Temperature Dependence Of Relaxation Time Research Articles

Emergent Research Trends on the Structural Relaxation Dynamics of Molecular Clusters: From Structure-Property Relationship to New Function Prediction.

ConspectusMolecular clusters (MCs) are monodispersed, precisely defined ensembles of atom collections featured with shape-persistent architectures that can deliver certain functions independently. Their molecular compositions and surface functionalities can be tailored feasibly in a predefined manner, and they can be applied as basic structural units to be engineered into materials with desirable hierarchical structures and enriched functions. The chemical systems also offer great opportunities for the design and fabrication of soft structural materials without the chain topologies of polymers. The bulks of MC assemblies demonstrate viscoelasticity that is used to be considered as the unique feature of polymers, while the MC systems are distinct from polymers since their elasticities are resilient even at temperatures 100 K above their glass transition temperatures. The understanding of their anomalous viscoelasticity and the extended studies of general structure-property relationships are desired for the development of new chemical systems for emergent functions and the possibilities to resolve the intrinsic trade-offs of traditional materials.Meanwhile, general macroscopic functions or properties of materials are related to the transportation of mass, momentum, and/or energy, and they are basically realized or directed by the motions of structural units at different length scales. Structural relaxation dynamics research is critical in quantifying motions ranging from fast bond deformation, bond break/formation, and diffusion of ions and particles to the cooperative motions of structure units. Due to the advancement of measurement technology for relaxation dynamics (e.g., quasi-elastic scattering and broadband dielectric spectroscopy), the structural relaxation dynamics of MC materials have been probed for the first time, and their multiple relaxation modes across several temporal scales were systematically studied to bridge the correlation between molecular structures and macroscopic functions. The fingerprint information from dynamics studies, e.g., the temperature dependence of relaxation time and certain property, e.g., ion conductivity, was proposed to quantify the structure-property relationship, and the microscopic mechanism on the mechanical properties, ion conduction, and gas absorption and separation of MC materials can be fully understood.In this Account, to elucidate the uniqueness of MC materials, especially in comparison with polymers, four topics are mainly summarized: structural features, relaxation dynamics characterization techniques, relaxation dynamics characteristics, and quantified understanding of the structure-property relationship. The capability for new function prediction from relaxation dynamics studies is also introduced, and the typical example in impact resistant materials is provided. The Account aims to prove the significance of relaxation dynamics characterization for material innovation, while it also confirms the potential of MCs for functional material fabrications.

Distinct ultrafast dynamics of bilayer and trilayer nickelate superconductors regarding the density-wave-like transitions

In addition to the pressurized high-temperature superconductivity, bilayer and trilayer nickelate superconductors Lan+1NinO3n+1 (n = 2 and 3) exhibit many intriguing properties at ambient pressure, such as orbital-dependent electronic correlation, non-Fermi liquid behavior, and density-wave transitions. Here, using ultrafast reflectivity measurement, we observe a drastic difference between the ultrafast dynamics of the bilayer and trilayer nickelates at ambient pressure. We observe a coherent phonon mode in La4Ni3O10 involving the collective vibration of La, Ni, and O atoms, which is absent in La3Ni2O7. Temperature-dependent relaxation time diverges near the density-wave transition temperature of La4Ni3O10, while it is inversely proportional to the temperature in La3Ni2O7 above ∼150 K, suggesting a dramatic difference in the density-wave states of the two compounds and a non-Fermi liquid behavior of La3Ni2O7. Moreover, we estimate the electron-phonon coupling constants to be 0.05–0.07 and 0.12–0.16 for La3Ni2O7 and La4Ni3O10, respectively, suggesting a relatively minor role of electron-phonon coupling in the electronic properties of Lan+1NinO3n+1. Our work not only sheds light on the relevant microscopic interaction but also establishes a foundation for further studying the interplay between superconductivity and density-wave transitions in nickelate superconductors.

Non-Debye Behavior of the Néel and Brown Relaxation in Interacting Magnetic Nanoparticle Ensembles.

We used ac-susceptibility measurements to study the superspin relaxation in Fe3O4/Isopar M nanomagnetic fluids of different concentrations. Temperature-resolved data collected at different frequencies, χ″ vs. T|f, reveal magnetic events both below and above the freezing point of the carrier fluid (TF = 197 K): χ″ shows peaks at temperatures Tp1 and Tp2 around 75 K and 225 K, respectively. Below TF, the Néel mechanism is entirely responsible for the superspin relaxation (as the carrier fluid is frozen), and we found that the temperature dependence of the relaxation time, τN(Tp1), is well described by the Dorman-Bessais-Fiorani (DBF) model: τNT=τrexp⁡EB+EadkB T. Above TF, both the internal (Néel) and the Brownian superspin relaxation mechanisms are active. Yet, we found evidence that the effective relaxation times, τeff, corresponding to the Tp2 peaks observed in the denser samples do not follow the typical Debye behavior described by the Rosensweig formula 1τeff=1τN+1τB. First, τeff is 5 × 10-5 s at 225 K, almost three orders of magnitude more that its Néel counterpart, τN~8 × 10-8 s, estimated by extrapolating the above-mentioned DBF analysis. Thus, 1τN≫1τeff, which is clearly not consistent with the Rosensweig formula. Second, the observed temperature dependence of the effective relaxation time, τeff(Tp2), is excellently described by τB-1T=Tγ0exp⁡-E'kBT-T0', a model solely based on the hydrodynamic Brown relaxation, τB(T)=3ηTVHkBT, combined with an activation law for the temperature variation of the viscosity, ηT=η0exp⁡E'/kB(T-T0'. The best fit yields γ0=3ηVHkB = 1.6 × 10-5 s·K, E'/kB = 312 K, and T0' = 178 K. Finally, the higher temperature Tp2 peaks vanish in the more diluted samples (δ ≤ 0.02). This indicates that the formation of larger hydrodynamic particles via aggregation, which is responsible for the observed Brownian relaxation in dense samples, is inhibited by dilution. Our findings, corroborating previous results from Monte Carlo calculations, are important because they might lead to new strategies to synthesize functional magnetic ferrofluids for biomedical applications.

Impact of Nickel doping on microstructure and impedance spectroscopy of multiferroic YCrO3

In this work, we study the effect of Ni-doping on the structural and impedance spectroscopy properties of the polycrystalline YCrO3 ceramic sample. The structural analysis shows all the samples crystallize in an orthorhombic structure with the Pnma space group. The depressed and asymmetric semicircle of complex impedance spectra indicates that the relaxation of charge carriers is of non-Debye type, where the thermally activated charge carriers control it. The temperature dependence of relaxation time and electrical conductivity exhibit an anomaly in the vicinity of diffuse-like relaxor transition temperature (TC ∼ 460 K). The analysis of conductivity data shows hopping-type charge conduction. The analysis further indicates that while the dc conductivity increases continuously, the activation energy shows a non-monotonous variation with Ni concentration.

Synergistic phases in isopropanol electrospun for Fe2O3/Fe3O4@C@MoS2 nanofibers for enhanced electromagnetic interference shielding characteristics and impedance analysis

Co-existence of phases in Fe2O3/Fe3O4@C@MoS2 nanofibers composite is synthesized via electrospinning and hydrothermal processes, where iso-propanol is utilized as a solvent. An extensive analysis is performed to evaluate the different properties, such as dielectric, morphological, structural, impedance, and electromagnetic shielding efficiency. A crystallite size of 24 nm is calculated using the Debye-Scherer formula. By using impedance spectroscopy, the electrical behavior of Fe2O3/Fe3O4@C@MoS2 nanofibers is described. Variations in frequency and temperature-dependent relaxation times are compared in an impedance plane plot. Changes in the conduction mechanism at different temperatures are observed. In Fe2O3/Fe3O4@C@MoS2 nanofibers composites, a number of distinctive characteristics in this work are explained, including stable dielectric constant, low tangent loss small polaronic hopping (SPH), and variable range hoping (VRH) model. The localization length of Fe2O3/Fe3O4@C@MoS2 nanofibers is calculated, 1/α = 1.2 Å. The typical EMI shielding efficiency of about 23 dB is demonstrated by the Fe2O3/Fe3O4@C@MoS2 nanofibers composite in the X-band frequency range. This extraordinary shielding capacity is observed in 3 mm thick nanofibers.

Tuning the Physical State of Aripiprazole by Mesoporous Silica.

The main purpose of our studies is to demonstrate that commercially available mesoporous silica (MS) can be used to control the physical state of aripiprazole (ARP). The investigations performed utilizing differential scanning calorimetry and broadband dielectric spectroscopy reveal that silica can play different roles depending on its concentration in the system with amorphous ARP. At low MS content, it activates recrystallization of the active pharmaceutical ingredient and supports forming the III polymorphic form of ARP. At intermediate MS content (between ca. 27 and 65 wt %), MS works as a recrystallization inhibitor of ARP. At these concentrations, the formation of III polymorphic form is no longer favorable; therefore, it is possible to use this additive to obtain ARP in either IV or X polymorphic form. At the same time, employing MS in concentrations >65 wt % amorphous form of ARP with high physical stability can be obtained. Finally, regardless of the polymorphic form it crystallizes into, each composite is characterized by the same temperature dependence of relaxation times in the supercooled and glassy states.

The Universal Scaling of Dielectric Response as a Tool in the Description of a Complex Dynamic of 4′-Butyl-4-(2-methylbutoxy)azoxybenzene (4ABO5*)

The results of dielectric relaxation spectroscopy of the chiral liquid crystal 4′-butyl-4-(2-methylbutoxy)azoxybenzene in the crystal phase are presented. The scaling procedure showed complex molecular dynamics and allows one to decompose the observed relaxation process into two closely located relaxation processes around the short molecular axis. Temperature dependences of relaxation times characterizing flip-flop motions (rotation around the short molecular axis) and rotation around the long molecular axis are of the Arrhenius type.

Cerium(III) and 5-methylisophthalate-based MOFs with slow relaxation of magnetization and photoluminescence emission.

Two novel Ce(III) metal organic frameworks (MOFs) with formulas [Ce(5Meip)(H-5Meip)]nGR-MOF-17 and [CeCl(5Meip)(DMF)]nGR-MOF-18 (5Meip = 5-methylisophthalate, DMF = N,N-dimethylformamide) have been synthesized, forming 3-dimensional frameworks. Magnetic measurements show that both compounds present field-induced slow magnetic relaxation under a small applied dc field. For GR-MOF-17, the temperature dependence of relaxation times is best described by a Raman mechanism, whereas for GR-MOF-18, relaxation occurs through a combination of Raman and local-mode pathways. Moreover, when avoiding short Ce⋯Ce interactions by magnetic dilution in GR-MOF-17@La and GR-MOF-18@La, only the local-mode mechanism is responsible for magnetic relaxation. Photophysical studies show the occurrence of ligand-centred luminescence in both compounds and phosphorescence emission at low temperature for GR-MOF-17.

Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation

In this proceedings contribution, we summarize recent findings concerning the presence of early- and late-time attractors in non-conformal kinetic theory. We study the effects of varying both the initial momentum-space anisotropy and initialization times using an exact solution of the 0+1D boostinvariant Boltzmann equation with a mass- and temperature-dependent relaxation time. Our findings support the existence of a longitudinal pressure attractor, but they do not support the existence of distinct attractors for the bulk viscous and shear pressures. Considering a large set of integral moments, we show that for moments with greater than one power of longitudinal momentum squared, both early- and late-time attractors are present.

Probing the heterogeneity of molecular level organization of ionic liquids: a comparative study using neutral Nile red and cationic Nile blue sulfate as fluorescent probes for butyrolactam-based protic ionic liquids.

Ionic liquids (ILs) are liquid salts composed of cations and anions, known for their significant local heterogeneity at the molecular level. To understand the microheterogeneity with regard to their local polarity and local viscosity, we have used two structurally similar but chemically distinguishable fluorescent probes: Nile red (NR), a neutral molecule, and Nile blue sulfate (NBS), a charged molecule. A comparative study of the response of the two probes to the molecular level heterogeneity of ILs is expected to provide a better clarity of understanding regarding the charged polar domain and the uncharged hydrophobic domain of ILs. Towards this, we synthesized two butyrolactam-based protic ionic liquids (PILs), i.e., BTF and BTD, with the same ionic headgroup ([BT]+) and different alkyl tails ([RCOO]-), where {R = H, C11H23}. BTF has no significant hydrophobic domain, whereas BTD has a larger hydrophobic domain. Temperature-dependent fluorescence parameters such as fluorescence intensity, lifetime, and anisotropy were measured for both NR and NBS molecules. The use of a pair of structurally similar but ionically different probes enables differential estimation of parameters like the microviscosity of a domain using the fluorescence anisotropy parameter (r). The absorption and emission spectra of both probe molecules are observed to be blue shifted upon going from BTF to BTD. NR showed a significant blue shift in absorption and emission band maxima. Conversely, NBS exhibited a small wavelength shift, possibly influenced by the preferred location of their charged head group domain. Temperature-dependent rotational relaxation time (θ) of NR in BTD is smaller than that of NBS by 60-70%, indicating that stronger charge-charge interactions exist between the polar domain of BTD and NBS. Moreover, it is observed that the local viscosity of the BTF IL around both probes is similar, whereas there is a considerable difference for the BTD IL. These results are an indication that NBS being charged prefers to locate itself in the charged head group region of the IL, whereas NR being neutral tends to reside both in the hydrophobic domain and in the head group but is predominantly located in the hydrophobic domain.

Structural, dielectric and electrical transport properties of thermal stable (1-x)K0.5Bi0.5TiO3-xBaTiO3 ceramics

Polycrystalline samples of (1-x)K0.5Bi0.5TiO3 - xBaTiO3 [(1-x)KBT - xBT] were synthesized using a solid-state reaction pathway. X-ray diffraction analysis confirmed the presence of a single-phase perovskite structure. To explore relaxation and conduction mechanisms, complex impedance spectroscopy was employed. Reduction in Curie temperature was observed as BT content increased. The grain and grain boundary contributions to relaxation was examined through complex impedance and modulus plots and quantified via fitting experimental data to an equivalent circuit model. Examination of the Complex impedance spectra uncovered the existence of dielectric relaxation characteristic of a non-Debye nature. Furthermore, the activation energy determined suggests commonalities in governing the conduction and relaxation processes in relation to temperature-dependent conductivity and relaxation time. A negative temperature coefficient of resistance behaviour was obtained from the temperature-dependent conductive study. Dielectric spectra revealed that these ceramic capacitors are useful in reduction of signal interference, signal attenuation and impedance matching circuits applications.

Slow magnetic relaxation behaviors and diamagnetic dilution studies of a carboxyl bridged dinuclear dysprosium(III) complex

By using a rigid bulky carboxylic ligand α-cyanocinnamic acid (CCA), a dinuclear dysprosium (III) complex [Dy2(CCA)6 (MeOH)4] (1) was synthesized. Single crystal X-ray crystallography reveals that the two eight-coordinate dysprosium ions are bridged by four deprotonated carboxyl groups, forming a centrosymmetric paddle-wheel-like structure. Dynamic magnetic property measurements indicate that complex 1 displays field-induced slow magnetic relaxation. The temperature-dependent relaxation times can be fitted using Orbach and Raman processes with parameters of n = 2.8 (2), C = 27 (8) s−1/Kn, τ0 = 5 (2) × 10−10 s and Ueff = 40 (3) cm−1. Magnetic studies on the diamagnetic YIII-diluted analogue [Dy0.206Y1.794(CCA)6 (MeOH)4] (2) reveal its slow magnetic relaxation behavior without external dc field and the antiferromagnetic coupling between the DyIII ions in 1. Fits on the obtained relaxation times of 2 lead to the parameters of n = 4.5 (3), C = 0.7 (2) s−1/Kn, τ0 = 2.8 (2) × 10−9 s and Ueff = 38 (2) cm−1. The results suggest that slow magnetic relaxation originates from the single-ion relaxation of DyIII ions. Moreover, the diamagnetic dilution can suppress other fast relaxation pathways at low temperature, on account of the elimination of magnetic coupling and dipolar interaction. Ab initio calculations were then performed on the single DyIII ion species {YDy} and indicate that the first excited Kramers doublets (KDs) lie at ca. 76 cm−1, which is slightly higher than the experimental Ueff value. The intramolecular magnetic interactions were also calculated and indicate a weak ferromagnetic dipole-diploe magnetic interaction and an antiferromagnetic exchange coupling.

Optoelectronic and thermoelectric properties of LiCuM (M=S, Se and Te) half-Heuslers: insights first principle calculations

The work is performed to study the structural stability and optoelectronic properties as well as thermoelectric properties of LiCuM (M=S, Se and Te) half-Heusler semiconductors using density functional theory (DFT) and semi-classical Boltzmann transport. The ground state results show that the compounds exhibit semiconducting behavior with a direct band-gap. The elastic parameters indicate that the present compounds are mechanically, dynamically stable and brittle. The calculated optical properties in GGA and GGA+U approaches show that the dominant response in the low ultraviolet and visible energy regions. The thermoelectric properties are evaluated using the Slack model and temperature dependent relaxation time in the temperature range of 100 K to 1000 K. The response of thermoelectric properties to temperature is evaluated and discussed in detail. The figure of merit with relaxation time is found to increase with temperature and reaches the optimal values in GGA and GGA+U at 1000 K are 0.69(0.01), 0.66(0.665) and 0.67(0.778) for LiCuS, LiCuSe and LiCuTe, respectively. The lattice thermal conductivity decreases with increasing temperature. These properties make these compounds promising candidates for optoelectronic and thermoelectric devices.

Low-frequency electrical response related to oxygen vacancies in Al3+ substituted M-type hexaferrite

The presence of oxygen vacancies is unavoidable in many complex metal oxide materials such as hexaferrites. This article investigates the role of crystal defects, such as oxygen vacancies, and different oxidation states of Fe ions, on the electrical conduction behaviors of Al3+ substituted Ba0.4La0.1Sr0.5Al x Fe12−x O19 hexaferrites by analyzing the temperature dependent AC impedance and AC conductivity. The optimal substitution of La3+ ions and high-temperature sintering is responsible for forming oxygen vacancies while reducing Fe from Fe3+ to Fe2+ cations, as observed in structural and XPS analysis, which affects electrical conduction behaviors. The departure from ideal Debye-type relaxation behavior is also one of the effects of crystal defects. Temperature variation of relaxation time shows a sharp change at around 403 K. This may be due to different electrical entities influencing the mode of electron hopping with temperature. The activation energy calculated from the temperature dependent relaxation time confirmed the presence of electron hopping through the bridging effects of the first ionization of oxygen vacancies Fe2+––Fe3+ below a temperature of 403 K. Above 403 K, electron hopping through different oxidation states of Fe3+ + e− → Fe2+ and migration of oxygen vacancies toward the bulk surface are responsible for the conduction mechanism. The DC resistivity and AC conductivity show that the bridging effects of oxygen defects can also induce Coulomb interaction between the defect sites resulting in Efros–Shklovskii variable range hopping and correlation barrier hopping below 403 K. Above 403 K, polaron-assisted electron hopping is more desirable, as confirmed by the non-overlapping small polaron tunneling model.

Chemically ordered structure and dynamics in Al80Ti20 liquids

We conducted ab initio molecular dynamics simulations to study the structural and dynamical properties in Al80Ti20 liquids. The prepeak that represents some chemically ordered structure, emerges in the partial static structure factors at low temperatures. By calculating coordination numbers, we found a preferred connection for Al–Ti pairs, which induces an excess Ti/Al concentration around the central Al/Ti atoms. An excess Ti concentration is even found in the second neighbour shells around Ti atoms, rationalizing the prepeak as the result of chemical concentration fluctuation in these neighbour shells. Concomitantly, slow structural relaxation occurs below 1400K, exhibited as the second step relaxation in self-intermediate scattering function. The slow dynamics induces a non-Arrhenius transition for the temperature-dependent diffusivity and structural relaxation time, as well as the breakdown of the Stokes–Einstein relation. These results unveil the detailed ordering structure for the chemical interaction and the associated dynamical behaviour in Al80Ti20 liquids.

Study of dielectric, impedance and transport properties of co-doped Ba0.5Sr0.5TiO3 ceramics

Dielectric properties and Electrical response of BST ceramics having composition Ba0.5Sr0.5Ti0.98Sn0.01Zr0.01O3 synthesized by solid state reaction route are studied in this piece of work. The structural part analysis is done using XRD technique and scanning electron microscopy and is confirmed to be of cubic structure. Electrical characterization through impedance and modulus spectroscopy is made over a frequency region of 1 kHz to 1 MHz from ambient temperature to 400 °C. Near constant value of Ɛr and significantly low and flat loss tangent at room temperature are achieved in the material which suggest possible application in electronic circuits. Temperature dependent broadened loss peaks observed beyond 250 °C indicated thermally activated conductivity/ relaxation process in the material. Impedance spectroscopy results were examined in alternate formalism for the role of grain boundary and grain in various processes. The computed activation energy for charge carriers provides information of the transport phenomena. The estimated values suggest that oxygen vacancies play important role in conduction process. The activation energy is estimated by fitting temperature dependent relaxation time with Arrhenius equation and the type of charge carriers involved in the relaxation process are suggested. Frequency dependent ac conductivity plots at various temperatures obey Johnscher’s law. Variation of exponent in Johnsher’s power law with temperature well agrees with correlated barrier hopping (CBH) model for ac conduction mechanism.

Temperature-dependent thermal phonon relaxation time and its influence on ballistic-diffusive heat transport in SOI transistor

A simple model of the average thermal phonon relaxation time including its temperature dependency for silicon (Si) is proposed and incorporated with the gray version of the phonon Boltzmann transport equation to investigate its effect on the temperature distribution of the Si-layer in a silicon-on-insulator (SOI) transistor with heat generation (qv). Our analysis showed that the peak temperatures both in the nonlocal heating region and at the Si/SiO2 interface increase quadratically with increasing values of qv, while in the case of the temperature-independent, however, they show a linear increase with increasing qv. The results from this work will help in understanding the phonon transport at the device-level based on Si and will provide a way how to do an efficient thermal analysis of the device-level including all the frequency and temperature dependencies of the phonon transport properties.

Janus 2H-MXTe (M = Zr, Hf; X = S, Se) monolayers with outstanding thermoelectric properties and low lattice thermal conductivities.

Two-dimensional (2D) materials have been one of the most popular objects in the research field of thermoelectric (TE) materials and have attracted substantial attention in recent years. Inspired by the synthesized 2H-MoSSe and numerous theoretical studies, we systematically investigated the electronic, thermal, and TE properties of Janus 2H-MXTe (M = Zr and Hf; X = S and Se) monolayers by using first-principles calculations. The phonon dispersion curves and AIMD simulations confirm the thermodynamic stabilities. Moreover, Janus 2H-MXTe were evaluated as indirect band-gap semiconductors with band gaps ranging from 0.56 to 0.90 eV using the HSE06 + SOC method. To evaluate the TE performance, firstly, we calculated the temperature-dependent carrier relaxation time with acoustic phonon scattering τac, impurity scattering τimp, and polarized scattering τpol. Secondly, the calculation of lattice thermal conductivity (κl) shows that these monolayers possess relatively poor κl with values of 3.4-5.4 W mK-1 at 300 K, which is caused by the low phonon lifetime and group velocity. After computing the electronic transport properties, we found that the n-type doped Janus 2H-MXTe monolayers exhibit a high Seebeck coefficient exceeding 200 μV K-1 at 300 K, resulting in a high TE power factor. Eventually, combining the electrical and thermal conductivities, the optimal dimensionless figure of merit (zT) at 300 K (900 K) can be obtained, which is 0.94 (3.63), 0.51 (2.57), 0.64 (2.72), and 0.50 (1.98) for n-type doping of ZrSeTe, HfSeTe, ZeSTe, and HfSTe monolayers. Particularly, the ZrSeTe monolayer shows the best TE performance with the maximal zT value. These results indicate the excellent application potential of Janus 2H-MXTe (M = Zr and Hf; X = S and Se) monolayers in TE materials.

Second order hydrodynamics based on effective kinetic theory and electromagnetic signals from QGP

We study the thermal dilepton and photon production from relativistic heavy ion collisions in presence of viscosities by employing the recently developed second order dissipative hydrodynamic formulation estimated within a quasiparticle description of thermal quantum chromo-dynamics (QCD) medium. The sensitivity of shear and bulk viscous pressures to the temperature dependence of relaxation time is analyzed within one- dimensional boost invariant expansion of quark gluon plasma (QGP). The dissipative corrections to the phase-space distribution functions up to first order in gradients are obtained from the Chapman–Enskog like iterative solution of effective Boltzmann equation in the relaxation time approximation. Thermal dilepton and photon production rates for QGP are calculated by employing this viscous modified distribution function. Yields of these particles are quantified for the longitudinal expansion of QGP with different temperature dependent relaxation times. Our analysis employing this second order hydrodynamic model indicates that the spectra of dileptons and photons get enhanced by both bulk and shear viscosities and are well behaved. Also, these particle yields are found to be sensitive to relaxation time. Further, we do a comparison of these particle spectra with a standard hydrodynamic formulation.

Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation

We investigate whether early and late time attractors for non-conformal kinetic theories exist by computing the time-evolution of a large set of moments of the one-particle distribution function. For this purpose we make use of a previously obtained exact solution of the 0+1D boost-invariant massive Boltzmann equation in relaxation time approximation. We extend prior attractor studies of non-conformal systems by using a realistic mass- and temperature-dependent relaxation time and explicitly computing the effect of varying both the initial momentum-space anisotropy and initialization time on the time evolution of a large set of integral moments. Our findings are consistent with prior studies, which found that there is an attractor for the scaled longitudinal pressure, but not for the shear and bulk viscous corrections separately. We further present evidence that both late- and early-time attractors exist for all moments of the one-particle distribution function that contain greater than one power of the longitudinal momentum squared.