High-temperature Limit Research Articles

Quantum distillation in QCD

We propose a grading protocol which assigns global symmetry associated phases to states in the Hilbert space. Without modifying the Hilbert space, this changes the state sum, a process that we call quantum distillation. We describe the image of quantum distillation in path integral in terms of (non-dynamical) flavor holonomy dependence of (dynamical) gauge holonomy potentials, in QCD with $N_f=N_c$ fundamental and one massive adjoint fermion on $\mathbb R^3 \times S^1$. The compactified theory possesses an exact zero-form color-flavor center symmetry for a special choice of flavor holonomy (under which Polyakov loop is charged), despite the absence of one-form center-symmetry. We prove that the CFC symmetry is stable at small-$\beta$. This is the opposite of the high-temperature limit of thermal theory and a dramatic manifestation of quantum distillation. We show chiral symmetry breaking at small $S^1$ and that the vacuum structure of the theory on $\mathbb R^4$ and $\mathbb R^3 \times S^1$ are controlled by the same mixed 't Hooft anomaly condition.

Bulk viscosity of resonating fermions revisited: Kubo formula, sum rule, and the dimer and high-temperature limits

The bulk viscosity of two-component fermions with a zero-range interaction is revisited both in two and three dimensions. We first point out that the "standard" Kubo formula employed in recent studies has flaws to give rise to an unphysical divergent bulk viscosity even in a limit where it is supposed to vanish. The corrected Kubo formula as well as the sum rule is then carefully rederived so as to confirm that the bulk viscosity indeed vanishes in the free, unitarity, and dimer limits. We also discuss that the recently found discrepancy between the Kubo formalism and the kinetic theory for the bulk viscosity is attributed to the fact that the quasiparticle approximation assumed by the latter breaks down even in the high-temperature limit.

Evaluation of alternative eutectic salt as heat transfer fluid for solar power tower coupling a supercritical CO2 Brayton cycle from the viewpoint of system-level analysis

Heat transfer fluids play a crucial role in solar thermal power plants. Several novel salt formulas with higher temperature limit, such as MgCl2-KCl, have been proposed to serve as heat transfer fluids in a solar power tower system with S-CO2 cycles. Although the thermophysical properties of these novel salt formulas have been obtained in previous studies, it is necessary to evaluate their performances from the viewpoint of system-level analysis. This paper develops an integrated model for the solar power tower plants with a recompression S-CO2 Brayton cycle, and the performances of the MgCl2-KCl salt are evaluated based on the thermodynamic analyses and multi-objective optimizations about the system. The results indicate that: (1) Attributed to the higher heat source temperature, the system with MgCl2-KCl can achieve a slightly higher system efficiency and a significantly larger specific work than the conventional solar salt; (2) Reheating is not recommended for solar power tower plant with supercritical CO2 Brayton cycles when high-temperature MgCl2-KCl serves as heat transfer fluid; (3) The MgCl2-KCl solar power tower system without reheating enlarges the temperature difference between hot salt and cold salt and thus needs less molten salt for the thermal storage than the solar salt system; (4) The novel MgCl2-KCl salt has no advantages under the conditions with the operating temperature lower than 565 °C, which yields lower system efficiency and smaller specific work than the conventional solar salt due to the higher pump consumption associated with its higher viscosity.

A tomography-based effective thermal conductivity model for ceramic fiber insulation

Ceramic fiber insulation is widely used in thermal systems due to its high temperature limits and light weight. In high temperature applications, radiation is the main mechanism of heat transfer in these materials due to high porosity (greater than 95 %), and orientation of the fibers in the construction of the insulation. A combined radiation and conduction computational model has been developed to calculate thermal conductivity in ceramic fiber materials using the Rosseland diffusion approximation to evaluate thermal radiation transfer, and a tortuosity-weighted effective thermal conductivity to evaluate gas and solid phase conduction. Tomographic reconstructions of sample insulation material were analyzed to determine fiber size and orientation distributions as well as tortuosity and volume fraction of the solid and void fraction. The model is validated by manufacturer data. Together, the conduction and radiation model accurately predicted effective thermal conductivity of ceramic fiber materials in the temperature range of 300–1673 K. The tortuosity-weighted conduction approach allows the model to capture the directional dependence of thermal conductivity in the highly an-isotropic fibrous structure. Critical parameters of fibrous ceramics to maximize insulating properties are also identified.

Low-temperature auto-ignition characteristics of NH3/diesel binary fuel: Ignition delay time measurement and kinetic analysis

Ammonia (NH3) is gaining increasing interest as a carbon-free alternative fuel in engine systems. Co-firing NH3 with diesel can overcome the high auto-ignition temperature and narrow flammability limits of pure NH3, while exploit its advantage. This study presents the auto-ignition properties of NH3/diesel binary fuel, at various NH3 blending ratios (10%, 30% and 50%) in a rapid compression machine. Ignition delay times (IDTs) were measured spanning a temperature range of 670–910 K, pressures of 10–20 bar, and equivalence ratios of 0.5–1.5. Typical two-stage ignition and negative temperature coefficient (NTC) response were identified for the blends. Both the first-stage and the total IDTs increase with the increasing NH3 blending ratio, and there exists a non-linear inhibiting effect of NH3 fraction on IDT. A blending mechanism was then constructed based on the existing diesel mechanism and NH3 mechanism. The mechanism can predict the inhibiting effect of NH3 addition, but fails to well capture the IDTs over the whole temperature range, especially for the first-stage IDT and the NTC response. Further kinetic analysis, including species mole fraction history, brute force sensitivity analysis and reaction pathway analysis, were conducted to gain deeper insight into the auto-ignition chemistry of the blending fuel. These analyses suggest the rate parameters of reactions NH3 + OH ⇒ NH2 + H2O and NH2 + NO ⇒ N2 + H2O are critical to accurately predict IDTs, and the competition role of NH3 for OH radical inhibits the diesel low-T chain-branching sequence, which eventually leads to restraining the reactivity of the whole reaction system.

Lorentzian Entropies and Olbert's κ - Distribution

This note derives the various forms of entropy of systems subject to Olbert distributions (generalized Lorentzian probability distributions known as $\kappa$-distributions) which are frequently observed particularly in high temperature plasmas. The general expression of the partition function in such systems is given as well in a form similar to the Boltzmann-Gibbs probability distribution, including a possible exponential high energy truncation. We find the representation of the mean energy as function of probability, and provide the implicit form of Olbert (Lorentzian) entropy as well as its high temperature limit. The relation to phase space density of states is obtained. We then find the entropy as function of probability, an expression which is fundamental to statistical mechanics and here to its Olbertian version. Lorentzian systems through internal collective interactions cause correlations which add to the entropy. Fermi systems do not obey Olbert statistics, while Bose systems might at temperatures sufficiently far from zero.

Topology and axions in QCD

QCD axions are at the crossroads of QCD topology and Dark Matter searches. We present here the current status of topological studies on the lattice, and their implication on axion physics. We outline the specific challenges posed by lattice topology, the different proposals for handling them, the observable effects of topology on the QCD spectrum and its interrelation with chiral and axial symmetries. We review the transition to the quark–gluon plasma, the fate of topology at the transition, and the approach to the high temperature limit. We discuss the extrapolations needed to reach the regime of cosmological relevance, and the resulting constraints on the QCD axion.

Black hole interiors via spin models

To model the interior of a black hole, a study is made of a spin system with long-range random four-spin couplings that exhibits quantum chaos. The black hole limit corresponds to a system where the microstates are approximately degenerate and equally likely, corresponding to the high temperature limit of the spin system. At the leading level of approximation, reconstruction of bulk physics implies that local probes of the black hole should exhibit free propagation and unitary local evolution. We test the conjecture that a particular mean field Hamiltonian provides such a local bulk Hamiltonian by numerically solving the exact Schrodinger equation and comparing the time evolution to the approximate mean field time values. We find excellent agreement between the two time evolutions for timescales smaller than the scrambling time. In earlier work, it was shown bulk evolution along comparable timeslices is spoiled by the presence of the curvature singularity, thus the matching found in the present work provides evidence of the success of this approach to interior holography. The numerical solutions also provide a useful testing ground for various measures of quantum chaos and global scrambling. A number of different observables, such as entanglement entropy, out-of-time-order correlators, and trace distance are used to study these effects. This leads to a suitable definition of scrambling time, and evidence is presented showing a logarithmic variation with the system size.

Splitting frequency of the (2 + 1)-dimensional Duffin-Kemmer-Petiau oscillator in an external magnetic field

We revisit the (2+1)-dimensional DKP oscillator in an external magnetic field by means of 4×4 and 6×6 representations of the DKP field, thus obtaining several cases studied in the literature. We found an splitting in the frequency of the DKP oscillator according to the spin projection that arises as an interplay between the oscillator, the magnetic field and the spin, from which the energies and the eigenfunctions are expressed in a unified way. For certain critical values of the magnetic field the oscillation in the components of spin projections 1 and −1 is cancelled. We study the thermodynamics of the canonical ensemble of the vectorial sector, where a phase transition is reported when the cancellation of the oscillation occurs. Thermodynamic potentials converge rapidly to their asymptotical expressions in the high temperature limit with the partition function symmetric under the reversion of the magnetic field.

High-Energy Standard Model from the Gauge Group Contraction

The evolution of properties and interactions of elementary particles is described, beginning with the Planck scale of $10^{19}$ GeV. The description is based on the hypothesis that high-temperature (high-energy) limit of the Standard Model is generated by the gauge group contraction. In the infinite-temperature limit, properties of particles fundamentally change: all particles lose their masses, only massless neutral $Z$ bosons and $u$ quarks together with neutrinos and photons survive. Weak interactions become long-range ones and are generated by neutral currents. Quarks have only one color degree of freedom.

Phonon scattering induced carrier resistivity in twisted double-bilayer graphene

In this work we carry out a theoretical study of the phonon-induced resistivity in twisted double bilayer graphene (TDBG), in which two Bernal-stacked bilayer graphene devices are rotated relative to each other by a small angle $\theta$. We show that at small twist angles ($\theta\sim 1^\circ$) the effective mass of the TDBG system is greatly enhanced, leading to a drastically increased phonon-induced resistivity in the high-temperature limit where phonon scattering leads to a linearly increasing resistivity with increasing temperature. We also discuss possible implications of our theory on superconductivity in such a system, and provide an order of magnitude estimation of the superconducting transition temperature.

Quantum corrections to the classical field approximation for one-dimensional quantum many-body systems in equilibrium

We present a semiclassical treatment of one-dimensional many-body quantum systems in equilibrium, where quantum corrections to the classical field approximation are systematically included by a renormalization of the classical field parameters. Our semiclassical approximation is reliable in the limit of weak interactions and high temperatures. As a specific example, we apply our method to the interacting Bose gas and study experimentally observable quantities, such as correlation functions of bosonic fields and the full counting statistics of the number of particles in an interval. Where possible, our method is checked against exact results derived from integrability, showing excellent agreement.

Landauer's Principle at Zero Temperature.

Landauer's bound relates changes in the entropy of a system with the inevitable dissipation of heat to the environment. The bound, however, becomes trivial in the limit of zero temperature. Here we show that it is possible to derive a tighter bound which remains nontrivial even as T→0. As in the original case, the only assumption we make is that the environment is in a thermal state. Nothing is said about the state of the system or the kind of system-environment interaction. Our bound is valid for all temperatures and is always tighter than the original one, tending to it in the limit of high temperatures.

Anomalous low-frequency conductivity in easy-plane XXZ spin chains

In the easy-plane regime of XXZ spin chains, spin transport is ballistic, with a Drude weight that has a discontinuous fractal dependence on the value of the anisotropy $\Delta = \cos \pi \lambda$ at nonzero temperatures. We show that this structure necessarily implies the divergence of the low-frequency conductivity for generic irrational values of $\lambda$. Within the framework of generalized hydrodynamics, we show that in the high-temperature limit the low-frequency conductivity at a generic anisotropy scales as $\sigma(\omega) \sim 1/\sqrt{\omega}$; anomalous response occurs because quasiparticles undergo L\'evy flights. For rational values of $\lambda$, the divergence is cut off at low frequencies and the corrections to ballistic spin transport are diffusive. We also use our approach to recover that at the isotropic point $\Delta=1$, spin transport is superdiffusive with $\sigma(\omega) \sim \omega^{-1/3}$. We support our results with extensive numerical studies using matrix-product operator methods.

Exploration of Machine Learning to Predict Hot Ductility of Cast Steel from Chemical Composition and Thermal Conditions

This study explores the use of machine learning (ML) as a data-driven approach to estimate hot ductility of cast steel from literature data. Four ML algorithms were used to predict hot ductility by considering elemental composition and thermal conditions. Experimentally-measured reduction of area (RA) values were converted to a low-temperature limit, center-temperature, and high-temperature limit, which were represented as Gaussian curves. The prediction accuracy of the four ML models was evaluated using RMSE for these three output variables. In a case study of three steels that had different contents of alloying elements, only the Neural-net model predicted the RA trough more accurately in all cases. These results demonstrate the utility of ML models to predict hot ductility of cast steels.

Advances in studies of the temperature dependence of the EXAFS amplitude and phase of FCC crystals

In this work, the temperature dependence of the extended x-ray absorption fine structure (EXAFS) amplitude and phase of the first shell of face-centered cubic crystals was studied using the anharmonic correlated Einstein model and quantum statistical theory with first-order perturbation. The thermodynamic parameters of a system are derived from an anharmonic effective potential that has taken into account the influence of all nearest neighbors of absorbing and backscattering atoms in the crystal lattice with thermal vibrations, where the Morse potential is assumed to characterize the interactions between each pair of atoms and the function of anharmonic EXAFS spectra presented in terms of the cumulant expansion up to the fourth-order. The analytical expressions of the temperature dependence of the first four EXAFS cumulants were calculated and evaluated in both low-temperature and high-temperature limits. The numerical results for crystalline copper were in good agreement with those obtained by the other theoretical procedures and experiments at several other temperatures. The analytical results of the contributions of the EXAFS cumulants to the amplitude reduction and phase shift of the EXAFS spectra discovered the role and meaning of high-order cumulants in the analysis of the temperature dependence of the EXAFS spectra.

Energy distribution of an ion cloud in a quadrupole Penning Trap

Ions are confined in Penning trap by the combination of electric field and magnetic field, as the electric field confines ions in the axial direction through an electric potential minimum and the magnetic field applied along the axis of the trap confines the ions in the radial direction. In the high temperature limit Coulomb interaction of ions can be neglected and the total energy is due to the electrostatic potential energy of the charge of ions and kinetic energy due to thermal energy. However, in the low temperature limit the trapping potential created by the dc voltage applied between the end cap and ring electrodes is cancelled by Coulomb interaction of ions and the total energy is mainly kinetic energy of ions. The probability density of energy distribution of ions along axial direction, in radial plane and total probability density of energy distribution due to resulting motion of both axial and radial motion of ions under high temperature and low temperature limits in a Quadrupole Penning trap are presented here. These results reveal the energy properties of ion cloud and are useful to carry out accurate measurement experiments on single stored particle, antiparticles with energy related parameters, under high temperature and low temperature limits in a Quadrupole Penning trap.

Quantum Coherence and Its Signatures in Extended Quantum Systems.

Quantum coherence controls almost every aspect of static and dynamic response of a strongly correlated quantum system, although details of this control have not been elucidated in many cases. We find that, in the presence of a significant static off-diagonal coupling, quantum coherence can survive much longer than the bath correlation time in a noisy environment. In the presence of time correlated noise (non-Markovian limit), coherence could propagate through the excited bath states, and this plays a nontrivial role in giving rise to a noncanonical temperature dependence of population distribution in an extended conjugated polymer-like system. The quantum coherence through the excited bath states vanishes in the high temperature limit, giving rise to the equilibrium Boltzmann distribution. Second, we discuss a role of quantum coherence in exciton localization that bears resemblance to Anderson localization. Calculations have been carried out not only with a chain of conjugated polymer but also with dimer and trimer subunits of the Fenna-Matthews-Olson (FMO) complex. We derive an analytical expression of the relation between steady state coherence and excitionic population distribution. We analytically showed that steady state coherence in equilibrium bath states is governed by interchromophoric coupling (J) whereas coherence in excited bath states is dictated by fluctuation strength (Vd) for the spatially correlated bath model. For the spatially uncorrelated bath model, we observe that at the low temperature limit coherence in the excited bath states dominates over coherence in equilibrium bath states and vice versa. In the study of the localization problem, we analytically show that, in the limit of a negligibly small fluctuation rate (bd), the diffusion coefficient is exactly proportional to the fluctuation rate, leading to complete breakdown of the Haken-Strobl-Silbey Markovian prediction.

Thermodynamic properties and transport coefficients of QCD matter within the nonextensive Polyakov–Nambu–Jona-Lasinio model

We present a non-extensive version of the Polyakov-Nambu-Jona-Lasinio model which is based on the non-extentive statistical mechanics. This new statistics is characterized by a dimensionless non-extensivity parameter $q$ that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs statistics (when $q\rightarrow1$, it returns to the Boltzmann-Gibbs case). Using this q-Polyakov-Nambu-Jona-Lasinio model and including two different Polyakov-loop potentials, we discussed the influence of the parameter $q$ on chiral and deconfinement phase transition, various thermodynamic quantities and transport coefficients at finite temperature and zero quark chemical potential. We found that the Stefan-Boltzmann limit is actually related to the choice of statistics. For example, in the Tsallis statistics, the thermodynamic quantities $\frac{\epsilon}{T^{4}}$, $\frac{p}{T^{4}}$ and $\frac{s}{T^{3}}$ all increase with $q$, exceed their usual Stefan-Boltzmann limits and tend to a new $q$-related Tsallis limit at temperature high enough. Interestingly, however, due to a surprising cancellation, the high temperature limit of $c_{s}^{2}$ is still its SB limit $1/3$. In addition, we found some similarities between the non-extensive effect and the finite-size effect. For example, as $q$ increases (size decreases), the criticality of $\frac{c_{v}}{T^{3}}$ and $c_{s}^{2}$ gradually disappears. Besides, in order to better study the non-extensive effect, we defined a new susceptibility and calculated the response of thermodynamic quantities and transport coefficients to $q$. And found that their response patterns are different.

Thermal tuning of light-emitting diode wavelength as an implication of the Varshni equation

In this article, we show that the variation of the wavelength of a non-pumped light-emitting diode (LED) is practically linear with temperature, a novel consequence of Varshni's widely accepted empirical expression. This formula models the bandgap variation for most semiconductors from 0K to their high-temperature limits, subject to fitting parameters. Therefore, we suggest an external thermal mechanism that can be used to tune the wavelength of a constant-current biased LED and also to stabilize its wavelength. Furthermore, we demonstrate the approach on published AlN data and show that the fitting parameters follow trivially. In addition, we suggest a novel method to characterize semiconductors. Finally, we present the results of experimental measurements on several commercial LEDs.