Cryptoasset networks: Flows and regular players in Bitcoin and XRP.

Cryptoassets flow among players as recorded in the ledger of blockchain for all the transactions, comprising a network of players as nodes and flows as edges. The last decade, on the other hand, has witnessed repeating bubbles and crashes of the price of cryptoassets in exchange markets with fiat currencies and other cryptos. We study the relationship between these two important aspects of dynamics, one in the bubble/crash of price and the other in the daily network of crypto, by investigating Bitcoin and XRP. We focus on "regular players" who frequently appear on a weekly basis during a period of time including bubble/crash, and quantify each player's role with respect to outgoing and incoming flows by defining flow-weighted frequency. During the most significant period of one-year starting from the winter of 2017, we discovered the structure of three groups of players in the diagram of flow-weighted frequency, which is common to Bitcoin and XRP in spite of the different nature of the two cryptos. By examining the identity and business activity of some regular players in the case of Bitcoin, we can observe different roles of them, namely the players balancing surplus and deficit of cryptoassets (Bal-branch), those accumulating the cryptoassets (In-branch), and those reducing it (Out-branch). Using this information, we found that the regime switching among Bal-, In-, Out-branches was presumably brought about by the regular players who are not necessarily dominant and stable in the case of Bitcoin, while such players are simply absent in the case of XRP. We further discuss how one can understand the temporal transitions among the three branches.

Rainbow Nambu-Goldstone Modes under a Shear Flow.

We study an O(N) scalar model under shear flow and its Nambu-Goldstone modes associated with spontaneous symmetry breaking O(N)→O(N-1). We find that the Nambu-Goldstone mode splits into an infinite number of gapless modes, which we call the rainbow Nambu-Goldstone modes. They have different group velocities and the fractional dispersion relation ω∼k_{1}^{2/3}, where k_{1} is the wave number along the flow. Such behaviors do not have counterparts in an equilibrium state.

Counting Nambu-Goldstone Modes of Higher-Form Global Symmetries.

We discuss the counting of Nambu-Goldstone (NG) modes associated with the spontaneous breaking of higher-form global symmetries. Effective field theories of NG modes are developed based on symmetry-breaking patterns, using a generalized coset construction for higher-form symmetries. We derive a formula of the number of gapless NG modes, which involves expectation values of the commutators of conserved charges, possibly of different degrees.

Electric Conductivity of Hot and Dense Quark Matter in a Magnetic Field with Landau Level Resummation via Kinetic Equations.

We compute the electric conductivity of quark matter at finite temperature T and a quark chemical potential µ under a magnetic field B beyond the lowest Landau level approximation. The electric conductivity transverse to B is dominated by the Hall conductivity σ_{H}. For the longitudinal conductivity σ_{∥}, we need to solve kinetic equations. Then, we numerically find that σ_{∥} has only a mild dependence on µ and the quark mass m_{q}. Moreover, σ_{∥} first decreases and then linearly increases as a function of B, leading to an intermediate B region that looks consistent with the experimental signature for the chiral magnetic effect. We also point out that σ_{∥} at a nonzero B remains within the range of the lattice-QCD estimate at B=0.

Magnetic Shift of the Chemical Freeze-out and Electric Charge Fluctuations.

We discuss the effect of a strong magnetic field on the chemical freeze-out points in ultrarelativistic heavy-ion collisions. As a result of inverse magnetic catalysis or magnetic inhibition, the crossover onset to hot and dense matter out of quarks and gluons should be shifted to a lower temperature. To quantify this shift we employ the hadron resonance gas model and an empirical condition for the chemical freeze-out. We point out that the charged particle abundances are significantly affected by the magnetic field so that the electric charge fluctuation is largely enhanced, especially at high baryon density. The charge conservation partially cancels the enhancement, but our calculation shows that the electric charge fluctuation could serve as a magnetometer. We find that the fluctuation exhibits a crossover behavior rapidly increased for eB≳(0.4 GeV)^{2}, while the charge chemical potential has smoother behavior with an increasing magnetic field.

Production and elliptic flow of dileptons and photons in a matrix model of the quark-gluon plasma.

We consider a nonperturbative approach to the thermal production of dileptons and photons at temperatures near the critical temperature in QCD. The suppression of colored excitations at low temperature is modeled by including a small value of the Polyakov loop, in a "semi"-quark-gluon plasma (QGP). Comparing the semi-QGP to the perturbative QGP, we find a mild enhancement of thermal dileptons. In contrast, to leading logarithmic order in weak coupling there are far fewer hard photons from the semi-QGP than the usual QGP. To illustrate the possible effects on photon and dilepton production in heavy-ion collisions, we integrate the rate with a simulation using ideal hydrodynamics. Dileptons uniformly exhibit a small flow, but the strong suppression of photons in the semi-QGP tends to weight the elliptical flow of photons to that generated in the hadronic phase.

Relativistic hydrodynamics from the projection operator method.

We study relativistic hydrodynamics in the linear regime, based on Mori's projection operator method. In relativistic hydrodynamics, it is considered that an ambiguity about the fluid velocity occurs from the choice of a local rest frame: the Landau and Eckart frames. We find that the difference of the frames is not the choice of the local rest frame, but rather that of dynamic variables in the linear regime. We derive hydrodynamic equations in both frames by the projection operator method. We show that the natural derivation gives the linearized Landau equation. Also we find that, even for the Eckart frame, the slow dynamics is actually described by the dynamic variables for the Landau frame.

Counting rule for Nambu-Goldstone modes in nonrelativistic systems.

The counting rule for Nambu-Goldstone modes is discussed using Mori's projection operator method in nonrelativistic systems at zero and finite temperatures. We show that the number of Nambu-Goldstone modes is equal to the number of broken charges, Q(a), minus half the rank of the expectation value of [Q(a), Q(b)].

Magnetic catalysis versus magnetic inhibition.

We discuss the fate of chiral symmetry in an extremely strong magnetic field B. We investigate not only quark fluctuations but also neutral meson effects. The former enhances the chiral-symmetry breaking at finite B according to the magnetic catalysis, while the latter suppresses the chiral condensate once B exceeds the scale of the hadron structure. Using a chiral model, we demonstrate how neutral mesons are subject to the dimensional reduction and the low dimensionality favors the chiral-symmetric phase. We point out that this effect, the magnetic inhibition, can be a feasible explanation for recent lattice-QCD data indicating the decreasing behavior of the chiral-restoration temperature with increasing B.

No-go theorem for critical phenomena in large-N(c) QCD.

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, N(c), based on the QCD inequalities and the large-N(c) orbifold equivalence. We show that critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD at finite temperature T and finite but not so large quark chemical potential µ for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential µ(B)=N(c)µ is ruled out, if the coordinate (T, µ) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential µ(I)=2µ.