arXiv subjects

Shi Pu

Publications and source records attributed to Shi Pu.

At least 127 records · Page 7Linked to original sources

arXiv2017

Relativistic Chiral Kinetic Theory from Quantum Field Theories

The chiral kinetic theory of Weyl fermions with collisions in the presence of weak electric and magnetic fields is derived from quantum field theories. It is found that the side-jump terms in the perturbative solution of Wigner functions play a significant role for the derivation. Moreover, such terms manifest the breaking of Lorentz symmetry for distribution functions. The Lorentz covariance of Wigner functions thus leads to modified Lorentz transformation associated with side-jump phenomena further influenced by background fields and collisions.

hep-th↗

arXiv2017

Covariant chiral kinetic equation in Wigner function approach

The covariant chiral kinetic equation (CCKE) is derived from the 4-dimensional Wigner function by an improved perturbative method under the static equilibrium conditions. The chiral kinetic equation in 3-dimensions can be obtained by intergation over the time component of the 4-momentum. There is freedom to add more terms to the CCKE allowed by conservation laws. In the derivation of the 3-dimensional equation, there is also freedom to choose coefficients of some terms in $dx_{0}/dτ$ and $d\mathbf{x}/dτ$ ($τ$ is a parameter along the worldline, and $(x_{0},\mathbf{x})$ denotes the time-space position of a particle) whose 3-mometum integrals are vanishing. So the 3-dimensional chiral kinetic equation derived from the CCKE is not uniquely determined in the current approach. To go beyond the current approach, one needs a new way of building up the 3-dimensional chiral kinetic equation from the CCKE or directly from covariant Wigner equations.

nucl-th↗

arXiv2017

Fixed points and flow analysis on off-equilibrium dynamics in the boson Boltzmann equation

We consider fixed points of steady solutions and flow directions using the boson Boltzmann equation that is a one-dimensionally reduced kinetic equation after the angular integration. With an elastic collision integral of the two-to-two scattering process, in the dense (dilute) regime where the distribution function is large (small), the boson Boltzmann equation has approximate fixed points with a power-law spectrum in addition to the thermal distribution function. We argue that the power-law fixed point can be exact in special cases. We elaborate a graphical presentation to display evolving flow directions similarly to the renormalization group flow, which explicitly exhibits how fixed points are connected and parameter space is separated by critical lines. We discuss that such a flow diagram contains useful information on thermalization processes out of equilibrium.

hep-ph↗

arXiv2017

Iterative Mechanisms for Electricity Markets

In order to deal with market power that sporadically results from contingencies (e.g., severe weather, plant outages) most electricity markets have institutions in charge of monitoring market performance and mitigating market power. The latter task is often achieved by producing estimates of marginal costs (also referred to as "reference levels") that may replace the actual bids by generators with market power. In this paper, we propose an iterative mechanism that constitutes an alternative to outright regulatory intervention in those sporadic situations in which market power is a significant concern. The iterative mechanism proposed is based upon relatively simple information exchange between the market maker and market participants and is equipped to handle general non-linear (convex) constraints related to technical and/or reliability requirements. We show the mechanism proposed has many desirable properties (approximately): incentive compatibility, efficiency, individual rationality and (weak) budget balance. In addition, we show it is robust to imperfect information regarding costs. To illustrate we consider its application to the joint clearing of day ahead dispatch and reserves, an approach that has been proposed for the large-scale integration of renewable generation. In this context, we relax the assumption that each generator has perfect information on its own expected marginal costs of adjustment and show the mechanism retains most of its properties.

math.OC↗

arXiv2016

Analytic Solutions of Transverse Magneto-hydrodynamics under Bjorken Expansion

We review the recent developments of analytic solutions in transverse magneto-hydrodynamics under Bjorken expansion. It is found that the time dependence of magnetic fields can either increase or reduce the energy density depending on the decay exponent of magnetic fields. Moreover, perturbative solutions under weak magnetic fields with spatial inhomogeneity results in transverse flow, where the directions of flow also depend on the decay exponent of magnetic fields in time.

hep-ph↗

arXiv2016

Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization

We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work Roy et al., [Phys. Lett. B 750, 45 (2015)], we consider the fluid to have a non-zero magnetization. First, we assume a constant magnetic susceptibility $χ_{m}$ and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with $χ_{m}>0$), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with $χ_{m}<0$), the energy density decays faster because it feeds energy into the magnetic field. Furthermore, when the magnetic field is taken to be external and to decay in proper time $τ$ with a power law $\simτ^{-a}$, two distinct solutions can be found depending on the values of $a$ and $χ_m$. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional Bjorken flow with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data. We find that the temperature and energy density decay more slowly because of the non-vanishing magnetization. For values of the magnetic field typical for heavy-ion collisions, this effect is, however, rather small. Only for magnetic fields which are about an order of magnitude larger than expected for heavy-ion collisions, the system is substantially reheated and the lifetime of the quark phase might be extended.

nucl-th↗

arXiv2016

Transverse flow induced by inhomogeneous magnetic fields in the Bjorken expansion

We investigate the magnetohydrodynamics in the presence of an external magnetic field following the power-law decay in proper time and having spatial inhomogeneity characterized by a Gaussian distribution in one of transverse coordinates under the Bjorken expansion. The leading-order solution is obtained in the weak-field approximation, where both energy density and fluid velocity are modified. It is found that the spatial gradient of the magnetic field results in transverse flow, where the flow direction depends on the decay exponents of the magnetic field. We suggest that such a magnetic-field-induced effect might influence anisotropic flow in heavy ion collisions.

nucl-th↗

arXiv2016

Nonlinear Chiral Transport Phenomena

We study the nonlinear responses of relativistic chiral matter to the external fields, such as the electric field ${\bf E}$, gradients of temperature and chemical potential, ${\bf \nabla} T$ and ${\bf \nabla} μ$. Using the kinetic theory with Berry curvature corrections under the relaxation time approximation, we compute the transport coefficients of possible new electric currents that are forbidden in usual chirally symmetric matter, but are allowed in chirally asymmetric matter by parity. In particular, we find a new type of electric current proportional to ${\bf \nabla} μ\times {\bf E}$ due to the interplay between the effects of the Berry curvature and collisions. We also derive an analogue of the "Wiedemann-Franz" law specific for anomalous nonlinear transport in relativistic chiral matter.

hep-th↗

arXiv2015

Relativistic viscous hydrodynamics order by order

In this paper, we propose a method of solving the viscous hydrodynamics order by order in a derivative expansion. In such a method, the zero-order solution is just one of the ideal hydrodynamics. All the other higher order corrections satisfy the same first-order partial differential equations but with different inhomogeneous terms. We take the Bjorken flow as an example to test the validity of our method and present how to deal with the problems about the initial condition and perturbation evolution in our formalism.

nucl-th↗

arXiv2015

Analytic Bjorken flow in one-dimensional relativistic magnetohydrodynamics

In the initial stage of relativistic heavy-ion collisions, strong magnetic fields appear due to the large velocity of the colliding charges. The evolution of these fields appears as a novel and intriguing feature in the fluid-dynamical description of heavy-ion collisions. In this work, we study analytically the one-dimensional, longitudinally boost-invariant motion of an ideal fluid in the presence of a transverse magnetic field. Interestingly, we find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite conductivity, and irrespective of the strength of the initial magnetization, the decay of the fluid energy density $e$ with proper time $τ$ is the same as for the time-honored "Bjorken flow" without magnetic field. Furthermore, when the magnetic field is assumed to decay $\sim τ^{-a}$, where $a$ is an arbitrary number, two classes of analytic solutions can be found depending on whether $a$ is larger or smaller than one. In summary, the analytic solutions presented here highlight that the Bjorken flow is far more general than formerly thought. These solutions can serve both to gain insight on the dynamics of heavy-ion collisions in the presence of strong magnetic fields and as testbeds for numerical codes.

nucl-th↗

arXiv2015

Event-by-event distribution of magnetic field energy over initial fluid energy density in $\sqrt{s_{\rm NN}}$= 200 GeV Au-Au collisions

We estimate the event-by-event (e-by-e) distribution of the ratio ($σ$) of the magnetic field energy to the fluid energy density in the transverse plane of Au-Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV. A Monte-Carlo (MC) Glauber model is used to calculate the $σ$ in the transverse plane for impact parameter b=0, 12 fm at time $τ_i\sim$0.5 fm. The fluid energy density is obtained by using Gaussian smoothing with two different smoothing parameter $σ_g$=0.25 , 0.5 fm. For $b=0~\rm fm$ collisions $σ$ is found to be $\ll$ 1 in the central region of the fireball and $σ\gtrsim$ 1 at the periphery. For b=12 fm collisions $σ\gtrsim$ 1. The e-by-e correlation between $σ$ and the fluid energy density ($\varepsilon$) is studied. We did not find strong correlation between $σ$ and $\varepsilon$ at the centre of the fireball, whereas they are mostly anti-correlated at the periphery of the fireball.

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arXiv2014

Chiral Hall Effect and Chiral Electric Waves

We investigate the vector and axial currents induced by external electromagnetic fields and chemical potentials in chiral systems at finite temperature. Similar to the normal Hall effect, we find that an axial Hall current is generated in the presence of the electromagnetic fields along with an axial chemical potential, which may be dubbed as the "chiral Hall effect"(CHE). The CHE is related to the interactions of chiral fermions and exists with the a nonzero axial chemical potential. We argue that the CHE could lead to nontrivial charge distributions at different rapidity in asymmetric heavy ion collisions. Moreover, we study the chiral electric waves(CEW) led by the fluctuations of the vector and axial chemical potentials along with the chiral electric separation effect(CESE), where a density wave propagates along the applied electric field. Combining with the normal/chiral Hall effects, the fluctuations of chemical potentials thus result in Hall density waves. The Hall density waves may survive even at zero chemical potentials and become non-dissipative. We further study the transport coefficients including the Hall conductivities, damping times, wave velocities, and diffusion constants of CEW in a strongly coupled plasma via the AdS/CFT correspondence.

hep-th↗

arXiv2014

Kinetic equations for massive Dirac fermions in electromagnetic field with non-Abelian Berry phase

We derive a semi-classical effective action and the kinetic equation for massive Dirac fermions in electromagnetic fields. The non-Abelian Berry phase structure emerges from two helicity states of massive fermions with positive energy. The classical spin emerges as a vector in SU(2) helicity space. The continuity equations for the fermion number and the classical spin are derived. The fermion number is conserved while the spin charge is not conserved by anomaly. Previous results about the coefficients of the chiral magnetic effect for the fermion and axial currents in the chiral limit can be reproduced after including the anti-fermion contributions. This provides an example for the emerging spin and non-Abelian Berry phase of Dirac fermions arising from the fermion mass.

hep-th↗

arXiv2014

Holographic Chiral Electric Separation Effect

We investigate the chiral electric separation effect, where an axial current is induced by an electric field in the presence of both vector and axial chemical potentials, in a strongly coupled plasma via the Sakai-Sugimoto model with an $U(1)_R\times U(1)_L$ symmetry. By introducing different chemical potentials in $U(1)_R$ and $U(1)_L$ sectors, we compute the axial direct current (DC) conductivity stemming from the chiral current and the normal DC conductivity. We find that the axial conductivity is approximately proportional to the product of the axial and vector chemical potentials for arbitrary magnitudes of the chemical potentials. We also evaluate the axial alternating current (AC) conductivity induced by a frequency-dependent electric field, where the oscillatory behavior with respect to the frequency is observed.

hep-th↗

arXiv2013

Negative Off-Diagonal Conductivities in a Weakly Coupled Quark Gluon Plasma

We calculate the conductivity matrix of a weakly coupled quark-gluon plasma at the leading-log order. By setting all quark chemical potentials to be identical, the diagonal conductivities become degenerate and positive, while the off-diagonal ones become degenerate but negative (or zero when the chemical potential vanishes). This means a potential gradient of a certain fermion flavor can drive backward currents of other flavors. A simple explanation is provided for this seemingly counter intuitive phenomenon. It is speculated that this phenomenon is generic and most easily measured in cold atom experiments.

hep-ph↗

arXiv2013

Berry curvature and 4-dimensional monopole in relativistic chiral kinetic equation

We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a 4-dimensional Euclidean Berry monopole which gives axial anomaly. By integrating out the zero-th component of the 4-momentum p, we reproduce the previous 3-dimensional results derived from the Hamiltonian approach, together with the newly derived vorticity terms. The phase space continuity equation has an anomalous source term proportional to the product of electric and magnetic fields ($F\tilde{F} \sim E.B$). This provides a unified interpretation of the chiral magnetic and vortical effects, chiral anomaly, Berry curvature, and the Berry monopole in the framework of Wigner functions.

hep-th↗

arXiv2013

Parity violating quantum kinetic theory in (2+1)-dimensions

We study the kinetic theory for a (2+1)-dimensional fermionic system with special emphasis on the parity violating properties associated with the fermion mass. The Wigner function approach is used to derive hydrodynamical transport coefficients to the first spatial derivative order. As a first attempt, the collisions between fermions are neglected. The resulting system is dissipationless. The parity violating Hall electric conductivity has the same temperature and chemical potential dependence as the quantum field theory result at one-loop. Vorticity dependent transport properties, which were not considered before, also emerge naturally in this approach.

nucl-th↗

arXiv2012

Chiral anomaly and local polarization effect from quantum kinetic approach

A power expansion scheme is set up to determine the Wigner function that satisfies the quantum kinetic equation for spin-1/2 charged fermions in a background electromagnetic field. Vector and axial-vector current induced by magnetic field and vorticity are obtained simultaneously from the Wigner function. The chiral magnetic and vortical effect and chiral anomaly are shown as natural consequences of the quantum kinetic equation. The axial-vector current induced by vorticity is argued to lead to a local polarization effect along the vorticity direction in heavy-ion collisions.

hep-ph↗