arXiv subjects

Naoyuki Sakumichi

Publications and source records attributed to Naoyuki Sakumichi.

25 records · Page 2Linked to original sources

arXiv2015

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 $β=5.8$ on $16^332$ and at $β=6.0$ 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 $σ_{3\mathrm{Q}} L_{\mathrm{min}}$, where $L_{\mathrm{min}}$ is the minimum flux-tube length connecting the three quarks. We find equivalence between the three-body string tension $σ_{3\mathrm{Q}}$ and its Abelian part $σ_{3\mathrm{Q}}^{\rm Abel}$ with an accuracy within a few percent deviation, i.e., $σ_{3\mathrm{Q}} \simeq σ_{3\mathrm{Q}}^{\rm Abel}$, which means Abelian dominance of the quark-confining force in 3Q systems.

hep-lat↗

arXiv2014

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., $β=6.4, 6.0$), 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 $V(r) \simeq V_{\mathrm{Abel}}(r) + V_{\mathrm{off}}(r)$.

hep-lat↗

arXiv2014

Lee-Yang cluster expansion approach to the BCS-BEC crossover: BCS and BEC limits

It is shown that a cluster expansion technique, which is usually applied in the high-temperature regime to calcutate virial coefficients, can be applied to evaluate the superfluid transition temperature of the BCS-BEC crossover à la Lee and Yang. The transition temperature is identified with the emergence of the singularity in the sum of a certain infinite series of cluster functions. In the weak-coupling limit, we reproduce the Thouless criterion and the number equation of Nozières and Schmitt-Rink, and hence the transition temperature of the BCS theory. In the strong-coupling limit, we reproduce the transition temperature of Bose-Einstein condensation of non-interacting tightly bound dimers.

cond-mat.quant-gas↗

arXiv2014

The Second Law of Thermodynamics under Unitary Evolution and External Operations

A microscopic definition of the thermodynamic entropy in an isolated quantum system must satisfy (i) additivity, (ii) extensivity and (iii) the second law of thermodynamics. We show that the diagonal entropy, which is the Shannon entropy in the energy eigenbasis at each instant of time, meets the first two requirements and that the third requirement is satisfied if an arbitrary external operation is performed at typical times. In terms of the diagonal entropy, thermodynamic irreversibility follows from the facts that the Hamiltonian dynamics restricts quantum trajectories under unitary evolution and that the external operation is performed without referring to any particular information about the microscopic state of the system.

cond-mat.stat-mech↗

arXiv2012

Criteria of off-diagonal long-range order in Bose and Fermi systems based on the Lee-Yang cluster expansion method

The quantum-statistical cluster expansion method of Lee and Yang is extended to investigate off-diagonal long-range order (ODLRO) in one- and multi-component mixtures of bosons or fermions. Our formulation is applicable to both a uniform system and a trapped system without local-density approximation and allows systematic expansions of one- and multi-particle reduced density matrices in terms of cluster functions which are defined for the same system with Boltzmann statistics. Each term in this expansion can be associated with a Lee-Yang graph. We elucidate a physical meaning of each Lee-Yang graph; in particular, for a mixture of ultracold atoms and bound dimers, an infinite sum of the ladder-type Lee-Yang 0-graphs is shown to lead to Bose-Einstein condensation of dimers below the critical temperature. In the case of Bose statistics, an infinite series of Lee-Yang 1-graphs is shown to converge and gives the criteria of ODLRO at the one-particle level. Applications to a dilute Bose system of hard spheres are also made. In the case of Fermi statistics, an infinite series of Lee-Yang 2-graphs is shown to converge and gives the criteria of ODLRO at the two-particle level. Applications to a two-component Fermi gas in the tightly bound limit are also made.

cond-mat.quant-gas↗

arXiv2012

Perron-Frobenius theorem on the superfluid transition of an ultracold Fermi gas

The Perron-Frobenius theorem is applied to identify the superfluid transition of a two-component Fermi gas with a zero-range s-wave interaction. According to the quantum cluster expansion method of Lee and Yang, the grand partition function is expressed by the Lee-Yang contracted 0-graphs. A singularity of an infinite series of ladder-type Lee-Yang contracted 0-graphs is analyzed. We point out that the singularity is governed by the Perron-Frobenius eigenvalue of a certain primitive matrix which is defined in terms of the two-body cluster functions and the Fermi distribution functions. As a consequence, it is found that there exists a unique fugacity at the phase transition point, which implies that there is no fragmentation of Bose-Einstein condensates of dimers and Cooper pairs at the ladder-approximation level of Lee-Yang contracted 0-graphs. An application to a Bose-Einstein condensate of strongly bounded dimers is also made.

cond-mat.quant-gas↗

arXiv2008

Three-quark systems in MA and MC projected QCD

We study three quark systems in Maximally Abelian (MA) and Maximal Center (MC) projected QCD on quenched SU(3) lattice, and also in the monopole/photon part, where only the color-electric/magnetic current exists, using the Hodge decomposition. First, we perform the quantitative study of the three-quark (3Q) potential V_{3Q} and the string tension σ_{3Q} in baryons. For MA projected QCD, the monopole part and MC projected QCD, we find that the confinement potential in V_{3Q} obeys the Y-Ansatz and the string tension σ_{3Q} is approximately equal to that in SU(3) QCD. The universality of the string tension, σ_{3Q} \simeq σ_{Q\bar Q}, is also found between the 3Q and the Q\bar Q potentials. We find a strong similarity of the inter-quark potential between the monopole part and MC projected QCD. In contrast, almost no confinement force is found in the inter-quark potential in the photon part. Next, we study the spectrum of light hadrons in MA projected QCD and the monopole/photon part, paying attention to the N-Δmass splitting. We find that the N-Δmass splitting is significantly reduced in MA projected QCD and the monopole part, where the one-gluon-exchange effect or the Coulomb-potential part is largely reduced due to the Abelianization or the Hodge decomposition. This fact seems to indicate that the main origin of the mass splitting is one-gluon exchange.

hep-lat↗