論文 - 青木　健一郎

On the construction of asymmetric orbifold models

Aoki K., D'Hoker E., Phong D.

Nuclear Physics B （Nuclear Physics B）  695 （ 1-2 ） 132 - 168 2004年09月

ISSN  05503213

　概要を見る

Various asymmetric orbifold models based on chiral shifts and chiral reflections are investigated. Special attention is devoted to the consistency of the models with two fundamental principles for asymmetric orbifolds: modular invariance and the existence of a proper Hilbert space formulation for states and operators. The interplay between these two principles is non-trivial. It is shown, for example, that their simultaneous requirement forces the order of a chiral reflection to be 4, instead of the naive 2. A careful explicit construction is given of the associated one-loop partition functions. At higher loops, the partition functions of asymmetric orbifolds are built from the chiral blocks of associated symmetric orbifolds, whose pairings are determined by degenerations to one-loop. © 2004 Elsevier B.V. All rights reserved.

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Time-reversible deterministic thermostats

青木 健一郎

Physica D: Nonlinear Phenomena （Physica D: Nonlinear Phenomena）  187 （ D187 ） 253-267 - 267 2004年

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  01672789

　概要を見る

Seven different time-reversible deterministic thermostats are considered here and applied to a simple particle-based nonequilibrium heat-flow problem. This approach is robust. Results for all these different thermostats agree rather well for system widths of ten particle diameters or more. The simplest of the thermostats is the Gauss-Nosé-Hoover thermostat, based on kinetic-energy control. Higher moments of the particle momenta can be controlled by extensions of this idea involving as many as three additional thermostat variables. Generalizations of the deterministic thermostats suited to simulating "stochastic" and "Brownian" dynamics are discussed here too. © 2003 Elsevier B.V. All rights reserved.

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Spatial distributions of observables in systems under thermal gradients

青木 健一郎

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics （Physical Review E - Statistical, Nonlinear, and Soft Matter Physics）  E70 （ 5 1 ） 051203 2004年

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  15393755

　概要を見る

The departure behavior of the observables from their thermal equilibrium expectation values was analyzed under heat flow in a steady-state nonequilibrium environment. The relationship between the momentum cumulants and the spatial distribution was also investigated. It was observed that the temperature profile for a given nonequilibrium steady state combined with deviations of physical observables could be used to develop a consistent description of spatial distribution of the observables. The results show that lower order cumulants characterize the difference of the nonequilibrium distribution from the one in local equilibrium.

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Two-loop superstrings on orbifold compactifications

青木 健一郎

Nuclear Physics B （Nuclear Physics B）  688 （ B688 ） 3-69 - 69 2004年

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  05503213

　概要を見る

The two-loop chiral measure for superstring theories compactified on Z 2 reflection orbifolds is constructed from first principles for even spin structures. This is achieved by a careful implementation of the chiral splitting procedure in the twisted sectors and the identification of a subtle worldsheet supersymmetric and supermoduli dependent shift in the Prym period. The construction is generalized to compactifications which involve more general NS backgrounds preserving worldsheet supersymmetry. The measures are unambiguous and independent of the gauge slice. Two applications are presented, both to superstring compactifications where 4 dimensions are Z 2 -twisted and where the GSO projection involves a chiral summation over spin structures. The first is an orbifold by a single Z 2 -twist; here, orbifolding reproduces a supersymmetric theory and it is shown that its cosmological constant indeed vanishes. The second model is of the type proposed by Kachru-Kumar-Silverstein and additionally imposes a Z 2 -twist by the parity of worldsheet fermion number; it is shown here that the corresponding cosmological constant does not vanish pointwise on moduli space. © 2004 Elsevier B.V. All rights reserved.

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Lyapunov exponents and the extensivity of dimensional loss for systems in thermal gradients

Aoki K., Kusnezov D.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics （Physical Review E - Statistical, Nonlinear, and Soft Matter Physics）  68 （ 5 2 ） 562041 - 5620416 2003年11月

ISSN  1063651X

　概要を見る

An explicit relation between the dimensional loss (δ), entropy production, and transport under thermal gradients was discussed. It was found that the extensivity of δD in systems with bulk behavior followed from the relation. It was found that the maximum Lyapunov exponents in thermal equilibrium and δD in nonequilibrium depended on the choice of heat baths while their prodcuts was unique and macroscopic. The statistical errors in the numerical computation of δD were also elaborated.

Violations of local equilibrium and linear response in classical lattice systems

Aoki K., Kusnezov D.

Physics Letters, Section A: General, Atomic and Solid State Physics （Physics Letters, Section A: General, Atomic and Solid State Physics）  309 （ 5-6 ） 377 - 381 2003年03月

ISSN  03759601

　概要を見る

We quantitatively and systematically analyze how local equilibrium, and linear response in transport are violated as systems move far from equilibrium. This is done by studying heat flow in classical lattice models with and without bulk transport behavior, in 1-3 dimensions, at various temperatures. Equations of motion for the system are integrated numerically to construct the non-equilibrium steady states. Linear response and local equilibrium assumptions are seen to break down in a similar manner. We quantify the breakdown through the analysis of both microscopic and macroscopic observables and examine its transformation properties under general redefinitions of the non-equilibrium temperature. © 2003 Elsevier Science B.V. All rights reserved.

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Microscopic and Macroscopic Physics of Non-equilibrium Steady States Near and Far from Equilibrium

青木 健一郎

物性研究  （ 80 ） 139-144 2003年

研究論文（学術雑誌）, 共著

Lyapunov exponents, transport and the extensivity of dimensional loss in thermal gradients

青木 健一郎

Physics Review  （ E68 ） 056204-1---6 2003年

研究論文（学術雑誌）, 共著, 査読有り

文化系学生が学ぶ物理学実験

青木 健一郎

大学の物理教育  （ 11月 ） 32-35 2002年11月

研究論文（学術雑誌）, 単著, 査読有り

Nonequilibrium statistical mechanics of classical lattice ∅⁴ field theory

Aoki K., Kusnezov D.

Annals of Physics （Annals of Physics）  295 （ 1 ） 50 - 80 2002年01月

ISSN  00034916

　概要を見る

We study the nonequilibrium statistical mechanics of classical lattice 4 theory in thermal gradients of arbitrary strength. The steady-state physics of the theory in (1 + 1) dimensions is investigated from first principles and classified into dynamical regimes. The bulk properties associated with thermal transport are derived. Starting with thermal equilibrium, we examine the relation to the kinetic theory description of the behavior of the system. Green-Kubo transport coefficients are computed and compared to measured transport near and far from equilibrium, defining the scope of linear response and including an analysis of long-time tails. Local equilibrium is investigated and seen to explicitly break down under sufficiently strong gradients. Additional measures of the nonequilibrium steady state are also discussed as well as the connections to irreversible thermodynamics. © 2002 Elsevier Science (USA).

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Remarks on non-Hamiltonian statistical mechanics: Lyapunov exponents and phase-space dimensionality loss

青木 健一郎

Europhysics Letters （Europhysics Letters）  60 （ 60 ） 337-341 - 341 2002年

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  02955075

　概要を見る

The dissipation associated with nonequilibrium flow processes is reflected by the formation of strange attractor distributions in phase space. The information dimension of these attractors is less than that of the equilibrium phase space, corresponding to the extreme rarity of nonequilibrium states. Here we take advantage of a simple model for heat conduction to demonstrate that the nonequilibrium dimensionality loss can definitely exceed the number of phase-space dimensions required to thermostat an otherwise Hamiltonian system.

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Non-Equilibrium Statistical Mechanics of Classical Lattice $phi^4$ Field Theory

青木 健一郎

Annals of Physics  （ 295 ） 50-80 2002年

研究論文（学術雑誌）, 共著, 査読有り

Violations of local equilibrium and linear response in classical lattice theories

青木 健一郎

素粒子論研究  （ 101 ） A98---A104 2002年

研究論文（学術雑誌）, 共著

Fermi-Pasta-Ulam β model: Boundary jumps, fourier's law, and scaling

Aoki K., Kusnezov D.

Physical Review Letters （Physical Review Letters）  86 （ 18 ） 4029 - 4032 2001年04月

ISSN  00319007

　概要を見る

The temperature and size dependence of the thermal conductivity in the Fermi-Pasta-Ulam β model were computed. A quantitative understanding of these effects was obtained. Further, dynamical regimes were defined based on the interplay of surface and volume effects.

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FPU $beta$ model: Boundary Jumps, Fourier's Law and Scaling

青木 健一郎

Physics Review Letters  （ 86 ） 4029---4032 2001年

研究論文（学術雑誌）, 共著, 査読有り

Meson mass differences in two dimensional gauged four-Fermi models

青木 健一郎

Physical Review D （Physical Review D）  65 （ D65 ） 025003-1---11 2001年

研究論文（学術雑誌）, 共著, 査読有り,  ISSN  05562821

　概要を見る

We quantitatively analyze the meson mass inequality relations of two dimensional gauged four-Fermi models in the large N limit. The class of models we study includes the 't Hooft model and the chiral and nonchiral Gross-Neveu models as special points in the space of field theories. Cases in which the chiral symmetry is spontaneously or explicitly broken are both studied. We study the meson mass differences quantitatively and define a susceptibility which allows us to systematically analyze these quantities. In the generalized Gross-Neveu model limit, we derive an analytic expression for this susceptibility. Even though no analytic proof of the validity of the classic mass inequality exists for the generic case, the mass difference is found to have the standard sign throughout most of the parameter space. We point out that the difference might have the opposite sign in certain cases. © 2001 The American Physical Society.

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Non-equilibrium steady states and transport in the classical lattice φ⁴ theory

Aoki K., Kusnezov D.

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics （Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics）  477 （ 1-3 ） 348 - 354 2000年03月

ISSN  03702693

　概要を見る

We study the classical non-equilibrium statistical mechanics of scalar field theory on the lattice. Steady states are analyzed near and far from equilibrium. The bulk thermal conductivity is computed, including its temperature dependence. We examine the validity of linear response predictions, as well as properties of the non-equilibrium steady state. We find that the linear response theory applies to visibly curved temperature profiles as long as the thermal gradients are not too strong. We also examine the transition from local equilibrium to local non-equilibrium. (C) 2000 Elsevier Science B.V.

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Bulk properties of anharmonic chains in strong thermal gradients: Non-equilibrium φ4 theory

Aoki K., Kusnezov D.

Physics Letters, Section A: General, Atomic and Solid State Physics （Physics Letters, Section A: General, Atomic and Solid State Physics）  265 （ 4 ） 250 - 256 2000年01月

ISSN  03759601

　概要を見る

We study nonequilibrium properties of a one-dimensional lattice Hamiltonian with quartic interactions in strong thermal gradients. Nonequilibrium temperature profiles, T(x), are found to develop significant curvature and boundary jumps. From the determination of the bulk thermal conductivity, we develop a quantitative description of T(x) including the jumps. (C) 2000 Published by Elsevier Science B.V.

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Classical $phi^4$ Lattice Field Theory in Strong Thermal Gradients

青木 健一郎

素粒子論研究  （ 100 ） E56-E59 2000年

研究論文（学術雑誌）, 共著

Bulk properties of anharmonic chains in strong thermal gradients: non-equilibrium $phi^4$ theory

青木 健一郎

Physics Letters  （ A265 ） 250-256 2000年

研究論文（学術雑誌）, 共著, 査読有り