Monopole Dominance of Confinement in SU(3) Lattice QCD

To check the dual superconductor picture for the quark-confinement mechanism, we evaluate monopole dominance as well as Abelian dominance of quark confinement for both quark-antiquark and three-quark systems in SU(3) quenched lattice QCD in the maximally Abelian (MA) gauge. First, we examine Abelian dominance for the static $Q\bar Q$ system in lattice QCD with various spacing $a$ at $\beta$=5.8-6.4 and various size $L^3$x$L_t$. For large physical-volume lattices with $La \ge$ 2fm, we find perfect Abelian dominance of the string tension for the $Q\bar Q$ systems: $\sigma_{Abel} \simeq \sigma$. Second, we accurately measure the static 3Q potential for more than 300 different patterns of 3Q systems with 1000-2000 gauge configurations using two large physical-volume lattices: ($\beta$,$L^3$x$L_t$)=(5.8,$16^3$x32) and (6.0,$20^3$x32). For all the distances, the static 3Q potential is found to be well described by the Y-Ansatz: two-body Coulomb term plus three-body Y-type linear term $\sigma L_{min}$, where $L_{min}$ is the minimum flux-tube length connecting the three quarks. We find perfect Abelian dominance of the string tension also for the 3Q systems: $\sigma^{Abel}_{3Q}\simeq \sigma_{3Q} \simeq \sigma$. Finally, we accurately investigate monopole dominance in SU(3) lattice QCD at $\beta$=5.8 on $16^3$x32 with 2,000 gauge configurations. Abelian-projected QCD in the MA gauge has not only the color-electric current $j^\mu$ but also the color-magnetic monopole current $k^\mu$, which topologically appears. By the Hodge decomposition, the Abelian-projected QCD system can be divided into the monopole part ($k_\mu \ne 0$, $j_\mu=0$) and the photon part ($j_\mu \ne 0$, $k_\mu=0$). We find monopole dominance of the string tension for $Q\bar Q$ and 3Q systems: $\sigma_{Mo}\simeq 0.92\sigma$. While the photon part has almost no confining force, the monopole part almost keeps the confining force.Comment: 8 pages, 8 figure

Perfect Abelian dominance of quark confinement in SU(3) QCD

We study the Abelian projection of quark confinement in SU(3) quenched lattice QCD, in terms of the dual superconductor picture. In the maximal Abelian gauge, we perform the Cartan decomposition of the non-Abelian gauge field on a $32^4$ lattice with spacing $a \simeq0.058, 0.10$ fm (i.e., $\beta =6.4, 6.0$), and investigate the interquark potential $V(r)$, the Abelian part $V_{\mathrm{Abel}}(r)$, and the off-diagonal part $V_{\mathrm{off}}(r)$. For the potential analysis, we use both on-axis data and several types of off-axis data, with larger numbers of gauge configurations. Remarkably, we find almost perfect Abelian dominance of the string tension (quark-confining force) on the large-volume lattice. Also, we find a simple but nontrivial relation of $V(r) \simeq V_{\mathrm{Abel}}(r) + V_{\mathrm{off}}(r)$.Comment: 6 pages, 4 figures; published versio

The three-quark potential and perfect Abelian dominance in SU(3) lattice QCD

We study the static three-quark (3Q) potential for more than 300 different patterns of 3Q systems with high statistics, i.e., 1000-2000 gauge configurations, in SU(3) lattice QCD at the quenched level. For all the distances, the 3Q potential is found to be well described by the Y-ansatz, i.e., one-gluon-exchange (OGE) Coulomb plus Y-type linear potential. Also, we investigate Abelian projection of quark confinement in the context of the dual superconductor picture proposed by Yoichiro~Nambu~{\it et al.} in SU(3) lattice QCD. Remarkably, quark confinement forces in both Q$\bar{\rm Q}$ and 3Q systems can be described only with Abelian variables in the maximally Abelian gauge, i.e., $\sigma_{\rm Q \bar Q} \simeq \sigma_{\rm Q \bar Q}^{\rm Abel} \simeq \sigma_{\rm 3Q} \simeq \sigma_{\rm 3Q}^{\rm Abel}$, which we call ``perfect Abelian dominance'' of quark confinement.Comment: 7 pages, 4 figure

Three-quark potential and Abelian dominance of confinement in SU(3) QCD

We study the baryonic three-quark (3Q) potential and its Abelian projection in terms of the dual-superconductor picture in SU(3) quenched lattice QCD. The non-Abelian SU(3) gauge theory is projected onto Abelian U(1)$^2$ gauge theory in the maximal Abelian gauge. We investigate the 3Q potential and its Abelian part for more than 300 different patterns of static 3Q systems in total at $\beta=5.8$ on $16^332$ and at $\beta=6.0$ on $20^332$ with 1000-2000 gauge configurations. For all the distances, both the 3Q potential and Abelian part are found to be well described by the Y ansatz, i.e., two-body Coulomb term plus three-body Y-type linear term $\sigma_{3\mathrm{Q}} L_{\mathrm{min}}$, where $L_{\mathrm{min}}$ is the minimum flux-tube length connecting the three quarks. We find equivalence between the three-body string tension $\sigma_{3\mathrm{Q}}$ and its Abelian part $\sigma_{3\mathrm{Q}}^{\rm Abel}$ with an accuracy within a few percent deviation, i.e., $\sigma_{3\mathrm{Q}} \simeq \sigma_{3\mathrm{Q}}^{\rm Abel}$, which means Abelian dominance of the quark-confining force in 3Q systems.Comment: 7pages, 7figures, 3tables; published versio

Perfect Abelian dominance of confinement in quark-antiquark potential in SU(3) lattice QCD

In the context of the dual superconductor picture for the confinement mechanism, we study maximally Abelian (MA) projection of quark confinement in SU(3) quenched lattice QCD with $32^4$ at $\beta$=6.4 (i.e., $a \simeq$ 0.058 fm). We investigate the static quark-antiquark potential $V(r)$, its Abelian part $V_{\rm Abel}(r)$ and its off-diagonal part $V_{\rm off}(r)$, respectively, from the on-axis lattice data. As a remarkable fact, we find almost perfect Abelian dominance for quark confinement, i.e., $\sigma_{\rm Abel} \simeq \sigma$ for the string tension, on the fine and large-volume lattice. We find also a nontrivial summation relation of $V(r) \simeq V_{\rm Abel}(r) + V_{\rm off}(r)$.Comment: Invited talk at International Conference on "Quark Confinement and the Hadron Spectrum XI" (confinement XI), St. Petersburg, Russia, 7-13 Sep. 201

The second law of thermodynamics under unitary evolution and external operations

The von Neumann entropy cannot represent the thermodynamic entropy of equilibrium pure states in isolated quantum systems. The diagonal entropy, which is the Shannon entropy in the energy eigenbasis at each instant of time, is a natural generalization of the von Neumann entropy and applicable to equilibrium pure states. We show that the diagonal entropy is consistent with the second law of thermodynamics upon arbitrary external unitary operations. In terms of the diagonal entropy, thermodynamic irreversibility follows from the facts that quantum trajectories under unitary evolution are restricted by the Hamiltonian dynamics and that the external operation is performed without reference to the microscopic state of the system.Fruitful discussions with Masahiro Hotta, Takashi Mori, Takahiro Sagawa, and Takanori Sugiyama are gratefully acknowledged. This work was supported by KAKENHI 26287088, a Grant-in-Aid for Scientific Research on Innovation Areas "Topological Quantum Phenomena" (KAKENHI 22103005), and the Photon Frontier Network Program, from MEXT of Japan. T.N.I. acknowledges the JSPS for financial support (Grant No. 248408). N.S. was supported by a Grant-in-Aid for JSPS Fellows (Grant No. 250588). (26287088 - KAKENHI; 22103005 - KAKENHI; Photon Frontier Network Program, from MEXT of Japan; 24840 - JSPS; 250588)Accepted manuscrip