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Kenichiro Aoki

Publications and source records attributed to Kenichiro Aoki.

At least 37 records · Page 2Linked to original sources
arXiv2007

A small tabletop experiment for a direct measurement of the speed of light

A small tabletop experiment for a direct measurement of the speed of light to an accuracy of few percent is described. The experiment is accessible to a wide spectrum of undergraduate students, in particular to students not majoring in science or engineering. The experiment may further include a measurement of the index of refraction of a sample. Details of the setup and equipment are given. Results and limitations of the experiment are analyzed, partly based on our experience in employing the experiment in our student laboratories. Safety considerations are also discussed.

physics.ed-ph↗
arXiv2006

Violations of local equilibrium and stochastic thermostats

We quantitatively investigate the violations of local equilibrium in the $ϕ^4$ theory under thermal gradients, using stochastic thermostats. We find that the deviations from local equilibrium can be quite well described by a behavior $\sim(\nabla T)^2$. The dependence of the quantities on the thermostat type is analyzed and its physical implications are discussed.

nlin.CD↗
arXiv2006

Energy Transport in Weakly Anharmonic Chains

We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier's law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed.

cond-mat.stat-mech↗
arXiv2004

On the Construction of Asymmetric Orbifold Models

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.

hep-th↗
arXiv2004

Two-Loop Superstrings on Orbifold Compactifications

The two-loop chiral measure for superstring theories compactified on $\bZ_2$ 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 $\bZ_2$-twisted and where the GSO projection involves a chiral summation over spin structures. The first is an orbifold by a single $\bZ_2$-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 $\bZ_2$-twist by the parity of worldsheet fermion number; it is shown here that the corresponding cosmological constant does not vanish pointwise on moduli space.

hep-th↗
arXiv2002

Non-Equilibrium Statistical Mechanics of Classical and Quantum Systems

We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum problem is set up using random matrix techniques, which allows for the construction of the master equation. Special solutions are discussed.

nlin.CD↗
arXiv2002

Lyapunov Exponents, Transport and the Extensivity of Dimensional Loss

An explicit relation between the dimensional loss ($ΔD$), entropy production and transport is established under thermal gradients, relating the microscopic and macroscopic behaviors of the system. The extensivity of $ΔD$ in systems with bulk behavior follows from the relation. The maximum Lyapunov exponents in thermal equilibrium and $ΔD$ in non-equilibrium depend on the choice of heat-baths, while their product is unique and macroscopic. Finite size corrections are also computed and all results are verified numerically.

nlin.CD↗
arXiv2001

Violations of local equilibrium and linear response in classical lattice theories

We study the dynamics of $ϕ^4$ theory and the FPU $β$ model under thermal gradients, from first principles. We analyze quantitatively how local equilibrium and linear response are violated, paying special care to how we find observables that unambiguously display these violations. Relations between these quantities to equations of state are also examined. Further, we discuss how we can approach similar dynamical problems in continuum quantum field theory. We analyze how close we are to obtaining the continuum results.

hep-ph↗
arXiv2001

Mass inequalities in two dimensional gauged four fermi models

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, the chiral and non-chiral Gross-Neveu models as special points in the space of field theories. Cases where the chiral symmetry is spontaneously or explicitly broken are both studied. We study the meson mass inequality quantitatively and define a susceptibility which allows us to systematically analyze the inequality. 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 inequality is found to be positive throughout most of the parameter space. We point out that the inequality might be negative in certain cases.

hep-ph↗
arXiv2001

On the Violations of Local Equilibrium and Linear Response

We study how local equilibrium, and linear response predictions of transport coefficients 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. We see that linear response and local equilibrium assumptions break down at the same rate. The equation of state is also found to develop non-local corrections in the steady state. We quantify the breakdown through the analysis of both microscopic and macroscopic observables, which are found to display non-trivial size dependence.

nlin.CD↗
arXiv2001

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

We examine the interplay of surface and volume effects in systems undergoing heat flow. In particular, we compute the thermal conductivity in the FPU $β$ model as a function of temperature and lattice size, and scaling arguments are used to provide analytic guidance. From this we show that boundary temperature jumps can be quantitatively understood, and that they play an important role in determining the dynamics of the system, relating soliton dynamics, kinetic theory and Fourier transport.

nlin.CD↗
arXiv2000

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

Classical $ϕ^4$ theory in weak and strong thermal gradients is studied on the lattice in (1+1) dimensions. Classical $ϕ^4$ theory in weak and strong thermal gradients is studied on the lattice in (1+1) dimensions. The steady state physics of the theory is investigated from first principles and classified into dynamical regimes. We derive the bulk properties associated with thermal transport, and explore in detail the non-equilibrium statistical mechanics of the theory as well as connections to equilibrium and irreversible thermodynamics. Linear response predictions are found to be valid for systems quite far from equilibrium and are seen to eventually break down simultaneously with local equilibrium.

hep-ph↗
arXiv1999

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

The dynamics of classical $ϕ^4$ theory under weak and strong thermal gradients is studied. We obtain the thermal conductivity of the theory including its temperature dependence. Under moderately strong thermal gradients, the temperature profiles become visibly non-linear, yet the phenomenon can be understood using the linear response theory. When we move further away from equilibrium, we find that the linear response theory eventually breaks down, and the concept of local equilibrium also fails.

hep-ph↗
arXiv1999

Non-Equilibrium Steady States and Transport in the Classical Lattice $ϕ^4$ Theory

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.

hep-ph↗
arXiv1999

Physics of the gauged four fermi model in $(1+1)$ dimensions

We analyze a two dimensional model of gauged fermions with quartic couplings in the large-N limit. This combines the 't Hooft model and the Gross-Neveu model where the coupling constants of both theories are arbitrary. Analytic equations describing the meson states of the theory are derived and are solved systematically using various methods. The physics of the model is investigated.

hep-ph↗
arXiv1997

Non-decoupling effects due to a dimensionful coupling

We show that the dimensionful scalar cubic coupling in 3+1 dimensions gives rise to non-decoupling effects and analyze the behavior of these effects. In the process, we clarify how it is perturbatively consistent to construct theories in which the cubic coupling is dominant. We use the scalar sector of the Supersymmetric Standard Model as an example. We discuss how the non-decoupling effects may be analyzed systematically.

hep-ph↗
arXiv1996

High energy scattering of non-critical strings

We summarize recent work, in which we consider scattering amplitudes of non-critical strings in the limit where the energy of all external states is large compared to the string tension. We show that the high energy limit is dominated by a saddle point that can be mapped onto an electrostatic equilibrium configuration of an assembly of charges associated with the external states, together with a density of charges arising from the Liouville field. The Liouville charges accumulate on line segments, which produce quadratic branch cuts on the worldsheet. The electrostatics problem is solved for string tree level in terms of hyperelliptic integrals and is given explicitly for the 3- and 4-point functions. For generic values of the central charge, the high energy limit behaves in a string-like fashion, with exponential energy dependence.

hep-th↗