Quantum coherence serves as a fundamental resource for generating intrinsic randomness, yet the quantification of randomness in quantum random number generators (QRNGs) based on spontaneous emission has remained largely phenomenological. Existing randomness analysis lacks rigorous adversarial models and a clear characterization of the role of quantum coherence in these systems. In this work, we develop a comprehensive quantum information-theoretic framework for randomness generation in spontaneous emission processes. We characterize two distinct eavesdropping strategies: one where the adversary directly accesses the atom ensemble, and the other where the adversary accesses only its purification. Our analysis reveals that when randomness is generated through single-photon detection and temporal mode measurements, the QRNG is vulnerable to the first adversary scenario, though it still guarantees a lower bound on intrinsic randomness against the second adversary scenario even under maximal information leakage from the atoms. In contrast, QRNGs based on spatial mode detection and phase fluctuations demonstrate security against both types of adversaries, providing robust randomness generation. Furthermore, we provide a quantitative calculation of intrinsic randomness for these spontaneous-emission-based QRNG schemes.

In this paper, a constrained control approach to variable speed limit (VSL) control for macroscopic partial differential equations (PDE) traffic models is developed. Control Lyapunov function (CLF) theory for ordinary differential equations (ODE) is extended to account for spatially and temporally varying states and control inputs. The stabilizing CLF is then unified with safety constraints through the introduction of spatially varying control barrier functions (sCBF). These methods are applied to in-domain VSL control of the Lighthill-Whitham-Richards (LWR) model to regulate traffic density to a desired profile while ensuring the density remains below prescribed limits enforced by the sCBF. Results show that incorporating constrained control minimally affects the stabilizing control input while successfully maintaining the density with the defined safe set.

In his book "Metric structures for Riemannian and non-Riemannian spaces", Gromov defined two properties of Riemannian manifolds, ellipticity and quasiregular ellipticity, and suggested that there may be a connection between the two. Since then, groups of researchers working independently have proved strikingly similar results about these two concepts. We obtain new topological obstructions to the two properties: most notably, we show that closed manifolds of both types must have virtually abelian fundamental group. We also give the first examples of open manifolds which are elliptic but not quasireguarly elliptic and vice versa. Whether there is a direct connection between these properties -- and, in particular, whether they are equivalent for closed manifolds -- remains elusive.

Hybrid quarkonia -exotic hadrons with explicit gluonic degrees of freedom- have gained increasing attention in hadron spectroscopy, particularly with the ongoing discovery of new XYZ mesons. In this work, we update the spectrum of heavy hybrid mesons in the charmonium and bottomonium sectors using the Born-Oppenheimer Effective Field Theory framework, by incorporating the latest lattice QCD results for hybrid static potentials. We refine earlier calculations and analyze allowed transitions from hybrids to conventional quarkonia, including both spin-conserved and spin-flip decays. We carry out a comprehensive error analysis and discuss the reliability of our results. We compare them to experimental data of the Particle Data Group, which allows us to identify hybrid candidates among the observed XYZ states. We provide hybrid or quarkonium interpretations for nearly all heavy isospin-zero mesons observed and incorporate new hybrid candidates.

We construct bulk-deformed orbifold Hamiltonian Floer theory for a global quotient orbifold, that is the quotient of a smooth closed symplectic manifold by a finite group acting faithfully via symplectomorphisms. The moduli spaces define an `ordered marked Flow category', which we equip with a coherent presentation via derived orbifolds. The global charts for orbifold Floer cylinders are built from moduli spaces of holomorphic curves in a quotient of projective space by a free action of the given finite group.

Episodic star formation cycles in both high- and low-redshift galaxies have gained more and more evidence. This paper aims to understand the detailed physical processes behind such behaviors and investigate how such an episodic star-forming scenario can explain the scatter in star-formation rate (SFR) of star-forming main-sequence galaxies. This is achieved through tracing back in time the history of z=0 star-forming central galaxies in the TNG100 simulation over the past 7-8 Gyrs. As the first paper in this series, we provide an overview of the episodic star formation history. We find that two branches of star formation typically develop during each episode: while one branch happens in heavily metal-enriched gas in the centers of galaxies, a secondary branch starts in lower-metallicity regions at galaxy outskirts where fresh gas first arrives, and gradually progresses to inner regions of galaxies. Additionally, the temporal variation in the SFR at galaxy outskirts is more significant than that at centers. As a consequence, the metallicities in both gas and young stars exhibit remarkably different distributions between SFR peaks and valleys. The resulting temporal SFR fluctuation within individual galaxies has an average of ~ 0.2 dex, while the intrinsic differentiation between (the historical mean of) galaxies is ~ 0.15 dex. These two together can well account for the scatter in SFR of ~ 0.25 dex as observed for z=0 star-forming main-sequence galaxies.

Bubble curtains are line bubble plumes that are used to mitigate saltwater intrusion in ship locks. When the lock gate that separates saline seawater from fresh river water is opened, a lock-exchange flow develops. Installing a bubble curtain at the gate location disrupts this flow and reduces saltwater infiltration. For real-world applications, it is important to quantify how effective the bubble curtain is as a function of the key governing parameters. To this end, we performed multiphase large-eddy simulations that faithfully reproduce earlier experimental results including the two distinct operating regimes: the breakthrough regime and the curtain-driven regime. This paper focuses on the curtain-driven regime and seeks to clarify how the effectiveness of bubble curtains evolves over time. The detailed spatial and temporal data from the simulations, together with the ability to systematically vary the governing parameters, enabled us to overcome several limitations inherent in previous experiments. Furthermore, the simulations were used to obtain parameter values to build a semi-analytical model. Both the simulations and the semi-analytical model successfully capture and elucidate the time evolution of the density field and of the bubble curtain's effectiveness. The findings highlight that the time elapsed since the gate opening and the transient dynamics play a crucial role in determining the performance of bubble curtains for mitigation of salt intrusion.

We define supersymmetric zeta functions and supersymmetric determinants, which can reveal spectral properties complementary to those captured by the supersymmetric indices. They play a crucial role in analyzing the Cardy-like behaviors of the supersymmetric indices and the supersymmetric Casimir energies associated with the supersymmetric partition functions. We investigate a variety of examples of the supersymmetric zeta functions and determinants for two-, four-, and six-dimensional supersymmetric field theories.

In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational dynamics with respect to this coherent state basis, which generates time evolution of the spacetime with respect to a clock at infinity. Since the coherent states are not orthogonal, an initial quasiclassical geometry is dynamically driven into a superposition of different amplitudes. Our framework provides a dynamical mechanism for tunneling between geometries that is ubiquitous in a number of approaches to quantum gravity, from loop quantum gravity to the Euclidean path integral. We apply our framework to the problem of black hole evaporation, providing a hint at how unitarity may be preserved with the inclusion of quantum corrections to the semiclassical evolution of the black hole.

We develop a continuous time discrete choice model of peer effects. The distinctive feature of the model is that agents might not consider all peers at the moment of making a decision. Instead, they select some of them on the basis of a mechanism that depends on recent choices. We characterize the equilibrium behavior and study the empirical content of the limited attention peer effect model. We allow changes in the choices of peers to affect both the set of peers to which the agent pays attention and her preferences over the alternatives. We exploit variation in choices together with variation in the size of the set of potential peers (or reference groups) to recover the preferences of the agents and the peer selection mechanisms. We apply our results to model expansion and contraction decisions by fast-food restaurants and find evidence of limited attention to actions of competitors.

We present a systematic comparison between {\it XMM-Newton} velocity maps of the Virgo, Centaurus, Ophiuchus and A3266 clusters and synthetic velocity maps generated from the Illustris TNG-300 simulations. Our goal is to constrain the physical conditions and dynamical states of the intracluster medium (ICM) through a data-driven approach. We employ a Siamese Convolutional Neural Network (CNN) designed to identify the most analogous simulated cluster to each observed system based on the morphology of their line-of-sight velocity maps. The model learns a high-dimensional similarity metric between observations and simulations, allowing us to capture subtle kinematic and structural patterns beyond traditional statistical tests. We find that the best-matching simulated halos reproduce the observed large-scale velocity gradients and local kinematic substructures, suggesting that the ICM motions in these clusters arise from a combination of gas sloshing, AGN feedback, and minor merger activity. Our results demonstrate that deep learning provides a powerful and objective framework for connecting X-ray observations to cosmological simulations, offering new insights into the dynamical evolution of galaxy clusters and the mechanisms driving turbulence and bulk flows in the hot ICM.

In this paper, we study an optimal dividend and capital-injection problem in a Cramér--Lundberg model where claim arrivals follow a Hawkes process, capturing clustering effects often observed in insurance portfolios. We establish key analytical properties of the value function and characterise the optimal capital-injection strategy through an explicit threshold. We also show that the value function is the unique viscosity solution of the associated HJB variational inequality. For numerical purposes, we first compute a benchmark solution via a monotone finite-difference scheme with Howard's policy iteration. We then develop a reinforcement learning approach based on policy-gradient and actor-critic methods. The learned strategies closely match the PDE benchmark and remain stable across initial conditions. The results highlight the relevance of policy-gradient techniques for dividend optimisation under self-exciting claim dynamics and point toward scalable methods for higher-dimensional extensions.

Through flat-folding, origami provides an extremely compact packaging strategy for deployable structures in aerospace, architecture, and robotics. However, origami's flat, volumeless facets limit the formation of smooth curvature, restricting its applicability in systems where smooth curved geometries are essential for performance, such as aerospace and electromagnetic communication systems. Here, we propose volumetric origami that preserves smooth curvature and an inverse design method that generates flat-foldable volumetric origami for given target curved surfaces. The flat-foldability enables arbitrarily prescribed compactness in volumetric origami folding, with its stowage efficiency governed by the number of cells and the target profile. The structural integrity and engineering feasibility of volumetric origami are validated through successful flight testing of a UAV equipped with flat-foldable volumetric origami wings replicating a target airfoil. Our approach bridges the gap between planar origami and the curvature requirements of engineering systems, expanding design freedom for curved structures under stringent spatial constraints.

Let $K$ be a discretely valued Henselian field. Creutz and Viray show that the degree set of a curve $C$ over a $p$-adic field can miss infinitely many multiples of the index of $C$, a phenomenon that cannot occur over finitely generated fields. For curves $C/K$ with a cyclic cover of $\mathbb{P}^1$ of prime degree, under mild assumptions, we completely characterize how and when this behavior can occur, and give a method for computing degree sets of curves of this type.

We present the mass-metallicity relation for star-forming galaxies in the MUSE Quasar Nebula 01 (MQN01) field, a massive cosmic web node at $z \sim 3.245$, hosting one of the largest overdensities of galaxies and AGNs found so far at $z > 3$. Through James Webb Space Telescope (JWST) Near Infrared Spectrograph (NIRSpec) spectra and images from JWST and Hubble Space Telescope (HST), we identify a sample of 9 star-forming galaxies in the MQN01 field with detection of nebular emission lines ($\rm Hβ$, [OIII], $\rm Hα$, [NII]), covering the mass range of $\rm 10^{7.5}M_\odot - 10^{10.5}M_\odot$. We present the relations of the emission-line flux ratios versus stellar mass for the sample and derive the gas-phase metallicity based on the strong line diagnostics of [OIII]$\lambda5008$/$\rm Hβ$ and [NII]$\lambda6585$/$\rm Hα$. Compared to the typical, field galaxies at similar redshifts, MQN01 galaxies show relatively higher [NII]$\lambda6585$/$\rm Hα$ and lower [OIII]$\lambda5008$/$\rm Hβ$ at the same stellar mass, which implies a higher metallicity by about $0.25\pm 0.07$ dex with respect to the field mass-metallicity relation. These differences are decreased considering the ``Fundamental Metallicity Relation'', i.e. if the galaxies' Star Formation Rates (SFR) are also taken into account. We argue that these results are consistent with a scenario in which galaxies in overdense regions assemble their stellar mass more efficiently (or, equivalently, start forming at earlier epochs) compared to field galaxies at similar redshifts.

The latest CMB data from ACT DR6, combined with Planck, DESI, and BICEP/Keck, indicate a slight upward shift in the scalar spectral index, placing several previously favored inflationary models under tension. We study an inflationary scenario within the framework of $f(R, T)$ gravity, featuring a nonminimal matter-curvature coupling, where the inflaton is a noncanonical scalar field with a generalized kinetic energy. Using the Hamilton-Jacobi formalism, we express the Hubble parameter as a function of the scalar field and consider two forms of $H(ϕ)$, a power-law and an exponential one, deriving the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$. Comparison with ACT DR6 allows us to explore the parameter space, showing that the power-law case is compatible with the data across a wide range, while the exponential form requires a large number of e-folds. We then study reheating, noting its close link with the inflationary dynamics. By imposing the bound on overproduction of primordial gravitational waves encoded in the constraint on $ΔN_{\text{eff}}$, we obtain a lower limit on the reheating temperature, which becomes particularly restrictive for the stiff reheating equation of state $ω_{\text{re}}$. This bound implies that the total number of e-folds should not exceed $N\lesssim 64(65)$. The predicted gravitational-wave spectrum shows an enhanced high-frequency amplitude, potentially observable by future detectors. We also examine consistency with the Swampland conjectures and the Trans-Planckian Censorship Conjecture, finding that combining $f(R, T)$ gravity with noncanonical dynamics provides a rich and testable framework for the early universe.

Radiation of a charged particle crossing an alternating stack of slabs in the optical region is considered. Both disordered and periodic stacks are investigated. It is shown that for special type of alternating disordered and periodic stacks the radiation problem can be solved exactly for backward and forward Brewster observation angles. Strong $N^2$ dependence of radiation intensity on slab number is re-established in special case of the disordered stack. This leads to strong directivity either on forward or on backward Brewster angles depending on the type of stack randomness. In certain type of periodic photonic crystal, a strong energy dependence $E^4$ for relativistic particles of the radiation intensity, observed at Brewster's angle is found. Further increment of particle energy leads to saturation. The band structure of the corresponding photonic crystal (PhC) has a behavior, analogous to the Dirac cones in graphene. We suggest this special type $1D$ photonic crystal for application as a detector of relativistic particles.

We introduce a new analytic method for studying Witten zeta function of a root system $Φ$, based on a refined manipulation of an integral representation involving the Hurwitz zeta function. As an application, we prove high-order vanishing at negative even integers. This technique also describes non-trivially, the arithmetic nature of the leading term, in which the highest root of $Φ$ makes a surprising appearance.

Earth-like exoplanets can create resonant structures in exozodiacal dust through mean motion resonances (MMRs). These structures not only suggest the presence of such planets, but also act as potential noise sources in future mid-infrared (MIR) nulling interferometry observations. We aim to investigate how resonant structures in exozodiacal dust vary across stellar spectral types (F4--M4), and to evaluate how stellar wind drag affects their morphology and brightness in mature planetary systems. We conducted numerical simulations of dust dynamics, extending earlier studies by including spectral type variation in stellar wind drag in addition to Poynting-Robertson (PR) drag. Our models represented systems of a few Gyr hosting an Earth-like exoplanet in the habitable zone (HZ). We produced spatially resolved maps of optical depth and thermal emission for different stellar spectral types. Our simulations showed that resonant ring structures were formed for all stellar spectral types considered. In particular, we found that stellar wind drag played a critical role in shaping dust dynamics around old M-type stars, where it could dominate over PR drag by a factor of approximately 44. This reduced the contrast of resonant rings relative to the background disk, compared to cases without spectral type variation in stellar wind. Across different spectral types, the optical depth contrast of the resonant ring increased for lower-mass stars, assuming a fixed background level. Asymmetric thermal emission distributions were derived across all spectral types, which peaked for K-type stars. Our findings highlight the importance of incorporating both resonant dynamics and stellar wind effects when modeling exozodiacal dust around stars of different spectral types.

Denote by $\mathbb F_q$ the finite field of order $q$ and by $\mathbb F_{q^n}$ its extension of degree $n$. Some $a\in\mathbb F_{q^n}$ is called primitive if it generates the multiplicative group $\mathbb F_{q^n}^*$ and it is called $q^n/q$-normal if its $\mathbb F_q$-conjugates form an $\mathbb F_q$-basis of $\mathbb F_{q^n}$ if the latter is viewed as an $\mathbb F_q$-vector space. Furthermore, some $a\in\mathbb F_{q^n}$ is called $q^n/q$-completely normal if it is $q^n/q^d$-normal for all $d\mid n$. In this work we prove a new construction of sets of completely normal elements and, we establish, under conditions, the existence of elements that are simultaneously primitive and $q^n/q$-completely normal, covering some yet unresolved cases of a 30-year-old conjecture by Morgan and Mullen.

We explore a method, initiated by Guichard in 1890, which allows to generate sequences of Voss surfaces, starting from an arbitrarily chosen pseudospherical surface and a seed solution of the Moutard equation, by means of two simple transformations. In this paper we 1) identify the Guichard transformations with the well-known recursion operator for symmetries of the sine-Gordon equation and its inverse; 2) prove a lemma which allows us to derive the length of Guichard's sequences from the invariance properties of the initial sine-Gordon solution; 3) introduce an extended class of inverted operators, expanding the class of Voss surfaces obtainable by quadratures. A number of Voss nets are presented explicitly. As the main instrument, we reinterpret Guichard's transformations in terms of the recursion operators for sine-Gordon symmetries. Simultaneously, we clarify relevant aspects of Guthrie's formalism, paving the way for the future employment of the entire division algebra of recursion operators.

If a complex $X$ is a subcomplex of a diagrammatically reducible 2-complex $Y$ that has locally indicable fundamental group, then $X$ has locally indicable fundamental group. This is a consequence of the Corson-Trace characterization of diagrammatic reducibility. In this paper we use a Corson-Trace like characterization of diagrammatic reducibility away from a subcomplex to obtain a considerable stronger result. We apply this to the question of local indicability in the context of Whitehead's asphericity conjecture. We show that an injective labeled oriented tree (LOT) that is diagrammatically reducible of degree 2, and all its quotients are as well, is locally indicable.

Quantifying the collision risk of birds and bats with offshore wind turbines requires an understanding of the drivers of flying animal behavior at offshore wind sites. An omnidirectional S-band radar system was deployed on a research barge on the Northeastern Shelf of the United States (40.9 deg N, 70.79 deg W) and collected data for a 5-week window during the 2024 autumn bird and bat migration. The barge also supported two profiling lidar systems that measured the wind speed and direction. This study presents a first methodological approach for analyzing radar and lidar data together, providing a framework for future analyses of offshore bird and bat movements that can be used to improve collision risk models. Coupling the radar animal tracks with measured wind speed profiles revealed that wind is a driver of animal presence, flight direction, flight height, and flight speed. Further, a hierarchical clustering methodology was developed to investigate behavior by approximate animal size. For example, smaller animals had concentrated flight direction distributions aligned with the wind and flew at a variety of altitudes, whereas bigger animals flew in a wide variety of directions but were concentrated at low altitudes. Our results provide the first insights into animal behavior at offshore wind sites with paired radar and lidar data.

We study the equilibrium glassy behavior of a multimode random laser model with nonlinear four-body quenched disordered interactions and a global smoothed-cubic constraint on mode intensities. This constraint, which provides a more realistic representation of gain saturation than the commonly used spherical constraint, prevents intensity condensation while preserving the dense, long-range interaction structure characteristic of many multistate random lasers. The model effective Hamiltonian is a function of mode amplitudes with random frequencies and is defined on a complete mode-locked graph. Using large-scale GPU-accelerated Monte Carlo simulations with the Parallel Tempering algorithm, we analyze systems of varying sizes to probe their thermodynamic-limit behavior. Finite-size scaling of the specific heat, of the Parisi overlap distributions, and of the inverse participation ratio's reveals a spin-glass transition, with critical exponents matching the mean-field Random Energy Model universality class. The smoothed-cubic constraint produces broad, non-condensed intensity distributions, avoiding the pseudo-condensation seen in spherical models on the same interaction graph. Our results show that more realistic gain-saturation constraints preserve spin-glass characteristics while enabling simulations of larger, more dilute systems, providing a robust framework for studying glassy random lasers with self-starting mode-locking.

Given a positive, non-increasing sequence $a$ with finite sum equal to $1$, we consider the family of all closed subsets of $[0,1]$ whose complementary open intervals have lengths given by a rearrangement of the sequence $a$. We study the full range of possible $θ$-intermediate dimensions of these sets and, under suitable assumptions on the sequence, we show that this range forms a closed interval, whose endpoints we compute explicitly. This paper fills a gap in the literature concerning the dimensional properties of complementary sets.

We study tunable nanoscale femtosecond coherent radiation based on a coupled nanowire pair (CNP) structure that is excited by a strong laser. The structure functions as a nanoscale undulator (NU): the electrons moving through the nanogap are driven by a spatially periodic, transverse optical near-field. We show that the transverse near-field can actively shape the electron wavefunction by inducing both a periodic oscillation and a quantum squeezing of its width. We then validate this theoretical framework by numerically solving the relativistically corrected time-dependent Schrödinger equation (RC-TDSE). The generated femtosecond pulse trains can be spectrally, temporally, and spatially controlled. This framework establishes the transverse optical near-field interaction as a novel mechanism to spatiotemporally shape electron wavefunctions, which illuminates a path to versatile platform for on-chip femtosecond coherent light source and the application in free-electron quantum optics.

In this paper, we generalize the notion of rational singularities for any reflexive sheaf of rank $1$, link our notion of rational singularities with the notion of rational singularities in [Kov11], and prove generalizations of standard facts about rational singularities. Moreover, by using a definition of non-rational locus, we introduce the notion of $(B_{q+1})$ as a dual notion of well-known Serre's notion of $(S_{q+1})$, and prove a theorem about $q$-birational morphisms.

In linear perturbation theory for Kerr black holes, there are two equivalent formalisms, namely the Teukolsky and the Sasaki-Nakamura (SN) formalism. Typically, one defaults to the Teukolsky formalism, especially when calculating extreme mass ratio inspiral waveforms, and uses the SN formalism when dealing with extended sources, as it offers superior convergence when employing the Green's function method for calculating the inhomogeneous solution. In this work, we present a new scheme for solving the inhomogeneous SN equation, based on integration by parts, that eliminates the extra radial integration step required in the standard formulation to construct the source term for convolution with the SN variable. We derive also a SN source term that is valid for point particles on arbitrary motions around Kerr black holes. Our approach enables efficient computations of gravitational waveforms within the SN formalism in all cases, from compact to extended sources. We validate our scheme and code implementation against the literature and find excellent agreement, achieving comparable performance without employing any special optimization techniques.

We present AC-2168, an almost NIRCam-dark, millimetre-bright galaxy in the COSMOS field. The source was identified blindly in ALMA Band-4 continuum data and remains undetected in the COSMOS-Web DR1 NIRCam catalogue. We spectroscopically confirm a redshift of $z_{\rm spec}=6.631$ from [CII] 158 $μ$m and four tentatively detected CO lines in NOEMA and ALMA data. SED fitting to near-IR to millimetre photometry yields $\rm L_{IR}=1.6\times10^{12}\,L_\odot$, an SFR of $\rm 244\,M_\odot/yr$, heavy dust attenuation $\rm A_V=5.4$ mag, and a stellar mass $\rm M_\star=3.7\times10^{10}\,M_\odot$. From the millimetre continuum and [CII] emission, we infer a warm ISM with $\rm T_{\rm dust}=60K$, $\rm M_{dust}=3.0\times10^{8}\,M_\odot$ and $\rm M_{gas}=4.1\times10^{10}\,M_\odot$. AC-2168 has a gas fraction ($f_{\rm gas}=M_{\rm gas}/(M_\star+M_{\rm gas})$) of $\sim52\%$, a short depletion time of $\rm \sim170Myr$, a compact ($\rm \sim1kpc$) dust-continuum size, and an SFR consistent with the star-forming main sequence at its mass. These properties match expectations for progenitors of massive quiescent galaxies at the peak of their assembly, as implied by NIRSpec-based SFHs of $z\sim4-5$ systems. Using the blind detection, we estimate a space density of $\rm 7.8^{+18.0}_{-6.5}\times10^{-6}\,cMpc^{-3}$ for AC-2168-like NIRCam-dark galaxies at $z\sim6-7$, $\sim42\%$ of the abundance of massive quiescent galaxies at $z\sim4-5$. No overdensity of Ly$α$ emitters or Lyman-break galaxies is found nearby, suggesting AC-2168 does not lie in a prominent protocluster and highlighting the importance of unbiased blind surveys for this population.

Galaxy clusters can be used as powerful cosmological probes, provided one can obtain accurate mass estimates, which requires a precise knowledge of the underlying astrophysics of galaxy clusters. For these purposes, spatially resolved measurements of the thermodynamic properties of intra-cluster medium (ICM), such as density and temperature, are necessary. In particular, temperature estimates are traditionally obtained through spatially resolved X-ray spectroscopy. Such measurements suffer from their sensitivity to the chosen energy calibration, may exhibit inherent biases, and are especially hard to perform at high redshift as they require deep observations. In recent years however, millimetre wavelength data with high spatial resolution, comparable to the one of current X-ray telescopes, have begun to be available. This has enabled the implementation of new methods to infer and map the cluster temperature in individual clusters, using the combination of density maps from X-ray data and pressure maps from millimetre data. In this paper, we present the first systematic validation of this approach on a large sample of synthetic clusters generated in The Three Hundred hydrodynamical simulations. We show that we are able to recover theoretical estimates of the temperature, namely the mass-weighted and spectroscopic-like temperatures, within biases of the order of $\lesssim 1\%$ in the best cases, up to $\sim 10\%$ in average, with scatters of the order of $10\%$. To prepare the application of this approach to observed data, we discuss the modelling of the effective length $l_\mathrm{eff}$, a key quantity necessary for the combination of X-ray and SZ projected data. In particular we provide templates calibrated on simulations for this quantity, and investigate their impact in the recovery of the temperature map, compared to other standard models.