Non-monotonic Energy Dependence Research Articles

Nonadiabatic quantum dynamics explores non-monotonic photodissociation branching of N2 into the N(4S) + N(2D) and N(4S) + N(2P) product channels.

Vacuum ultraviolet (VUV) photodissociation of N2 molecules is a source of reactive N atoms in the interstellar medium. In the energy range of VUV optical excitation of N2, the N-N triple bond cleavage leads to three types of atoms: ground-state N(4S) and excited-state N(2P) and N(2D). The latter is the highest reactive and it is believed to be the primary participant in reactions with hydrocarbons in Titan's atmosphere. Experimental studies have observed a non-monotonic energy dependence and non-statistical character of the photodissociation of N2. This implies different dissociation pathways and final atomic products for different wavelength regions in the sunlight spectrum. We here apply ab initio quantum chemical and nonadiabatic quantum dynamical techniques to follow the path of an electronic state from the excitation of a particular singlet 1Σ+u and 1Πu vibronic level of N2 to its dissociation into different atomic products. We simulate dynamics for two isotopomers of the nitrogen molecule, 14N2 and 14N15N for which experimental data on the branching are available. Our computations capture the non-monotonic energy dependence of the photodissociation branching ratios in the energy range 108 000-116 000 cm-1. Tracing the quantum dynamics in a bunch of electronic states enables us to identify the key components that determine the efficacy of singlet to triplet population transfer and therefore predissociation lifetimes and branching ratios for different energy regions.

Energy dependence of intermittency for charged hadrons in Au+Au collisions at RHIC

Density fluctuations near the QCD critical point can be probed via an intermittency analysis in relativistic heavy-ion collisions. We report the first measurement of intermittency in Au+Au collisions at sNN = 7.7-200 GeV measured by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The scaled factorial moments of identified charged hadrons are analyzed at mid-rapidity and within the transverse momentum phase space. We observe a power-law behavior of scaled factorial moments in Au+Au collisions and a decrease in the extracted scaling exponent (ν) from peripheral to central collisions. The ν is consistent with a constant for different collisions energies in the mid-central (10-40%) collisions. Moreover, the ν in the 0-5% most central Au+Au collisions exhibits a non-monotonic energy dependence that reaches a minimum around sNN = 27 GeV. The physics implications on the QCD phase structure are discussed.

Searching for QCD critical point with light nuclei

Density fluctuations and correlations due to a first-order quark-gluon plasma to hadronic matter phase transition and its critical end point, if they remain present after the hadronic evolution in a heavy ion collisions, can lead to an enhanced production of light nuclei in these collisions. This would then result in a non-monotonic collision energy dependence of the yield ratio $$N_\text {t} N_\text {p} / N_\text {d}^2$$ of proton number $$N_\text {p}$$ , deuteron number $$N_\text {d}$$ , and triton number $$N_\text {t}$$ . Measurements of this yield ratio as a function of collision energy thus provides the possibility to probe the equation of state of strong-interaction matter and its phase diagram.

Study of strange quark density fluctuations in Au + Au Collisions at $$\sqrt{\textrm{s}_{_{\textrm{NN}}}}$$ = 7.7–200 GeV from AMPT Model

The strangeness production is an important observable to study the QCD phase diagram. The yield ratios of strange quark can be helpful to search for the QCD critical end point (CEP) and/or first-order phase transition. In this work, we studied the production of $$K^{\pm }$$ , $$\Xi ^-({\bar{\Xi }}^{+})$$ , $$\phi $$ and $$\Lambda ({\bar{\Lambda }})$$ in Au + Au collisions at $$\sqrt{\textrm{s}_{_{\textrm{NN}}}}$$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV from A Multi-Phase Transport model with string melting version (AMPT-SM). We calculated the invariant yield of these strange hadrons using a different set of parameters compared to those reported in earlier studies and also by varying the hadronic cascade time ( $$t_{max}$$ ) in the AMPT-SM model. We also calculated the yield ratios, $${\mathcal {O}}_{K^{\pm }-\Xi ^{-}({\bar{\Xi }}^{+})-\phi -\Lambda (\bar{\Lambda })}$$ which are reported as sensitive to the strange quark density fluctuations and found that the AMPT-SM model fails to describe the non-monotonic trend observed by the experimental data. The negative particle ratio are found to be higher than the ratio of positive particles which is consistent with the experimental data. A significant effect is also seen on these ratios by varying the $$t_{max}$$ . For a crossover transition between the Quark-Gluon Plasma (QGP) and hadronic matter, the double yield ratios considered in the present study based on AMPT-SM model do not show any non-monotonic behaviors and thus providing a baseline for the search of CEP, because there is no first-order or second-order phase transition in the AMPT model. The more realistic equation of state based dynamical modeling is still required for the heavy-ion collisions in order to extract the definite physics conclusion about the non-monotonic energy dependence behavior.

A non-perturbative study of the interplay between electron–phonon interaction and Coulomb interaction in undoped graphene

In condensed-matter systems, electrons are subjected to two different interactions under certain conditions. Even if both interactions are weak, it is difficult to perform perturbative calculations due to the complexity caused by the interplay of two interactions. When one or two interactions are strong, ordinary perturbation theory may become invalid. Here we consider undoped graphene as an example and provide a non-perturbative quantum-field-theoretic analysis of the interplay of electron–phonon interaction and Coulomb interaction. We treat these two interactions on an equal footing and derive the exact Dyson–Schwinger (DS) integral equation of the full Dirac-fermion propagator. This equation depends on several complicated correlation functions and thus is difficult to handle. Fortunately, we find that these correlation functions obey a number of exact identities, which allows us to prove that the DS equation of full fermion propagator is self-closed. After solving this self-closed equation, we obtain the renormalized fermion velocity and show that its energy (momentum) dependence of renormalized fermion velocity is dominantly determined by the electron–phonon (Coulomb) interaction. In particular, the renormalized velocity exhibits a logarithmic momentum dependence and a non-monotonic energy dependence.

Cumulants and correlation functions of net-proton, proton, and antiproton multiplicity distributions in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider

We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton multiplicity distributions, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the BNL Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| <$ 0.5) and transverse momentum 0.4 $<$ $p_{\rm T}$ $<$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ($\sqrt{s_{\mathrm {NN}}}$ = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with $\sqrt{s_{\mathrm {NN}}}$. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be understood by the effect of baryon number conservation.

Study on higher moments of net-charge multiplicity distributions using a multiphase transport model * *Supported in part by the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030000), the National Natural Science Foundation of China (11890710, 11890714, 11835002, 11961131011) and the Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008)

The moments and moment products of conserved charges are believed to be sensitive to critical fluctuations, which have been adopted in determining the QCD critical point. Using a dynamical multiphase transport model, we reproduce the centrality and energy dependences of moments and moment products of net-charge multiplicity distributions in Au+Au collisions, measured by the Beam Energy Scan program at the RHIC. No non-monotonic energy dependence is observed. We infer that the moment products develop during the dynamical evolution of heavy-ion collisions. The observed difference based on the expectation of the Poisson baseline indicates a positive two-particle correlation between positively and negatively charged particles, which can arise from different dynamical processes at different stages. Therefore, to adopt moments and moment products of net-charge multiplicity distributions in determining the QCD critical point of relativistic heavy-ion collisions, it is essential to consider the dynamical evolution.

Light Nuclei (d, t) Production in Au + Au Collisions at [formula omitted

In high-energy nuclear collisions, light nuclei can be regarded as a cluster of baryons and their yields are sensitive to the baryon density fluctuations. Thus, the production of light nuclei can be used to study the QCD phase transition, at which the baryon density fluctuation will be enhanced. A yield ratio of light nuclei, defined as N(t)×N(p)/N2(d), is predicted to be a sensitive observable to search for the 1st-order phase transition and/or QCD critical point in heavy-ion collisions. In this paper, we present the energy and centrality dependence of (anti)deuteron and triton production in Au+Au collisions at sNN=7.7,11.5,14.5,19.6,27,39,54.4,62.4,and200GeV measured by the STAR experiment at RHIC. We show beam-energy dependence for the coalescence parameter, B2(d) and B3(t), particle ratios, d/p, t/p, and t/d, and the yield ratio of N(t)×N(p)/N2(d). More importantly, non-monotonic energy dependence is observed for the yield ratio, N(t)×N(p)/N2(d), in 0-10% central Au+Au collisions with a peak around 20-30 GeV. Their physics implications on QCD critical point search and change of the equation of state will be discussed.

The production of triton and reconstruction of [formula omitted] with the Heavy Flavor Tracker in Au+Au collisions at STAR

The transverse momentum spectra of triton with STAR Beam Energy Scan data from Au+Au collisions at sNN=7.7,11.5,14.5,19.6,27,39,62.4,200GeV in the centrality classes 0 – 10%, 10 – 20%, 20 – 40% and 40 – 80% are reported. The centrality dependence of the coalescence parameter B3 of triton and the collision energy dependence of the relative neutron density fluctuation are then calculated. The results indicate that the B3 decreases from peripheral to central collisions and the neutron density fluctuation shows a non-monotonic collision energy dependence with a peak around collision energy of 20-30 GeV. In addition, we report details about the reconstruction method of HΛ3 via HΛ3→3He+π− and HΛ3→d+p+π− using high statistics data in Au+Au collisions at sNN=200GeV collected in 2014 and 2016 with the Heavy Flavor Tracker.

Critical point of nuclear matter and beam-energy dependence of net-proton number fluctuations

The beam energy dependence of net baryon number susceptibilities is studied in the framework of the hadron resonance gas model with the attractive and repulsive van der Waals interactions between baryons. The collision energy dependences for the skewness $S\sigma$ and kurtosis $\kappa\sigma^2$ deviate significantly from the Poisson baseline and demonstrate the existence of rich structures at moderate collision energies. This behavior may result from the critical end point of the nuclear liquid-gas first order phase transition. In particular, $\kappa\sigma^2$ shows a non-monotonic energy dependence, and, in contrast to the standard scenario for the QCD critical point, it does not decrease at low collision energies. It is also found that the measurable net proton fluctuations differ significantly from the net baryon fluctuations when interactions between baryons cannot be neglected. The results are compared with the experimental net proton number fluctuations measured by the STAR collaboration.

Thermal plasmon resonantly enhances electron scattering in Dirac/Weyl semimetals

We study the inelastic scattering rate due to the Coulomb interaction in three-dimensional Dirac/Weyl semimetals at finite temperature. We show that the perturbation theory diverges because of the long-range nature of the interaction, hence, thermally induced screening must be taken into account. We demonstrate that the scattering rate has a non-monotonic energy dependence with a sharp peak owing to the resonant decay into thermal plasmons. We also consider the Hubbard interaction for comparison. We show that, in contrast to the Coulomb case, it can be well described by the second-order perturbation theory in a wide energy range.

Probing medium-induced jet splitting and energy loss in heavy-ion collisions

The nuclear modification of jet splitting in relativistic heavy-ion collisions at RHIC and the LHC energies is studied based on the higher twist formalism. Assuming coherent energy loss for the two splitted subjets, a non-monotonic jet energy dependence is found for the nuclear modification of jet splitting function: strongest modification at intermediate jet energies whereas weaker modification for larger or smaller jet energies. Combined with the smaller size and lower density of the QGP medium at RHIC than at the LHC, this helps to understand the groomed jet measurements from CMS and STAR Collaborations: strong modification of the momentum sharing zg distribution at the LHC and no obvious modification of zg distribution at RHIC. In addition, the observed nuclear modification pattern of the groomed jet zg distribution cannot be explained solely by independent energy loss of the two subjets. Our result may be tested in future measurements of groomed jets with lower jet energies at the LHC and larger jet energies at RHIC, for different angular separations between the two subjets.

Dynamical resonant neutralization of low-energy Na+ ions scattered from Au(111), Pd(111), Cu(111), and Cu(110) surfaces

The nonmonotonic energy dependence of the $\mathrm{L}{\mathrm{i}}^{0}$ fraction on high-work-function surfaces has not been understood so far. To further study this phenomenon, in this work, efficient neutralization of $\mathrm{N}{\mathrm{a}}^{+}$ ions has been reported on various surfaces, instead of $\mathrm{L}{\mathrm{i}}^{+}$ ions. The nonmonotonic energy dependence of the $\mathrm{N}{\mathrm{a}}^{0}$ fraction becomes more and more obvious with the increase of the surface work function. For Cu(111) and Cu(110) at the scattering angle of 7\ifmmode^\circ\else\textdegree\fi{}, the energy dependence of the neutral fraction is still nonmonotonic as compared to the scattering angles of 135\ifmmode^\circ\else\textdegree\fi{} and 53\ifmmode^\circ\else\textdegree\fi{}. For the scattering angle of 53\ifmmode^\circ\else\textdegree\fi{}, the nonmonotonic angle dependence has been observed for these surfaces. The essences of the nonmonotonic angle and energy dependences are the same. The quantum-mechanical calculations reveal that the width and position of the atomic level below the Fermi level at short ion-surface distances are responsible for high neutral fractions at large exit energies, and that the neutral fraction at much smaller exit energies is probably related to the neutralization at large distances. For the exit angle dependence, the competition between neutralization at short and large distances strongly depends on the surface work function. In particular, the neutralization is enhanced by the relatively large parallel velocity.

Proton cumulants and correlation functions in Au + Au collisions at [formula omitted] GeV from UrQMD model

We studied the acceptance dependence of proton cumulants (up to fourth order) and correlation functions in 0–5% most central Au+Au collisions at sNN=7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV from UrQMD model. We found that high order proton cumulants show suppressions at large acceptance. By decomposing the proton cumulants into linear combination of multi-proton correlation functions, we observed the two-proton correlation functions always show negative values due to the effects of baryon number conservations. The three and four-proton correlation functions are close to zero and show negligible acceptance dependence. We further observed that the proton cumulants and correlation functions follow similar trends and show a scaling behavior when plotting the results versus mean number of protons. The comparisons between experimental data and the UrQMD calculations show that the non-monotonic energy dependence of proton correlation functions measured by STAR experiment cannot be described by the UrQMD model. The UrQMD calculations can provide us baselines for the experimental studies of the proton cumulants and correlation functions. Finally, we propose to measure the rapidity dependence of the reduced proton correlation functions to search for the QCD critical point in heavy-ion collisions.

Measurement of the cumulants of net-proton multiplicity distribution in Au+Au collisions at [formula omitted] – 200 GeV from the STAR experiment

One of the main goals of the RHIC Beam Energy Scan program is to search for the QCD Critical Point (CP) and phase transition in heavy-ion collisions. Fluctuations of conserved quantities are highly sensitive to the correlation length, and are directly connected to the susceptibilities in the Lattice QCD. Therefore, they are ideal observables for finding the CP and phase transition signatures. We present measurements of the cumulants of net-proton distributions from Au+Au collisions at sNN=7.7,11.5,14.5,19.6,27,39,62.4 (up to the fourth-order) and 200 GeV (up to the sixth-order) measured by the STAR experiment at RHIC. We also present the multiparticle correlation functions extracted from the proton and anti-proton cumulants. It is observed that the four-particle correlations are positive and show non-monotonic energy dependence in the fourth-order fluctuations. Finally, we discuss the corresponding physics implications.

Impact of resonance decays on critical point signals in net-proton fluctuations

The non-monotonic beam energy dependence of the higher cumulants of net-proton fluctuations is a widely studied signature of the conjectured presence of a critical point in the QCD phase diagram. In this work we study the effect of resonance decays on critical fluctuations. We show that resonance effects reduce the signatures of critical fluctuations, but that for reasonable parameter choices critical effects in the net-proton cumulants survive. The relative role of resonance decays has a weak dependence on the order of the cumulants studied with a slightly stronger suppression of critical effects for higher-order cumulants.

Cumulants of net-proton, net-kaon, and net-charge multiplicity distributions in Au + Au collisions atsNN=7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV within the UrQMD model

Fluctuations of conserved quantities are sensitive observables to probe the signature of QCD phase transition and critical point in heavy-ion collisions. With the UrQMD model, we have studied the centrality and energy dependence of various order cumulants and cumulant ratios (up to fourth order) of net-proton,net-charge and net-kaon multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}}$= 7.7, 11.5, 19.6, 27, 39, 62.4, 200 GeV. The model results show that the production mechanism of the particles and anti-particles have significant impacts on the cumulants of net-particles multiplicity distributions and show strong energy dependence. We also made comparisons between model calculations and experimental data measured in the first phase of the beam energy scan (BES) program by the STAR experiment at RHIC. The comparisons indicate that the baryon conservation effect strongly suppress the cumulants of net-proton distributions at low energies and the non-monotonic energy dependence for the net-proton {\KV} at the most central Au+Au collisions measured by the STAR experiment can not be described by the UrQMD model. Since there has no physics of QCD phase transition and QCD critical point implemented in the UrQMD, the model results provide us baselines and qualitative estimates about the non-critical background contributions to the fluctuations observables in heavy-ion collisions.

Propagation of collective pair excitations in disordered Bose superfluids

We study the effect of disorder on the propagation of collective excitations in a disordered Bose superfluid. We incorporate local density depletion induced by strong disorder at the meanfield level, and formulate the transport of the excitations in terms of a screened scattering problem. We show that the competition of disorder, screening, and density depletion induces a strongly non-monotonic energy dependence of the disorder parameter. In three dimensions, it results in a rich localization diagram with four different classes of mobility spectra, characterized by either no or up to three mobility edges. Implications on experiments with disordered ultracold atoms are discussed.

Coulomb interaction in graphene: Relaxation rates and transport

We analyze the inelastic electron-electron scattering in undoped graphene within the Keldysh diagrammatic approach. We demonstrate that finite temperature strongly affects the screening properties of graphene, which, in turn, influences the inelastic-scattering rates as compared to the zero-temperature case. Focusing on the clean regime, we calculate the quantum scattering rate which is relevant for dephasing interference processes. We identify a hierarchy of regimes arising due to the interplay of a plasmon enhancement of the scattering and finite-temperature screening of the interaction. We further address the energy relaxation and transport scattering rates in graphene. We find a nonmonotonic energy dependence of the inelastic relaxation rates in clean graphene, which is attributed to the resonant excitation of plasmons. Finally, we discuss the temperature dependence of the conductivity at the Dirac point in the presence of both interaction and disorder. Our results complement the kinetic equation and hydrodynamic approaches for the collision-limited conductivity of clean graphene and can be generalized to the treatment of physics of inelastic processes in strongly nonequilibrium setups.

Oscillations of tunnel magnetoresistance in ferromagnet-insulator-ferromagnet structures

A model of spin-dependent electron transport in ferromagnet-insulator-ferromagnet structures that takes into account the potential relief, applied voltage, image forces, and scattering by the potential relief is developed. It is shown that tunnel magnetoresistance oscillations are caused by the nonmonotonic energy dependence of transmission coefficients and their split in the molecular field of the ferromagnet. Conditions are found under which the tunnel magnetoresistance is virtually independent of scattering by the interfaces.