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Jian Deng

Publications and source records attributed to Jian Deng.

34 records · Page 2Linked to original sources
arXiv2017

Universal relations between nongaussian fluctuations in heavy-ion collisions

We show that universality near a critical end point implies a characteristic relation between third- and fourth-order baryon susceptibilities $χ_3$ and $χ_4$, resulting in a banana-shaped loop when $χ_4$ is plotted as a function of $χ_3$ along a freeze-out line. Including the individual enhancements of $χ_3$ and $χ_4$ near a critical point, these features may be a consistent set of observations supporting the interpretation of baryon fluctuations data as arising from criticality.

hep-ph↗
arXiv2015

Robust characteristics of nongaussian fluctuations from the NJL model

We evaluate the third- and fourth-order baryon, charge and strangeness susceptibilities near a chiral critical point using the Nambu-Jona-Lasinio model. We identify robust qualitative behaviours of the susceptibilities along hypothetical freeze-out lines that agree with previous model studies. Quantitatively, baryon number fluctuations are the largest in magnitude and thus offer the strongest signal when freeze-out occurs farther away from a critical point. Charge and strangeness susceptibilities also diverge at a critical point, but the area where the divergence dominates is smaller, meaning freeze-out must occur closer to a critical point for a signal to be visible in these observables. In case of strangeness, this is attributable to the relatively large strange quark mass. Plotting the third- and fourth-order susceptibilities against each other along the freeze-out line exhibits clearly their non-montonicity and robust features.

hep-ph↗
arXiv2015

Baryon susceptibilities, nongaussian moments and the QCD critical point

We calculate model-independently the impact of the critical point on higher order baryon susceptibilities $χ_n$, showing how they depend on fluctuations of the order parameter. Including all tree level diagrams, we find new contributions to $χ_4$ equally important to the kurtosis of the order parameter fluctuations, and we characterize the kurtosis and other nonguassian moments as functions on the phase diagram. Important features of this analysis are then confirmed by a Gross-Neveu model study with good agreement with other model studies as well as lattice and experimental data. This suggests the universality of the characteristic peak in baryon susceptibilities as a signal of the critical point. We discuss leveraging measurements of different $χ_n$ to extrapolate the location of the critical point.

hep-ph↗
arXiv2013

Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases

From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.

cond-mat.stat-mech↗
arXiv2013

Shear and Bulk Viscosities of a Gluon Plasma in Perturbative QCD: Comparison of Different Treatments for the gg<->ggg Process

The leading order contribution to the shear and bulk viscosities, ηand ζ, of a gluon plasma in perturbative QCD includes the gg -> gg (22) process, gg <-> ggg (23) process and multiple scattering processes known as the Landau-Pomeranchuk-Migdal (LPM) effect. Complete leading order computations for ηand ζwere obtained by Arnold, Moore and Yaffe (AMY) and Arnold, Dogan and Moore (ADM), respectively, with the inelastic processes computed by an effective g <-> gg gluon splitting. We study how complementary calculations with 22 and 23 processes and a simple treatment to model the LPM effect compare with the results of AMY and ADM. We find that our results agree with theirs within errors. By studying the contribution of the 23 process to η, we find that the minimum angle θamong the final state gluons in the fluid local rest frame has a distribution that is peaked at θ\sim \sqrt{α_{s}}, analogous to the near collinear splitting asserted by AMY and ADM. However, the average of θis much bigger than its peak value, as its distribution is skewed with a long tail. The same θbehavior is also seen if the 23 matrix element is taken to the soft gluon bremsstrahlung limit in the center-of-mass (CM) frame. This suggests that the soft gluon bremsstrahlung in the CM frame still has some near collinear behavior in the fluid local rest frame. We also generalize our result to a general SU(N_c) pure gauge theory and summarize the current viscosity computations in QCD.

hep-ph↗
arXiv2013

Collision Rate and Symmetry Factor in Gluon Plasma

The elastic and inelastic collision rates in a gluon gas are calculated. The symmetry factor and the phase space integral are discussed in detail. With a symmetry factor and well constrained phase space, the same result can be obtained as that of the full phase space without the factor. Such an equivalence is illustrated by analytic and numerical calculations for $gg \rightarrow gg$ and $gg\rightarrow ggg$ processes.

nucl-th↗
arXiv2012

Some Results on the Schiffer's Conjecture in R^2

Let $Ω$ be an open, bounded domain in the plane with connected and smooth boundary, and $ω$ an eigenfunction of the Neumann Laplacian corresponding to some Neumann eigenvalue $μ> 0$. If the boundary value of $ω$ is a nonzero constant along the boundary, denoting $0 = μ_1(Ω) < μ_2(Ω) <= ...$ the set of all Neumann eigenvalues for the Laplacian on $Ω$, we show that 1) if $μ< μ_8(Ω)$; or 2) if $Ω$ is strictly convex and centrally symmetric, $μ< μ_13(Ω)$, then $Ω$ must be a disk.

math.DG↗
arXiv2011

On the steady states of weakly reversible chemical reaction networks

A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the associated mass-action system. Furthermore, an index formula is given for the set of equilibria in a given stoichiometric compatibility class.

q-bio.QM↗
arXiv2011

Dilepton flow and deconfinement phase transition in heavy ion collisions

The dilepton radial flow in Au+Au collisions at \sqrt{s_{NN}}=200 GeV is investigated. The space-time evolution of the fireball is described by a 2+1 dimensional ideal hydrodynamics with a variety of equations of state. The slope parameters of the transverse momentum spectra from the partonic and hadronic phases show distinct features and are sensitive to equation of state parameters. The elliptic flow and breaking of M_T scaling are also studied and have distinct features for the two phases. These features can serve as clean signals for the formation of a quark-gluon plasma in ultra-relativistic heavy ion collisions.

nucl-th↗
arXiv2011

How Perfect a Gluon Plasma Can Be in Perturbative QCD?

The shear viscosity to entropy density ratio, η/s, characterizes how perfect a fluid is. We calculate the leading order η/s of a gluon plasma in perturbation using the kinetic theory. The leading order contribution only involves the elastic gg -> gg (22) process and the inelastic gg<->ggg (23) process. The Hard-Thermal-Loop (HTL) treatment is used for the 22 matrix element, while the exact matrix element in vacuum is supplemented by the gluon Debye mass insertion for the 23 process. Also, the asymptotic mass is used for the external gluons in the kinetic theory. The errors from not implementing HTL and the Landau-Pomeranchuk-Migdal effect in the 23 process, and from the uncalculated higher order corrections, are estimated. Our result for η/s lies between that of Arnold, Moore and Yaffe (AMY) and Xu and Greiner (XG). Our result shows that although the finite angle contributions are important at intermediate α_s (α_s \sim 0.01-0.1), the 22 process is still more important than 23 when α_s < 0.1. This is in qualitative agreement with AMY's result. We find no indication that the proposed perfect fluid limit η/s \simeq 1/(4π) can be achieved by perturbative QCD alone.

hep-ph↗
arXiv2008

BCS-BEC crossover in a relativistic boson-fermion model beyond mean field approximation

We investigate the fluctuation effect of the di-fermion field in the crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) in a relativistic superfluid. We work within the boson-fermion model obeying a global U(1) symmetry. To go beyond the mean field approximation we use Cornwall-Jackiw-Tomboulis (CJT) formalism to include higher order contributions. The quantum fluctuations of the pairing condensate is provided by bosons in non-zero modes, whose interaction with fermions gives the two-particle-irreducible (2PI) effective potential. It changes the crossover property in the BEC regime. With the fluctuations the superfluid phase transition becomes the first order in grand canonical ensemble. We calculate the condensate, the critical temperature $T_{c}$ and particle abundances as functions of crossover parameter the boson mass.

hep-ph↗
arXiv2007

Relativistic BCS-BEC crossover in a boson-fermion model

We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) in a relativistic superfluid within a boson-fermion model. The model includes, besides the fermions, separate bosonic degrees of freedom, accounting for the bosonic nature of the Cooper pairs. The crossover is realized by tuning the difference between the boson mass and boson chemical potential as a free parameter. The model yields populations of condensed and uncondensed bosons as well as gapped and ungapped fermions throughout the crossover region for arbitrary temperatures. Moreover, we observe the appearance of antiparticles for sufficiently large values of the crossover parameter. As an application, we study pairing of fermions with imbalanced populations. The model can potentially be applied to color superconductivity in dense quark matter at strong couplings.

nucl-th↗
arXiv2006

Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation

In this article we apply the technique proposed in Deng-Hou-Yu (Comm. PDE, 2005) to study the level set dynamics of the 2D quasi-geostrophic equation. Under certain assumptions on the local geometric regularity of the level sets of $θ$, we obtain global regularity results with improved growth estimate on $| \nabla^{\bot} θ|$. We further perform numerical simulations to study the local geometric properties of the level sets near the region of maximum $| \nabla^{\bot} θ|$. The numerical results indicate that the assumptions on the local geometric regularity of the level sets of $θ$ in our theorems are satisfied. Therefore these theorems provide a good explanation of the double exponential growth of $| \nabla^{\bot} θ|$ observed in this and past numerical simulations.

math.AP↗
arXiv2005

Classical simulation of Quantum Entanglement using Optical Transverse Modes in Multimode Waveguides

We discuss mode-entangled states based on the optical transverse modes of the optical field propagating in multi-mode waveguides, which are classical analogs of the quantum entangled states. The analogs are discussed in detail, including the violation of the Bell inequality and the correlation properties of optical pulses' group delays. The research on these analogs may be important, for it not only provides useful insights into fundamental features of quantum entanglement, but also yields new insights into quantum computation and quantum communication.

quant-ph↗
arXiv2004

Geometric properties and non-blowup of 3-D incompressible Euler flow

By exploring a local geometric property of the vorticity field along a vortex filament, we establish a sharp relationship between the geometric properties of the vorticity field and the maximum vortex stretching. This new understanding leads to an improved result of the global existence of the 3-D Euler equation under mild assumptions that are consistent with the observations from recent numerical computations.

math-ph↗