arXiv subjects

G. Pupillo

Publications and source records attributed to G. Pupillo.

At least 19 recordsLinked to original sources

arXiv2025

Supersolid crystals of dipolar excitons in a lattice

In condensed-matter physics, long-range correlations introduce quantum states of matter that challenge intuition. For instance, supersolids combine symmetry-breaking crystalline structure, i.e. density order, and frictionless superfluid flow. Envisioned over fifty years ago, supersolids have proven to only exist under very stringent conditions, with experimental evidence limited to few observations. Many-body phases with supersolid properties in fact reduce to a few recent observations for weakly interacting Bose gases. Here, we demonstrate a new framework to realize supersolid crystals in the strong interaction regime, by confining dipolar bosons in a lattice with long-range hopping. We study dipolar excitons that genuinely realize this lattice model. At fractional lattice fillings - 1/4, 1/3 and 1/2 - we report mesoscopic quantum solids, across over 100 sites, spontaneously breaking translational symmetry. At the same time, we show that off-diagonal long-range order is induced by long-range hopping, such that exciton solids are superfluids. State-of-the-art numerical methods quantitatively confirm that supersolidity builds up in the ground-state of the lattice Hamiltonian. Our studies of strongly-correlated supersolid crystals open new frontiers for exploration in condensed matter physics.

cond-mat.quant-gas↗

arXiv2025

The Northern Cross Fast Radio Burst project: V. Search for transient radio emission from Galactic magnetars

Context. The radio emission from magnetars is poorly understood and poorly characterized observationally, in particular for what concerns single pulses and sporadic events. The interest in it was boosted by the detection in 2020 of an extremely bright ms radio signal from the Galactic magnetar designated Soft Gamma Repeater (SGR) SGR J1935+2154, which occurred almost simultaneously with a typical magnetar short burst of X-rays. As of now, this event remains the Galactic radio pulse that is the most reminiscent of fast radio bursts (FRBs) and the only one with a sound association with a known progenitor. Aims. We aim to constrain the rate of impulsive radio events from magnetars, by means of an intensive monitoring using a high-sensitivity radio telescope. Methods. We performed a long-term campaign on seven Galactic magnetars (plus one candidate) using the Northern Cross transit radio telescope (in Medicina, Italy) searching for short timescales and dispersed radio pulses. Results. We obtained no detections in more than 560 hours of observation, setting an upper limit at 95% confidence level of <52 yr$^{-1}$ on the rate of events with energy >10$^{28}$ erg, which is consistent with limits in literature. Furthermore, under some assumptions on the magnetars properties and energetic behavior, we found that our upper limits point towards the fact that the entire population of FRBs observed cannot be explained by radio bursts emitted by magnetars.

astro-ph.HE↗

arXiv2024

The Northern Cross Fast Radio Burst project IV. Multi-wavelength study of the actively repeating FRB 20220912A

Fast radio bursts (FRBs) are energetic, millisecond-duration radio pulses observed at extragalactic distances and whose origins are still a subject of heated debate. A fraction of the FRB population have shown repeating bursts, however it's still unclear whether these represent a distinct class of sources. We investigated the bursting behaviour of FRB 20220912A, one of the most active repeating FRBs known thus far. In particular, we focused on its burst energy distribution, linked to the source energetics, and its emission spectrum, with the latter directly related to the underlying emission mechanism. We monitored FRB 20220912A at $408$ MHz with the Northern Cross radio telescope and at $1.4$ GHz using the $32$-m Medicina Grueff radio telescope. Additionally, we conducted $1.2$ GHz observations taken with the upgraded Giant Meter Wave Radio Telescope (uGMRT) searching for a persistent radio source coincident with FRB 20220912A, which included high energy observations in the $0.3-10$ keV, $0.4-100$ MeV and $0.03-30$ GeV energy range. We report $16$ new bursts from FRB 20220912A at $408$ MHz during the period between October 16$^{\rm th}$ 2022 and December 31$^{\rm st}$ 2023. Their cumulative spectral energy distribution follows a power law with slope $\alpha_E = -1.3 \pm 0.2$ and we measured a repetition rate of $0.19 \pm 0.03$ hr$^{-1}$ for bursts having a fluence of $\mathcal{F} \geq 17$ Jy ms. Furthermore, we report no detections at 1.4 GHz for $\mathcal{F} \geq 20$ Jy ms. These non-detections imply an upper limit of $\beta < -2.3$, with $\beta$ being the $408$ MHz $-$ $1.4$ GHz spectral index of FRB 20220912A. This is inconsistent with positive $\beta$ values found for the only two known cases in which an FRB has been detected in separate spectral bands. We find that FRB 20220912A shows a decline of four orders of magnitude in its bursting activity at $1.4$ GHz over a .. (abridged)

astro-ph.HE↗

arXiv2024

Study of solar brightness profiles in the 18-26 GHz frequency range with INAF radio telescopes II. Evidence for coronal emission

One of the most important objectives of solar physics is the physical understanding of the solar atmosphere, the structure of which is also described in terms of the density (N) and temperature (T) distributions of the atmospheric matter. Several multi-frequency analyses show that the characteristics of these distributions are still debated, especially for the outer coronal emission. We aim to constrain the T and N distributions of the solar atmosphere through observations in the centimetric radio domain. We employ single-dish observations from two of the INAF radio telescopes at the K-band frequencies (18 - 26 GHz). We investigate the origin of the significant brightness temperature ($T_B$) level that we detected up to the upper corona ($\sim 800$ Mm of altitude with respect to the photospheric solar surface). To probe the physical origin of the atmospheric emission and to constrain instrumental biases, we reproduced the solar signal by convolving specific 2D antenna beam models. The analysis of the solar atmosphere is performed by adopting a physical model that assumes the thermal bremsstrahlung as the emission mechanism, with specific T and N distributions. The modelled $T_B$ profiles are compared with those observed by averaging solar maps obtained during the minimum of solar activity (2018 - 2020). The T and N distributions are compatible (within $25\%$ of uncertainty) with the model up to $\sim 60$ Mm and $\sim 100$ Mm of altitude, respectively. The analysis of the role of the antenna beam pattern on our solar maps proves the physical nature of the atmospheric emission in our images up to the coronal tails seen in our $T_B$ profiles. The challenging analysis of the coronal radio emission at higher altitudes, together with the data from satellite instruments will require further multi-frequency measurements.

astro-ph.SR↗

arXiv2024

Study of solar brightness profiles in the 18-26 GHz frequency range with INAF radio telescopes I: solar radius

The Sun is an extraordinary workbench, from which several fundamental astronomical parameters can be measured with high precision. Among these parameters, the solar radius $R_{\odot}$ plays an important role in several aspects, such as in evolutionary models. Despite the efforts in obtaining accurate measurements of $R_{\odot}$, the subject is still debated and measurements are puzzling and/or lacking in many frequency ranges. We aimed to determine the mean, equatorial, and polar radii of the Sun ($R_c$, $R_{eq}$, and $R_{pol}$) in the frequency range 18.1 - 26.1 GHz. We employed single-dish observations from the newly-appointed Medicina "Gavril Grueff" Radio Telescope and the Sardinia Radio Telescope (SRT) throughout 5 years, from 2018 to mid-2023, in the framework of the SunDish project for solar monitoring. Two methods to calculate the radius at radio frequencies are considered and compared. To assess the quality of our radius determinations, we also analysed the possible degrading effects of the antenna beam pattern on our solar maps, using two 2D-models. We carried out a correlation analysis with the evolution of the solar cycle through the calculation of Pearson's correlation coefficient $\rho$. We obtained several values for the solar radius - ranging between 959 and 994 arcsec - and $\rho$, with typical errors of a few arcsec. Our $R_{\odot}$ measurements, consistent with values reported in literature, suggest a weak prolatness of the solar limb ($R_{eq}$ > $R_{pol}$), although $R_{eq}$ and $R_{pol}$ are statistically compatible within 3$\sigma$ errors. The correlation analysis using the solar images from Grueff shows (1) a positive correlation between the solar activity and the temporal variation of $R_c$ (and $R_{eq}$) at all observing frequencies, and (2) a weak anti-correlation between the temporal variation of $R_{pol}$ and the solar activity at 25.8 GHz.

astro-ph.SR↗

arXiv2022

Solar observations with single-dish INAF radio telescopes: continuum imaging in the 18-26 GHz range

We present a new solar radio imaging system implemented through the upgrade of the large single-dish telescopes of the Italian National Institute for Astrophysics (INAF), not originally conceived for solar observations. During the development and early science phase of the project (2018-2020), we obtained about 170 maps of the entire solar disk in the 18-26 GHz band, filling the observational gap in the field of solar imaging at these frequencies. These solar images have typical resolutions in the 0.7-2 arcmin range and a brightness temperature sensitivity <10 K. Accurate calibration adopting the Supernova Remnant Cas A as a flux reference, provided typical errors <3% for the estimation of the quiet-Sun level components and for active regions flux measurements. As a first early science result of the project, we present a catalog of radio continuum solar imaging observations with Medicina 32-m and SRT 64-m radio telescopes including the multi-wavelength identification of active regions, their brightness and spectral characterization. The interpretation of the observed emission as thermal bremsstrahlung components combined with gyro-magnetic variable emission pave the way to the use of our system for long-term monitoring of the Sun. We also discuss useful outcomes both for solar physics (e.g. study of the chromospheric network dynamics) and space weather applications (e.g. flare precursors studies).

astro-ph.SR↗

arXiv2022

What is the SKA-Low Sensitivity for Your Favourite Radio Source ?

The SKA will be the largest radio astronomy observatory ever built, providing unprecedented sensitivity over a very broad frequency (50 MHz to 15.3 GHz). The SKA-Low (50 - 350 MHz), will be built at the MRO in Western Australia. It will consist of 512 stations each composed of 256 dual-polarised antennas, and the sensitivity of an individual station is pivotal to the performance of the entire SKA-Low telescope. The answer to the question in the title is, it depends. The sensitivity of a low frequency array, such as an SKA-Low station, depends strongly on the pointing direction of the digitally formed station beam and the local sidereal time (LST), and is different for the two orthogonal polarisations of the antennas. The accurate prediction of the SKA-Low sensitivity in an arbitrary direction in the sky is crucial for future observation planning. We present here a sensitivity calculator for the SKA-Low radio telescope, using a database of pre-computed sensitivity values for two realisations of an SKA-Low station architecture. One realisation uses the log-periodic antennas selected for SKA-Low. The second uses a known benchmark, in the form of the bowtie dipoles of the MWA. Data collected by both stations (deployed at the MRO in 2019) were used to measure their sensitivity at selected frequencies and over at least 24 h intervals, and were compared to the predictions described in this paper. The sensitivity values stored in the SQLite database were pre-computed for the X, Y and Stokes I polarisations in 10 MHz frequency steps, 0.5 hour LST intervals, and 5 degree resolution in pointing directions. The database allows users to estimate the sensitivity of SKA-Low for their favourite object using interactive web-based or command line interface, which can also calculate the sensitivity for arbitrary pointing directions, frequencies, and times without interpolations.

astro-ph.IM↗

arXiv2022

The Northern Cross Fast Radio Burst project - II. Monitoring of repeating FRB 20180916B, 20181030A, 20200120E and 20201124A

In this work we report the results of a nineteen-month Fast Radio Burst observational campaign carried out with the North-South arm of the Medicina Northern Cross radio telescope at 408~MHz in which we monitored four repeating sources: FRB20180916B, FRB20181030A, FRB20200120E and FRB20201124A. We present the current state of the instrument and the detection and characterisation of three bursts from FRB20180916B. Given our observing time, our detections are consistent with the event number we expect from the known burst rate ($2.7 \pm 1.9$ above our 10$\sigma$, 38~Jy~ms detection threshold) in the 5.2 day active window of the source, further confirming the source periodicity. We detect no bursts from the other sources. We turn this result into a 95\% confidence level lower limit on the slope of the differential fluence distribution $\alpha$ to be $\alpha > 2.1$ and $\alpha > 2.2$ for FRB20181030A and FRB20200120E respectively. Given the known rate for FRB20201124A, we expect $1.0 \pm 1.1$ bursts from our campaign, consistent with our non-detection.

astro-ph.HE↗

arXiv2021

The Aperture Array Verification System 1: System overview and early commissioning results

The design and development process for the Square Kilometre Array (SKA) radio telescope, the Low Frequency Aperture Array component, was progressed during the SKA pre-construction phase by an international consortium, with the goal of meeting requirements for a critical design review. As part of the development process a full-sized prototype SKA Low station was deployed, the Aperture Array Verification System 1 (AAVS1). We provide a system overview and describe the commissioning results of AAVS1, which is a low frequency radio telescope with 256 dual-polarisation log-periodic dipole antennas working as a phased array. A detailed system description is provided, including an in-depth overview of relevant sub-systems, ranging from hardware, firmware, software, calibration,and control sub-systems. Early commissioning results cover initial bootstrapping, array calibration, stability testing, beam-forming,and on-sky sensitivity validation. Lessons learned are presented, along with future developments.

astro-ph.IM↗

arXiv2021

New results on proton-induced reactions on Vanadium for $^{47}$Sc production and the impact of level densities on theoretical cross sections

New data for the $^\mbox{nat}$V(p,x) reactions have been measured in the range 26-70 MeV, with production of the nuclides $^{47}$Sc, $^{43}$Sc, $^{44m}$Sc, $^{44g}$Sc, $^{46}$Sc, $^{48}$Sc, $^{42}$K, $^{43}$K, $^{48}$V, $^{48}$Cr, $^{49}$Cr, and $^{51}$Cr. The focus is on the production of $^{47}$Sc, a $\beta^-$-emitter suitable for innovative radiotheranostic applications in nuclear medicine. The measured cross sections for this radionuclide and its contaminants are compared with the theoretical excitation functions calculated with the TALYS code. In view of novel radiopharmaceutical applications, it is essential to accurately describe these cross-sections for the evaluation of yields, purities, and dose releases. Hence, we optimize the level-density parameters of the microscopic models in the TALYS code to obtain the best possible descriptions of the new data. We consider different irradiation conditions to estimate the production yields from the cross sections determined in this work.

nucl-ex↗

arXiv2021

A Southern-Hemisphere all-sky radio transient monitor for SKA-Low prototype stations

We present the first southern-hemisphere all-sky imager and radio-transient monitoring system implemented on two prototype stations of the low-frequency component of the Square Kilometre Array. Since its deployment the system has been used for real-time monitoring of the recorded commissioning data. Additionally, a transient searching algorithm has been executed on the resulting all-sky images. It uses a difference imaging technique, and has enabled identification of a wide variety of transient classes, ranging from human-made radio-frequency interference to genuine astrophysical events. Observations at the frequency 159.4 MHz and higher in a single coarse channel (0.926 MHz) were made with 2s time resolution, and multiple nights were analysed. Despite having modest sensitivity (~few Jy/beam), using a single coarse channel and 2-s imaging, the system detected bright transients from PSR B0950+08, proving that it can be used to detect bright transients of an astrophysical origin. The unusual, extreme activity of the pulsar PSR B0950+08 (up to ~155 Jy/beam) was initially detected in a "blind" search in the 2020-04-10/11 data and later assigned to this specific pulsar. The limitations of our data, however, prevent use from making firm conclusions of the effect being due to a combination of refractive and diffractive scintillation or intrinsic emission mechanisms. The system can routinely collect data over many days without interruptions; the large amount of recorded data at 159.4 and 229.7 MHz allowed us to determine a preliminary transient surface density upper limit of $1.32 \times 10^{-9} \text{deg}^{-2}$ for a timescale and limiting flux density of 2s and 42 Jy, respectively. We plan to extend the observing bandwidth to tens of MHz and improve time resolution to tens of milliseconds in order to increase the sensitivity and enable detections of Fast Radio Bursts below 300 MHz.

astro-ph.IM↗

arXiv2021

Multi-frequency observations of SGR J1935+2154

Magnetars are a promising candidate for the origin of Fast Radio Bursts (FRBs). The detection of an extremely luminous radio burst from the Galactic magnetar SGR J1935+2154 on 2020 April 28 added credence to this hypothesis. We report on simultaneous and non-simultaneous observing campaigns using the Arecibo, Effelsberg, LOFAR, MeerKAT, MK2 and Northern Cross radio telescopes and the MeerLICHT optical telescope in the days and months after the April 28 event. We did not detect any significant single radio pulses down to fluence limits between 25 mJy ms and 18 Jy ms. Some observing epochs overlapped with times when X-ray bursts were detected. Radio images made on four days using the MeerKAT telescope revealed no point-like persistent or transient emission at the location of the magnetar. No transient or persistent optical emission was detected over seven days. Using the multi-colour MeerLICHT images combined with relations between DM, NH and reddening we constrain the distance to SGR J1935+2154, to be between 1.5 and 6.5 kpc. The upper limit is consistent with some other distance indicators and suggests that the April 28 burst is closer to two orders of magnitude less energetic than the least energetic FRBs. The lack of single-pulse radio detections shows that the single pulses detected over a range of fluences are either rare, or highly clustered, or both. It may also indicate that the magnetar lies somewhere between being radio-quiet and radio-loud in terms of its ability to produce radio emission efficiently.

astro-ph.HE↗

arXiv2020

An X-Ray Burst from a Magnetar Enlightening the Mechanism of Fast Radio Bursts

Fast radio bursts (FRBs) are short (millisecond) radio pulses originating from enigmatic sources at extragalactic distances so far lacking a detection in other energy bands. Magnetized neutron stars (magnetars) have been considered as the sources powering the FRBs, but the connection is controversial because of differing energetics and the lack of radio and X-ray detections with similar characteristics in the two classes. We report here the detection by the AGILE satellite on April 28, 2020 of an X-ray burst in coincidence with the very bright radio burst from the Galactic magnetar SGR 1935+2154. The burst detected by AGILE in the hard X-ray band (18-60 keV) lasts about 0.5 seconds, it is spectrally cutoff above 80 keV, and implies an isotropically emitted energy ~ $10^{40}$ erg. This event is remarkable in many ways: it shows for the first time that a magnetar can produce X-ray bursts in coincidence with FRB-like radio bursts; it also suggests that FRBs associated with magnetars may emit X-ray bursts of both magnetospheric and radio-pulse types that may be discovered in nearby sources. Guided by this detection, we discuss SGR 1935+2154 in the context of FRBs, and especially focus on the class of repeating-FRBs. Based on energetics, magnetars with fields B ~ $10^{15}$ G may power the majority of repeating-FRBs. Nearby repeating-FRBs offer a unique occasion to consolidate the FRB-magnetar connection, and we present new data on the X-ray monitoring of nearby FRBs. Our detection enlightens and constrains the physical process leading to FRBs: contrary to previous expectations, high-brightness temperature radio emission coexists with spectrally-cutoff X-ray radiation.

astro-ph.HE↗

arXiv2020

Gamma-Ray and X-Ray Observations of the Periodic-Repeater FRB 180916 During Active Phases

FRB 180916 is a most intriguing source at 150 Mpc distance capable of producing repeating fast radio bursts with a periodic 16.35 day temporal pattern. We report on the X-ray and $γ$-ray observations of FRB 180916 obtained by AGILE and Swift. We focused on the recurrent 5-day time intervals of active radio bursting and present results obtained on Feb. 3 - 8; Feb. 25; Mar. 5 - 10; Mar. 22 - 28, 2020 during a multiwavelength campaign involving high-energy and radio observations. We also searched for temporal coincidences at millisecond timescales between all known radio bursts of FRB 180916 and X-ray and MeV events detectable by AGILE. We do not detect any simultaneous event or any extended X-ray and $γ$-ray emission on timescales of hours/days/weeks. Our cumulative X-ray (0.3-10 keV) flux upper limit of $5 \times\,10^{-14} \rm \, erg \, cm^{-2} s^{-1}$ (obtained during 5-day active intervals) translates into an isotropic luminosity upper limit of $L_{X,UL} \sim 1.5 \times\, 10^{41} \rm erg \, s^{-1}$. Observations above 100 MeV over a many-year timescale provide an average luminosity upper limit one order of magnitude larger. These results provide the so-far most stringent limits on high-energy emission from FRB 180916 and constrain the dissipation of magnetic energy from a magnetar-like source of radius $R_m$, internal magnetic field $B_m$ and dissipation timescale $τ_d$ to satisfy the relation $R_{m,6}^3 B_{m,16}^2 τ_{d,8}^{-1} \lesssim 1$, where $R_{m,6}$ is $R_m$ in units of $10^6$ cm, $B_{m,16}$ is $B_m$ in units of $10^{16}$ G, and $τ_{d,8}$ in units of $10^8$ s.

astro-ph.HE↗

arXiv2020

The lowest frequency Fast Radio Bursts: Sardinia Radio Telescope detection of the periodic FRB 180916 at 328 MHz

We report on the lowest-frequency detection to date of three bursts from the fast radio burst FRB 180916, observed at 328 MHz with the Sardinia Radio Telescope (SRT). The SRT observed the periodic repeater FRB 180916 for five days from 2020 February 20 to 24 during a time interval of active radio bursting, and detected the three bursts during the first hour of observations; no more bursts were detected during the remaining ~ 30 hours. Simultaneous SRT observations at 1548 MHz did not detect any bursts. Burst fluences are in the range 37 to 13 Jy ms. No relevant scattering is observed for these bursts. We also present the results of the multi-wavelength campaign we performed on FRB 180916, during the five days of the active window. Simultaneously with the SRT observations, others with different time spans were performed with the Northern Cross at 408 MHz, with XMM-Newton, NICER, INTEGRAL, AGILE, and with the TNG and two optical telescopes in Asiago, which are equipped with fast photometers. XMM-Newton obtained data simultaneously with the three bursts detected by the SRT, and determined a luminosity upper limit in the 0.3-10 keV energy range of ~$10^{45}$ erg/s for the burst emission. AGILE obtained data simultaneously with the first burst and determined a fluence upper limit in the MeV range for millisecond timescales of $ 10^{-8}$ erg cm$^{-2}$.Our results show that absorption from the circumburst medium does not significantly affect the emission from FRB 180916, thus limiting the possible presence of a superluminous supernova around the source, and indicate that a cutoff for the bursting mechanism, if present, must be at lower frequencies. Our multi-wavelength campaign sensitively constrains the broadband emission from FRB 180916, and provides the best limits so far for the electromagnetic response to the radio bursting of this remarkable source of fast radio bursts.

astro-ph.HE↗

arXiv2017

SKA Aperture Array Verification System: Electromagnetic modeling and beam pattern measurements using a micro UAV

In this paper we present the electromagnetic modeling and beam pattern measurements of a 16-elements ultra wideband sparse random test array for the low frequency instrument of the Square Kilometer Array telescope. We discuss the importance of a small array test platform for the development of technologies and techniques towards the final telescope, highlighting the most relevant aspects of its design. We also describe the electromagnetic simulations and modeling work as well as the embedded-element and array pattern measurements using an Unmanned Aerial Vehicle system. The latter are helpful both for the validation of the models and the design as well as for the future instrumental calibration of the telescope thanks to the stable, accurate and strong radio frequency signal transmitted by the UAV. At this stage of the design, these measurements have shown a general agreement between experimental results and numerical data and have revealed the localized effect of un-calibrated cable lengths in the inner side-lobes of the array pattern.

astro-ph.IM↗

arXiv2016

Loops and Strings in a Superconducting Lattice Gauge Simulator

We propose an architecture for an analog quantum simulator of electromagnetism in 2+1 dimensions, based on an array of superconducting fluxonium devices. The encoding is in the integer (spin-1 representation of the quantum link model formulation of compact U(1) lattice gauge theory. We show how to engineer Gauss' law via an ancilla mediated gadget construction, and how to tune between the strongly coupled and intermediately coupled regimes. The witnesses to the existence of the predicted confining phase of the model are provided by nonlocal order parameters from Wilson loops and disorder parameters from 't Hooft strings. We show how to construct such operators in this model and how to measure them nondestructively via dispersive coupling of the fluxonium islands to a microwave cavity mode. Numerical evidence is found for the existence of the confined phase in the ground state of the simulation Hamiltonian on a ladder geometry.

quant-ph↗

arXiv2016

Topological Massive Dirac Edge Modes and Long-Range Superconducting Hamiltonians

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower band eigenvector and the winding number of the Hamiltonians. For exponentially-decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive non-local Dirac fermion localised at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.

cond-mat.str-el↗