Critical Dynamical Exponent of the Two-Dimensional Scalar ϕ4\phi^4 Model with Local Moves

We study the scalar one-component two-dimensional (2D) $\phi^4$ model by computer simulations, with local Metropolis moves. The equilibrium exponents of this model are well-established, e.g. for the 2D $\phi^4$ model $\gamma= 1.75$ and $\nu= 1$. The model has also been conjectured to belong to the Ising universality class. However, the value of the critical dynamical exponent $z_c$ is not settled. In this paper, we obtain $z_c$ for the 2D $\phi^4$ model using two independent methods: (a) by calculating the relative terminal exponential decay time $\tau$ for the correlation function $\langle \phi(t)\phi(0)\rangle$, and thereafter fitting the data as $\tau \sim L^{z_c}$, where $L$ is the system size, and (b) by measuring the anomalous diffusion exponent for the order parameter, viz., the mean-square displacement (MSD) $\langle \Delta \phi^2(t)\rangle\sim t^c$ as $c=\gamma/(\nu z_c)$, and from the numerically obtained value $c\approx 0.80$, we calculate $z_c$. For different values of the coupling constant $\lambda$, we report that $z_c=2.17\pm0.03$ and $z_c=2.19\pm0.03$ for the two methods respectively. Our results indicate that $z_c$ is independent of $\lambda$, and is likely identical to that for the 2D Ising model. Additionally, we demonstrate that the Generalised Langevin Equation (GLE) formulation with a memory kernel, identical to those applicable for the Ising model and polymeric systems, consistently capture the observed anomalous diffusion behavior.Comment: 14 pages, 4 figures, 6 figure files, to appear in Phys. Rev.

Transverse momentum broadening of vector boson production in high energy nuclear collisions

We calculate in perturbative QCD the transverse momentum broadening of vector boson production in high energy nuclear collisions. We evaluate the effect of initial-state parton multiple scattering for the production of the Drell-Yan virtual photon and $W/Z$ bosons. We calculate both the initial- and final-state multiple scattering effect for the production of heavy quarkonia and their transverse momentum broadening in both NRQCD and Color Evaporation model of quarkonium formation. We find that J/$\psi$ and $\Upsilon$ broadening in hadron-nucleus collision is close to $2C_A/C_F$ times the corresponding Drell-Yan broadening, which gives a good description of existing Fermilab data. Our calculations are also consistent with RHIC data on J/$\psi$ broadening in relativistic heavy ion collisions. We predict the transverse momentum broadening of vector boson (J/$\psi$, $\Upsilon$, and $W/Z$) production in relativistic heavy ion collisions at the LHC, and discuss the role of the vector boson broadening in diagnosing medium properties.Comment: 22 pages, 10 figures, revised version to appear in Phys. Rev.

Quantum Correction in Exact Quantization Rules

An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the quantum correction is an invariant, independent of the number of nodes in the wave function. In those systems, the energy levels of all the bound states can be easily calculated from the exact quantization rule and the solution for the ground state, which can be obtained by solving the Riccati equation. With this new method, we re-calculate the energy levels for the one-dimensional systems with a finite square well, with the Morse potential, with the symmetric and asymmetric Rosen-Morse potentials, and with the first and the second P\"{o}schl-Teller potentials, for the harmonic oscillators both in one dimension and in three dimensions, and for the hydrogen atom.Comment: 10 pages, no figure, Revte

Low-mass lepton pair production at large transverse momentum

We study the transverse momentum distribution of low-mass lepton pairs produced in hadronic scattering, using the perturbative QCD factorization approach. We argue that the distribution at large transverse momentum, $Q_T \gg Q$, with the pair's invariant mass $Q$ as low as $Q \sim \Lambda_{\mathrm{QCD}}$, can be systematically factorized into universal parton-to-lepton pair fragmentation functions, parton distributions, and perturbatively calculable partonic hard parts evaluated at a short distance scale $\sim {\cal O}(1/Q_T)$. We introduce a model for the input lepton pair fragmentation functions at a scale $\mu_0\sim 1$ GeV, which are then evolved perturbatively to scales relevant at RHIC. Using the evolved fragmentation functions, we calculate the transverse momentum distributions in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions at RHIC. We also discuss the sensitivity of the transverse momentum distribution of low-mass lepton pairs to the gluon distribution.Comment: 16 pages, 11 figures, revised version to appear in Phys. Rev.

Electric Field Effect in Multilayer Cr2Ge2Te6: a Ferromagnetic Two-Dimensional Material

The emergence of two-dimensional (2D) materials has attracted a great deal of attention due to their fascinating physical properties and potential applications for future nanoelectronic devices. Since the first isolation of graphene, a Dirac material, a large family of new functional 2D materials have been discovered and characterized, including insulating 2D boron nitride, semiconducting 2D transition metal dichalcogenides and black phosphorus, and superconducting 2D bismuth strontium calcium copper oxide, molybdenum disulphide and niobium selenide, etc. Here, we report the identification of ferromagnetic thin flakes of Cr2Ge2Te6 (CGT) with thickness down to a few nanometers, which provides a very important piece to the van der Waals structures consisting of various 2D materials. We further demonstrate the giant modulation of the channel resistance of 2D CGT devices via electric field effect. Our results illustrate the gate voltage tunability of 2D CGT and the potential of CGT, a ferromagnetic 2D material, as a new functional quantum material for applications in future nanoelectronics and spintronics.Comment: To appear in 2D Material

Harnessing high-dimensional hyperentanglement through a biphoton frequency comb

Quantum entanglement is a fundamental resource for secure information processing and communications, where hyperentanglement or high-dimensional entanglement has been separately proposed towards high data capacity and error resilience. The continuous-variable nature of the energy-time entanglement makes it an ideal candidate for efficient high-dimensional coding with minimal limitations. Here we demonstrate the first simultaneous high-dimensional hyperentanglement using a biphoton frequency comb to harness the full potential in both energy and time domain. The long-postulated Hong-Ou-Mandel quantum revival is exhibited, with up to 19 time-bins, 96.5% visibilities. We further witness the high-dimensional energy-time entanglement through Franson revivals, which is observed periodically at integer time-bins, with 97.8% visibility. This qudit state is observed to simultaneously violate the generalized Bell inequality by up to 10.95 deviations while observing recurrent Clauser-Horne-Shimony-Holt S-parameters up to 2.76. Our biphoton frequency comb provides a platform in photon-efficient quantum communications towards the ultimate channel capacity through energy-time-polarization high-dimensional encoding

Accessing tri-gluon correlations in the nucleon via the single spin asymmetry in open charm production

We calculate the single transverse-spin asymmetry for open charm production in $pp$ collisions within the QCD collinear factorization approach. We include contributions from both twist-three quark-gluon and tri-gluon correlation functions. We find that the quark-gluon correlation functions alone generate only a very small asymmetry for open charm production in the kinematic region of current interest at RHIC, so that the observation of any significant single-spin asymmetry would be a clear indication of the presence of tri-gluon correlations inside a polarized proton. We furthermore demonstrate that the tri-gluon contribution could be very different for the production of $D$ and $\bar{D}$ mesons. These features make the single spin asymmetry in open charm production in polarized $pp$ collisions at RHIC an excellent probe of tri-gluon correlation functions.Comment: 10 pages, 7 figure