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DOE OSTI2025

Framework for phase transitions between the Maxwell and Gibbs constructions at finite temperature

The characteristics of the hadron-to-quark first-order phase transition differ depending on whether charge neutrality is locally or globally fulfilled. In 𝛽-equilibrated matter, these two possibilities correspond to the Maxwell and Gibbs constructions. Recently, we presented a new framework in which a continuously varying parameter allows one to describe a first-order phase transition in intermediate scenarios to the two extremes of fully local and fully global charge neutrality. In this work, we extend the previous framework to finite temperatures and out-of-𝛽 equilibrium conditions, making it available for simulations of core-collapse supernovae and binary neutron star mergers. We investigate its impact on key thermodynamic quantities across a range of baryon densities, temperatures, and electron fractions. We find that when matter is not in 𝛽 equilibrium, the pressure in the mixed phase is not constant even for the case of fully local charge neutrality. Moreover, we compute the thermal index using three different approaches, demonstrating that the finite-temperature extension of an equation of state using a constant thermal index can be ill defined when applied to the mixed phase.

QCD phase transitions↗

DOE OSTI2025

Pauli potential formalism at finite temperature

At zero temperature, the Pauli potential—the functional derivative of the Pauli kinetic energy density functional—is the key to the accuracy of the orbital-free density functional theory (OFDFT) as it is supposed to capture all the effects associated with the Pauli exclusion principle. Here, we extend this concept to finite temperature by defining Pauli free energy and the modified Pauli free energy, both representing the natural generalizations of the Pauli term from zero- T to finite- T . We discuss their physical interpretation, the mathematical nuances, and the applicability, arguing that the modified Pauli potential should be used as an extension of the zero- T counterpart within the OF-DFT framework. Through analytical and numerical methods, we then analyze some of the exact properties concerning the modified Pauli free- and kinetic-energy terms and examine the temperature dependence of the modified Pauli potential.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2011

Spontaneous radiation of a finite-size dipole emitter in hyperbolic media

We study the radiative decay and Purcell effect for a finite-size dipole emitter placed in a homogeneous uniaxial medium. We demonstrate that the radiative rate is strongly enhanced when the signs of the medium longitudinal and transverse dielectric constants are opposite, and that the isofrequency contour corresponds to a hyperbolic medium. We reveal that the Purcell enhancement factor remains finite even in the absence of losses and that it depends on the emitter size.

36 MATERIALS SCIENCE↗

DOE OSTI2011

Finite-temperature properties of one-dimensional hard-core bosons in a quasiperiodic optical lattice

We investigate the properties of impenetrable bosons confined in a one-dimensional lattice at finite temperature in the presence of an additional incommensurate periodic potential. Relying on the exact Fermi-Bose mapping, we study the effects of temperature on the one-particle density matrix and related quantities such as the momentum distribution function and the natural orbitals. We found evidence of a finite-temperature crossover related to the zero-temperature superfluid-to-Bose-glass-transition that induces a delocalization of the lowest natural orbitals.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Tensor network study of the m = 1/2 magnetization plateau in the Shastry-Sutherland model at finite temperature

The two-dimensional infinite projected entangled pair state tensor network is evolved in imaginary time with the full update (FU) algorithm to simulate the Shastry-Sutherland model in a magnetic field at finite temperature directly in the thermodynamic limit. We focus on the phase transition into the m = 1/2 magnetization plateau, which was observed in experiments on SrCu 2 (BO 3 ) 2 . For the largest simulated bond dimension, the early evolution in the high-temperature regime is simulated with the simple update (SU) scheme and then, as the correlation length increases, continued with the FU scheme towards the critical regime. We apply a small symmetry-breaking bias field and then extrapolate towards zero bias using a simple scaling theory in the bias field. The combined SU + FU scheme provides an accurate estimate of the critical temperature, even though the results could not be fully converged in the bond dimension in the vicinity of the transition. Here, the critical temperature estimate is improved with a generalized scaling theory that combines two divergent length scales: One due to the bias, and the other due to the finite bond dimension. The obtained results are consistent with the transition being in the universality class of the two-dimensional classical Ising model. The estimated critical temperature is 3.5(2) K, which is well above the temperature 2.1 K used in the experiments.

2-dimensional systems↗

DOE OSTI2022

Nonclassical light from finite-range interactions in a two-dimensional quantum mirror

Excitons in a semiconductor monolayer form a collective resonance that can reflect resonant light with extraordinarily high efficiency. We investigate the nonlinear optical properties of such atomistically thin mirrors and show that finite-range interactions between excitons can lead to the generation of highly nonclassical light. We describe two scenarios, in which optical nonlinearities arise either from direct photon coupling to excitons in excited Rydberg states or from resonant two-photon excitation of Rydberg excitons with finite-range interactions. The latter case yields conditions of electromagnetically induced transparency and thereby provides an efficient mechanism for single-photon switching between high transmission and reflectance of the monolayer, with a tunable dynamical timescale of the emerging photon-photon interactions. Remarkably, it turns out that the resulting high degree of photon correlations remains virtually unaffected by Rydberg-state decoherence, in excess of nonradiative decoherence observed for ground-state excitons in two-dimensional semiconductors. This robustness to imperfections suggests a promising approach to quantum photonics at the level of individual photons.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Universal and nonuniversal features of Bardeen-Cooper-Schrieffer theory with finite-range interactions

Here, we study analytic solutions to the Bardeen-Cooper-Schrieffer (BCS) gap equation for isotropic superconductors with finite-range interaction potentials over the full range of temperatures from absolute zero to the superconducting critical temperature 0 ≤ T ≤ T c . Using these solutions Δ (ε,T), we provide a proof of the universality of the temperature dependence of the BCS gap ratio at the Fermi level Δ (ε = 0,T)/T c . Moreover, by examining the behavior of this ratio as a function of energy ε, we find that nonuniversal features emerge away from the Fermi level, and these features take the form of a temperature-independent multiplicative factor F(ε), which is equal to Δ (ε,T)/Δ(ε = 0,T) up to exponentially small corrections, i.e., the error terms vanish like e -1/λ in the weak-coupling limit λ → 0. We discuss the model-dependent features of both F(ε) and T c , and we illustrate their behavior focusing on several concrete examples of physically relevant finite-range potentials. Comparing these cases for fixed coupling constants, we highlight the importance of the functional form of the interaction potential in determining the size of the critical temperature and provide guidelines for choosing potentials which lead to higher values of T c . We also propose experimental signatures which could be used to probe the energy dependence of the gap and potentially shed light on the underlying mechanisms giving rise to superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

Aspects of renormalization in finite-density field theory

We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Equation of state at finite densities for QCD matter in nuclear collisions

We construct the QCD equation of state at finite chemical potentials including net baryon, electric charge, and strangeness, based on the conserved charge susceptibilities determined from lattice QCD simulations and the equation of state of the hadron resonance gas model. For the application to relativistic heavy-ion collisions we consider the situation of strangeness neutrality and matter with a fixed electric charge-to-baryon ratio, resembling that of heavy nuclei. The importance of finite electric charge and strangeness chemical potentials for particle production in heavy-ion collisions is demonstrated using hydrodynamic simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Finite-temperature electron-capture rates for neutron-rich nuclei near N = 50 and effects on core-collapse supernova simulations

In this paper the temperature dependence of stellar electron-capture (EC) rates is investigated, with a focus on nuclei near N = 50, just above Z = 28, which play an important role during the collapse phase of core-collapse supernovae (CCSN). Two new microscopic calculations of stellar EC rates are obtained from relativistic and nonrelativistic finite-temperature quasiparticle random-phase approximation approaches, for a conventional grid of temperatures and densities. In both approaches, EC rates due to Gamow-Teller transitions are included. In the relativistic calculation, contributions from first-forbidden transitions are also included and add strongly to the EC rates. The new EC rates are compared with large-scale shell-model calculations for the specific case of 86 Kr, providing insight into the finite-temperature effects on the EC rates. At relevant thermodynamic conditions for core collapse, the discrepancies between the different calculations of this paper are within about one order of magnitude. Numerical simulations of CCSN are performed with the spherically symmetric gr1d simulation code to quantify the impact of such differences on the dynamics of the collapse. These simulations also include EC rates based on two parametrized approximations. A comparison of the neutrino luminosities and enclosed mass at core bounce shows that differences between simulations with different sets of EC rates are relatively small (≈ 5 %), suggesting that the EC rates used as inputs for these simulations have become well constrained.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2016

Quantum Monte Carlo calculations of two neutrons in finite volume

Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial for determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

Effect of finite particle number sampling on baryon number fluctuations

The effects of finite particle number sampling on the net baryon number cumulants, extracted from fluid dynamical simulations, are studied. The commonly used finite particle number sampling procedure introduces an additional Poissonian (or multinomial if global baryon number conservation is enforced) contribution which increases the extracted moments of the baryon number distribution. If this procedure is applied to a fluctuating fluid dynamics framework, one severely overestimates the actual cumulants. We show that the sampling of so-called test particles suppresses the additional contribution to the moments by at least one power of the number of test particles. We demonstrate this method in a numerical fluid dynamics simulation that includes the effects of spinodal decomposition due to a first-order phase transition. Furthermore, in the limit where antibaryons can be ignored, we derive analytic formulas which capture exactly the effect of particle sampling on the baryon number cumulants. These formulas may be used to test the various numerical particle sampling algorithms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Finite naturalness and quark-lepton unification

We study the implications of finite naturalness in Pati-Salam models where SU⁢(3)C is embedded in SU(4). For the minimal realization at low scale of quark-lepton unification, which employs the inverse seesaw for neutrino masses, we find that radiative corrections to the Higgs boson mass are at least δm$^{2}_{ℎ}$/m$^{2}_{ℎ}$ ~O⁡(104). The one-loop contributions to the Higgs mass are suppressed by four powers of the hypercharge gauge coupling. We find that for the vector leptoquarks the naively leading part of the two-loop corrections cancel. We assume the Dirac Yukawa couplings for neutrinos are equal to the up-type quark Yukawa couplings as predicted in the minimal theory for quark-lepton unification. Despite these findings, the two-loop corrections still dominate the finite naturalness bound. We mention a way to relax the lower bound on the vector leptoquark mass and have δm$^{2}_{ℎ}$/m$^{2}_{ℎ}$ ~O⁡(10 2 ).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Finite-temperature instantons from first principles

We derive the finite-temperature quantum-tunneling rate from first principles. The tunneling rate depends on both temperature and time. We demonstrate that the relevant instantons should, therefore, be defined on a Keldysh-Schwinger contour, and we discuss how the familiar Euclidean time result arises from the limit of large physical times. We identify distinct behavior in the high- and low-temperature limits, incorporating effects from background fields. We construct a consistent perturbative scheme that incorporates large finite-temperature effects. Published by the American Physical Society 2024

Steingasser, Thomas (ORCID:0000000217262117)↗

DOE OSTI2011

Quark number susceptibility and QCD phase transition in the predictive soft-wall AdS/QCD model with finite temperature

Based on the infrared improved soft-wall AdS/QCD model which can lead to a consistent prediction for the mass spectra of light resonance mesons, we extend it to the finite temperature system and carry out the calculation for the quark number susceptibility with finite quark mass. As a consequence, we show that the quark number susceptibility grows rapidly with a continuous blowup in a narrow temperature interval as the temperature increases, and there is a peak when the temperature is around T{approx_equal}160{approx}190 MeV depending slightly on the models. The resulting critical temperature is about 170 MeV, which agrees remarkably with the lattice QCD calculation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2011

Charmonium spectral functions with the variational method in zero and finite temperature lattice QCD

We propose a method to evaluate spectral functions on the lattice based on a variational method. On a lattice with a finite spatial extent, spectral functions consist of discrete spectra only. Adopting a variational method, we calculate the locations and the heights of spectral functions at low-lying discrete spectra. We first test the method in the case of analytically solvable free Wilson quarks at zero and finite temperatures and confirm that the method well reproduces the analytic results for low-lying spectra. We find that we can systematically improve the results by increasing the number of trial states. We then apply the method to calculate the charmonium spectral functions for S and P-wave states at zero-temperature in quenched QCD and compare the results with those obtained using the conventional maximum entropy method (MEM). The results for the ground state are consistent with the location and the area of the first peak in spectral functions from the MEM, while the variational method leads to a mass which is closer to the experimental value for the first excited state. We also investigate the temperature dependence of the spectral functions for S-wave states below and above T{sub c}. We obtain no clear evidences for dissociation of J/{psi} and {eta}{sub c} up to 1.4T{sub c}.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2013

Does the finite size of the proto-neutron star preclude supernova neutrino flavor scintillation due to turbulence?

Here, the transition probabilities describing the evolution of a neutrino with a given energy along some ray through a turbulent supernova profile are random variates unique to each ray. If the proto-neutron-star source of the neutrinos were a point, then one might expect the evolution of the turbulence would cause the flavor composition of the neutrinos to vary in time i.e. the flavor would scintillate. But in reality the proto-neutron star is not a point source—it has a size of order ˜10km, so the neutrinos emitted from different points at the source will each have seen different turbulence. The finite source size will reduce the correlation of the flavor transition probabilities along different trajectories and reduce the magnitude of the flavor scintillation. To determine whether the finite size of the proto-neutron star will preclude flavor scintillation, we calculate the correlation of the neutrino flavor transition probabilities through turbulent supernova profiles as a function of the separation δx between the emission points. The correlation will depend upon the power spectrum used for the turbulence, and we consider two cases: when the power spectrum is isotropic, and the more realistic case of a power spectrum which is anisotropic on large scales and isotropic on small. Although it is dependent on a number of uncalibrated parameters, we show the supernova neutrino source is not of sufficient size to significantly blur flavor scintillation in all mixing channels when using an isotropic spectrum, and this same result holds when using an anisotropic spectrum, except when we greatly reduce the similarity of the turbulence along parallel trajectories separated by ˜10km or less.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Two-particle multichannel systems in a finite volume with arbitrary spin

The quantization condition for two-particle systems with arbitrary number of two-body open coupled channels, spin and masses in a finite cubic volume with either periodic or twisted boundary conditions is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is relativistic, holds for all momenta below the three- and four-particle thresholds, and is exact up to exponential volume corrections that are governed by L/r, where L is the spatial extent of the volume and r is the range of the interactions between the particles. With hadronic systems the range of the interaction is set by the inverse of the pion mass, m π , and as a result the formalism presented is suitable for m π L>>1. Implications of the formalism for the studies of multichannel baryon-baryon systems are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗