the Savvidy vacuum where it is exponentially suppressed. The minimum of this energy will deepen with a shrinking radius of the flux tube. It can be expected that this process can be stopped by adding quantum effects. Using the high-temperature expansion of the effective potential, it can be expected that the symmetry, which is broken by the condensate, will be restored at sufficiently high temperatures. Full article

We examine the flux density ratio anomaly in the quadruply imaged strong gravitational lens, B1422+231, and consider the contribution of 10–${10}^3{M}_{\odot }$ primordial black holes (PBHs) as a potential dark matter constituent. We describe the first flux density ratio measurement of B1422+231 in the millimeter-wave band using the Atacama Large Millimeter Array (ALMA). The flux density of the quasar at 233 GHz is dominated by synchrotron emission and the source size is estimated to be less than 66.9 pc. The observed flux density ratios at 233 GHz are similar to those measured in other wave bands, which cannot be explained by a simple smooth mass model of the lens galaxy. We examine the probability of the flux density ratio anomaly arising from PBH microlensing using ray tracing simulations. The simulations consider the cases where 10% and 50% of dark matter are 10–${10}^3{M}_{\odot }$ PBHs with a power law mass function. The simulated scenarios are consistent with the ALMA observations, so PBH dark matter cannot be ruled out as a cause of flux density ratio anomalies. Our analysis shows that the anomalous flux density ratio for B1422+231 can be explained by a lens model with a significant fraction of dark matter being PBHs. This study demonstrates the potential for new constraints on PBH dark matter using ALMA observations of multiply imaged strong gravitational lenses. Full article

Within the framework of the quantum-statistical approach, utilizing both non-Hermitian Hamiltonian and Lindblad’s jump operators, one can derive various generalizations of the von Neumann equation for reduced density operators, also known as hybrid master equations. If one considers the evolution of pure states only, i.e., disregarding the coherence between states and spontaneous transitions from pure to mixed states, then one can resort to quantum-mechanical equations of the Schrödinger type. We derive them from the hybrid master equations and study their main properties, which indicate that our equations have a larger range of applicability compared to other generalized Schrödinger equations proposed hitherto. Among other features, they can describe not only systems which remain in the stationary eigenstates of the Hamiltonian as time passes, but also those which evolve from those eigenstates. As an example, we consider a simple but important model, a quantum harmonic oscillator driven by both Hamiltonian and non-Hamiltonian terms, and derive its classical limit, which turns out to be the damped harmonic oscillator. Using this model, we demonstrate that the effects of dissipative environments of different types can cancel each other, thus resulting in an effectively dissipation-free classical system. Another discussed phenomenon is whether a non-trivial quantum system can reduce to a classical system in free motion, i.e., without experiencing any classical Newtonian forces. This uncovers a large class of quantum-mechanical non-Hamiltonian systems whose dynamics are not determined by conventional mechanics’ potentials and forces, but rather come about through quantum statistical effects caused by the system’s environment. Full article

In this study, we developed a new method for finding the quantum probability density of arrival at the detector. The evolution of the quantum state restricted to the region outside of the detector is described by a restricted Hamiltonian that contains a non-Hermitian boundary term. The non-Hermitian term is shown to be proportional to the flux of the probability current operator through the boundary, which implies that the arrival probability density is equal to the flux of the probability current. Full article

Combining gravity with quantum theory is still a work in progress. On the one hand, classical gravity is the geometry of space-time determined by the energy–momentum tensor of matter and the resulting nonlinear equations; on the other hand, the mathematical description of a quantum system is Hilbert space with linear equations describing evolution. In this paper, various measures in Hilbert space will be presented. In general, distance measures in Hilbert space can be divided into measures determined by energy and measures determined by entropy. Entropy measures determine quasi-distance because they do not satisfy all the axioms defining distance. Finding a general rule to determine such a measure unambiguously seems to be fundamental. Full article

We study the evolution of quantum fluctuations of gravity around an inflationary solution in renormalizable quantum gravity, in which the initial scalar-fluctuation dominance is shown by the background-free nature expressed by a special conformal invariance. Inflation ignites at the Planck scale and continues until spacetime phase transition occurs at a dynamical scale of about ${10}^{17}$ GeV. We show that during inflation, the initially large scale-invariant fluctuations reduce in amplitude to the appropriate magnitude suggested by tiny CMB anisotropies. The goal of this research is to derive the spectra of scalar fluctuations at the phase transition point, that is, the primordial spectra. A system of nonlinear evolution equations for the fluctuations is derived from the quantum gravity effective action. The running coupling constant is then expressed by a time-dependent average following the spirit of the mean field approximation. In this paper, we determine and examine various nonlinear terms, not treated in previous studies such as the exponential factor of the conformal mode. These contributions occur during the early stage of inflation when the amplitude is still large. Moreover, in order to verify their effects concretely, we numerically solve the evolution equation by making a simplification to extract the most contributing parts of the terms in comoving momentum space. The result indicates that they serve to maintain the initial scale invariance over a wide range beyond the comoving Planck scale. This is a challenge toward the derivation of the precise primordial spectra, and we expect in the future that it will lead to the resolution of the tensions that have arisen in cosmology. Full article

At the Relativistic Heavy Ion Collider (RHIC), the Polarized Atomic Hydrogen Gas Jet Target polarimeter (HJET) is employed for the precise measurement of the absolute transverse (vertical) polarization of proton beams, achieving low systematic uncertainties of approximately ${\sigma }_P^{\mathrm{syst}}/P\le 0.5\%$. The acquired experimental data not only facilitated the determination of single $A_{\mathrm{N}}\left(t\right)$ and double $A_{\mathrm{NN}}\left(t\right)$ spin analyzing powers for 100 and 255 GeV proton beams, but also revealed a non-zero Pomeron spin-flip contribution through a Regge fit. Preliminary results obtained for forward inelastic $p^{\uparrow }p$ and elastic $p^{\uparrow }A$ analyzing powers will be discussed. The success of the HJET at RHIC suggests its potential application for proton beam polarimetry at the upcoming Electron–Ion Collider (EIC), aiming for an accuracy of 1%. Moreover, the provided analysis indicates that the RHIC HJET target can serve as a tool for the precision calibration, with the required accuracy, of the ${}^3$He beam polarization at the EIC. Full article

The real-time light curve classification of transients is helpful in searching for rare transients. We propose a new algorithm based on machine learning, namely the Temporary Convective Network and Light Gradient Boosting Machine Combined with Weight Module Algorithm (TLW). The TLW algorithm can classify the photometric simulation transients data in g, r, i bands provided via PLAsTiCC, typing Tidal Disruption Event (TDE), Kilonova (KN), Type Ia supernova (SNIa), and Type I Super-luminous supernova (SLSN-I). When comparing the real-time classification results of the TLW algorithm and six other algorithms, such as Rapid, we found that the TLW algorithm has the best comprehensive performance indexes and has the advantages of high precision and high efficiency. The average accuracy of TLW is 84.54%. The average implementation timings of the TLW algorithm for classifying four types of transients is 123.09 s, which is based on TensorFlow’s architecture in windows and python. We use three indicators to prove that the TLW algorithm is superior to the classical Rapid algorithm, including Confusion Matrix, PR curve, and ROC curve. We also use the TLW algorithm to classify ZTF real transients. The real-time classification results for ZTF transients show that the accuracy of the TLW algorithm is higher than the other six algorithms. Full article

The ALICE collaboration recently reported the mean transverse momentum as a function of charged-particle multiplicity for different pp-collision classes defined based on the “jettiness” of the event. The event “jettiness” is quantified using transverse spherocity that is measured at midpseudorapidity ($\left|\eta \right|<0.8$) considering charged particles with transverse momentum within $0.15<p_{\mathrm{T}}<10$ GeV/c. Comparisons to PYTHIA 8 (tune Monash) predictions show a notable disagreement between the event generator and data for jetty events that increases as a function of charged-particle multiplicity. This paper reports on the origin of such a disagreement. Since at intermediate and high $p_{\mathrm{T}}$ ($2<p_{\mathrm{T}}<10$ GeV/c), the spectral shape is expected to be modified by color reconnection or jets, their effects on the average $p_{\mathrm{T}}$ are studied. The results indicate that the origin of the discrepancy is the overpredicted multijet yield by PYTHIA 8, which increases with the charged-particle multiplicity. This finding is important to understand the way transverse spherocity and multiplicity bias the pp collisions and how well models like PYTHIA 8 reproduce those biases. The studies are pertinent since transverse spherocity is currently used as an event classifier by experiments at the LHC. Full article

The origin of the broad-line region (BLR) clouds in active galactic nuclei is still under discussion. We develop a scenario in which the clouds in the outer, less ionized part of the BLR are launched by the radiation pressure acting on dust. Most of the outflow forms a failed wind, so we refer to it as failed radiatively accelerated dusty outflow (FRADO), but, for a certain parameter range, actual outflow also takes place. We aim to test the model predictions. In this paper, we present the calculation of the angular distribution of clouds and the net covering factor as this affects the fraction of radiation that can be intercepted and reprocessed in the form of the H$\beta$ or Mg II emission line. The results reveal that the covering factor is intricately linked to the mass, accretion rate, and metallicity of the clouds. Notably, as these parameters increase, so does the covering factor, shedding light on the dynamic interplay between the central engine and the surrounding material in AGNs. Full article

We reconstruct type II supergravities by using building blocks of $O(d)\times O(d)$ invariants. These invariants are obtained by explicitly analyzing $O(d)\times O(d)$ transformations of 10 dimensional massless fields. Similar constructions are performed by employing double field theory or generalized geometry, but we completed the reconstruction within the framework of the supergravities. Full article

A search has been carried out for Magnetized Quark Nuggets (MQNs) accumulating in iron ore over geologic time. MQNs, which are theoretically consistent with the Standard Models of Physics and of Cosmology, have been suggested as dark-matter candidates. Indirect evidence of MQNs has been previously inferred from observations of magnetars and of non-meteorite impact craters. It is shown in this paper that MQNs can accumulate in taconite (iron ore) and be transferred into ferromagnetic rod-mill liners during processing of the ore. When the liners are recycled to make fresh steel, they are heated to higher than the Curie temperature so that their ferromagnetic properties are destroyed. The MQNs would then be released and fall into the ferromagnetic furnace bottom where they would be trapped. Three such furnace bottoms have been magnetically scanned to search for the magnetic anomalies consistent with trapped MQNs. The observed magnetic anomalies are equivalent to an accumulation rate of ~1 kg of MQNs per 1.2 × 10⁸ kg of taconite ore processed. The results are consistent with MQNs but there could be other, unknown explanations. We propose an experiment and calculations to definitively test the MQN hypothesis for dark matter. Full article

In this article, we study the form of the deviation of geodesics (tidal forces) and the Raychaudhuri equation in a Schwarzschild–Finsler–Randers (SFR) spacetime which has been investigated in previous papers. This model is obtained by considering the structure of a Lorentz tangent bundle of spacetime and, in particular, the kind of the curvatures in generalized metric spaces where there is more than one curvature tensor, such as Finsler-like spacetimes. In these cases, the concept of the Raychaudhuri equation is extended with extra terms and degrees of freedom from the dependence on internal variables such as the velocity or an anisotropic vector field. Additionally, we investigate some consequences of the weak-field limit on the spacetime under consideration and study the Newtonian limit equations which include a generalization of the Poisson equation. Full article

Past studies have empirically demonstrated a surprising agreement between gravitational waveforms computed using adiabatic–driven–inspiral point–particle black hole perturbation theory (ppBHPT) and numerical relativity (NR) following a straightforward calibration step, sometimes referred to as $\alpha$-$\beta$ scaling. Specifically focusing on the quadrupole mode, this calibration technique necessitates only two time-independent parameters to scale the overall amplitude and time coordinate. In this article, part of a Special Issue, we investigate this scaling for non-spinning binaries at the equal-mass limit. Even without calibration, NR and ppBHPT waveforms exhibit an unexpected degree of similarity after accounting for different mass scale definitions. Post-calibration, good agreement between ppBHPT and NR waveforms extends nearly up to the point of the merger. We also assess the breakdown of the time-independent assumption of the scaling parameters, shedding light on current limitations and suggesting potential generalizations for the $\alpha$-$\beta$ scaling technique. Full article

Axions can be stimulated to decay into photons by ambient photons of the right frequency or by photons from the decay of neighboring axions. If the axion density is high enough, the photon intensity can be amplified, which is a type of lasing or an axion maser. Here, we review the astrophysical situations where axion lasing can appear and possibly be detected. Full article

The evolution of hard probes in a medium is a complex multiscale problem that significantly benefits from the use of Effective Field Theories (EFTs). Within the EFT framework, we aim to define a series of EFTs in a way that addresses each energy scale individually in separate steps. However, studying hard probes in a medium presents challenges. This is because an EFT is typically constructed by formulating the most general Lagrangian compatible with the problem’s symmetries. Nevertheless, medium effects may not always be encoded adequately in an effective action. In this paper, we construct an EFT that is valid for studying the evolution of a heavy quark in a QCD plasma containing few other heavy quarks, where degrees of freedom with an energy of the order of the temperature scale are integrated out. Through this example, we explicitly demonstrate how to handle the doubling of degrees that arise in non-equilibrium field theory. As a result, we derive a Fokker–Planck equation using only symmetry and power counting arguments. The methods introduced in this paper will pave the way for future developments in the study of quarkonium suppression. Full article