Characterizing the Larkin-Ovchinnikov-Fulde-Ferrel phase induced by the chromomagnetic instability

We discuss possible destinations from the chromomagnetic instability in color superconductors with Fermi surface mismatch $\delta\mu$. In the two-flavor superconducting (2SC) phase we calculate the effective potential for color vector potentials $A_\alpha$ which are interpreted as the net momenta $q$ of pairing in the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) phase. When $1/\sqrt{2}<\delta\mu/\Delta<1$ where $\Delta$ is the gap energy, the effective potential suggests that the instability leads to a LOFF-like state which is characterized by color-rotated phase oscillations with small $q$. In the vicinity of $\delta\mu/\Delta=1/\sqrt{2}$ the magnitude of $q$ continuously increases from zero as the effective potential has negative larger curvature at vanishing $A_\alpha$ that is the Meissner mass squared. In the gapless 2SC (g2SC) phase, in contrast, the effective potential has a minimum at $gA_\alpha\sim\delta\mu\sim\Delta$ even when the negative Meissner mass squared is infinitesimally small. Our results imply that the chromomagnetic instability found in the gapless phase drives the system toward the LOFF state with $q\sim\delta\mu$.Comment: 6 pages, 3 figures; fatal typo about the conclusion corrected; reference adde

Confinement Properties in the Multi-Instanton System

We investigate the confinement properties in the multi-instanton system, where the size distribution is assumed to be $\rho^{-5}$ for the large instanton size $\rho$. We find that the instanton vacuum gives the area law behavior of the Wilson loop, which indicates existence of the linear confining potential. In the multi-instanton system, the string tension increases monotonously with the instanton density, and takes the standard value $\sigma \simeq 1 GeV/fm$ for the density $(N/V)^{{1/4}} = 200 MeV$. Thus, instantons directly relate to color confinement properties.Comment: Talk presented by M. Fukushima at ``Lattice '97'', the International Symposium on Lattice Field Theory, 22 - 26 July 1997, in Edinburgh, Scotland, 3 pages, Plain Late

Dielectric correction to the Chiral Magnetic Effect

We derive an electric current density $j_{em}$ in the presence of a magnetic field $B$ and a chiral chemical potential $\mu_5$. We show that $j_{em}$ has not only the anomaly-induced term $\propto \mu_5 B$ (i.e. Chiral Magnetic Effect) but also a non-anomalous correction which comes from interaction effects and expressed in terms of the susceptibility. We find the correction characteristically dependent on the number of quark flavors. The numerically estimated correction turns out to be a minor effect on heavy-ion collisions but can be tested by the lattice QCD simulation.Comment: 4 pages, 1 figur

Views of the Chiral Magnetic Effect

My personal views of the Chiral Magnetic Effect are presented, which starts with a story about how we came up with the electric-current formula and continues to unsettled subtleties in the formula. There are desirable features in the formula of the Chiral Magnetic Effect but some considerations would lead us to even more questions than elucidations. The interpretation of the produced current is indeed very non-trivial and it involves a lot of confusions that have not been resolved.Comment: 19 pages, no figure; typos corrected, references significantly updated, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Instability of a gapless color superconductor with respect to inhomogeneous fluctuations

We systematically apply density functional theory to determine the kind of inhomogeneities that spontaneously develop in a homogeneous gapless phase of neutral two-flavor superfluid quark matter. We consider inhomogeneities in the quark and electron densities and in the phases and amplitude of the order parameter. These inhomogeneities are expected to lead the gapless phase to a BCS-normal coexisting phase, a Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state with phase oscillations alone, and a LOFF state with amplitude oscillations. We find that which of them the homogeneous system tends towards depends sensitively on the chemical potential separation between up and down quarks and the gradient energies.Comment: 15 pages, 3 figures; corrected Eq. (36) and changed content associated with d quark clustering instabilit

Effective Model Approach to the Dense State of QCD Matter

The first-principle approach to the dense state of QCD matter, i.e. the lattice-QCD simulation at finite baryon density, is not under theoretical control for the moment. The effective model study based on QCD symmetries is a practical alternative. However the model parameters that are fixed by hadronic properties in the vacuum may have unknown dependence on the baryon chemical potential. We propose a new prescription to constrain the effective model parameters by the matching condition with the thermal Statistical Model. In the transitional region where thermal quantities blow up in the Statistical Model, deconfined quarks and gluons should smoothly take over the relevant degrees of freedom from hadrons and resonances. We use the Polyakov-loop coupled Nambu--Jona-Lasinio (PNJL) model as an effective description in the quark side and show how the matching condition is satisfied by a simple ansatz on the Polyakov loop potential. Our results favor a phase diagram with the chiral phase transition located at slightly higher temperature than deconfinement which stays close to the chemical freeze-out points.Comment: 8 pages, 4 figures; Talk at International Workshop on High Density Nuclear Matter, Cape Town, South Africa, April 6-9, 201

Magnetic-field Induced Screening Effect and Collective Excitations

We explicitly construct the fermion propagator in a magnetic field background B to take the lowest Landau-level approximation. We analyze the energy and momentum dependence in the polarization tensor and discuss the collective excitations. We find there appear two branches of collective modes in one of two transverse gauge particles; one represents a massive and attenuated gauge particle and the other behaves similar to the zero sound at finite density.Comment: 5 pages, 3 figures; references on the zero sound added and typos correcte

Asymptotics for the Wiener sausage among Poissonian obstacles

We consider the Wiener sausage among Poissonian obstacles. The obstacle is called hard if Brownian motion entering the obstacle is immediately killed, and is called soft if it is killed at certain rate. It is known that Brownian motion conditioned to survive among obstacles is confined in a ball near its starting point. We show the weak law of large numbers, large deviation principle in special cases and the moment asymptotics for the volume of the corresponding Wiener sausage. One of the consequence of our results is that the trajectory of Brownian motion almost fills the confinement ball.Comment: 19 pages, Major revision made for publication in J. Stat. Phy

Are You Tampering With My Data?

We propose a novel approach towards adversarial attacks on neural networks (NN), focusing on tampering the data used for training instead of generating attacks on trained models. Our network-agnostic method creates a backdoor during training which can be exploited at test time to force a neural network to exhibit abnormal behaviour. We demonstrate on two widely used datasets (CIFAR-10 and SVHN) that a universal modification of just one pixel per image for all the images of a class in the training set is enough to corrupt the training procedure of several state-of-the-art deep neural networks causing the networks to misclassify any images to which the modification is applied. Our aim is to bring to the attention of the machine learning community, the possibility that even learning-based methods that are personally trained on public datasets can be subject to attacks by a skillful adversary.Comment: 18 page