論文

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.

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.

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.

We study the spectral properties of thermal fluctuations on simple liquid surfaces, sometimes called ripplons. Analytical properties of the spectral function are investigated and are shown to be composed of regions with simple analytic behavior with respect to the frequency or the wave number. The derived expressions are compared to spectral measurements performed orders of magnitude below shot-noise levels, which is achieved using a novel noise reduction method. The agreement between the theory of thermal surface fluctuations and the experiment is found to be excellent, elucidating the spectral properties of the surface fluctuations. The measurement method requires relatively only a small sample both spatially (few μm) and temporally (∼20s). The method also requires relatively weak light power (∼0.5mW) so that it has a broad range of applicability, including local measurements, investigations of time-dependent phenomena, and noninvasive measurements. © 2012 American Physical Society.

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.

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.

Thermal transport properties of the FPU β model with a quadratic pinning term are investigated for various couplings and temperatures. In particular, the size dependence of the thermal conductivity, κ α Lα, is studied. α agrees with that of the FPU β model (with no pinning) at high temperatures but decreases at low temperatures. This crossover behavior occurs at a temperature depending on the strength of the quadratic pinning.

© 2018 Physical Society of Japan. All rights reserved. Spectra of thermal fluctuations of a wide range of interfaces, from liquid/air, viscoelastic material/ air, liquid/liquid to liquid/viscoelastic material interfaces, were measured over a 100 Hz to 10MHz frequency range. The obtained spectra were compared with the fluctuation theory of interfaces, and found to be mostly in quite good agreement, when the theory was generalized to apply to thermal fluctuations of liquid/viscoelastic material interfaces. The loss modulus of viscoelastic materials has been incorporated into the theory, and its effects observed experimentally. The spectra were measured using a system that combines light reflection, statistical noise reduction through averaged correlations, and confocal microscopy. It requires only a small area of the interface (∼1μm2), relatively short times for measurements (≲ few min), and can also be applied to highly viscous materials.

© 2017 Elsevier B.V. We revisit the equilibrium one-dimensional ϕ4 model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit positive Lyapunov exponents! The periodic orbits confine every particle in a periodic chain to trace out either the same or a mirror-image trajectory in its two-dimensional phase space. These “computationally stable” sets of pairs of single-particle orbits are either symmetric or antisymmetric to the very last computational bit. In such a periodic chain the odd-numbered and even-numbered particles’ coordinates and momenta are either identical or differ only in sign. “Positive Lyapunov exponents” can and do result if an infinitesimal perturbation breaking a perfect two-dimensional antisymmetry is introduced so that the motion expands into a four-dimensional phase space. In that extended space a positive exponent results. We formulate a standard initial condition for the investigation of the microcanonical chaotic number dependence of the model. We speculate on the uniqueness of the model's chaotic sea and on the connection of such collections of deterministic and time-reversible states to the Second Law of Thermodynamics.

© 2016 American Physical Society. Periodic orbits for the classical φ4 theory on the one-dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, free and fixed boundary conditions. Through the process, we investigate which normal modes of the linear theory can or cannot be extended to the full nonlinear theory and why. We then analyze the stability of these orbits, clarifying the link between the stability, parametric resonance, and Lyapunov spectra for these orbits. The construction of the periodic orbits and the stability analysis is applicable to theories governed by Hamiltonians with quadratic intersite potentials and a general on-site potential. We also apply the analysis to theories with on-site potentials that have qualitatively different behavior from the φ4 theory, with some concrete examples.

The topological theory of OSp(2|1;R) flat gauge connections is shown to be equivalent to two-dimensional supergravity. By choosing a particular gauge fixing of the SL(2;R) (OSp(2|1;R) invariance we make contact with the Liouville theory approach to two-dimensional gravity (supergravity). We discuss the scaling and multriritical behavior of two-dimensional supergravity. © 1990.

We compute the large-mt contributions to the Zbb vertex in the Standard Model non-perturbatively using both the 1/Nc and the 1/NF expansions. Triviality and its consequences for the perturbative result are systematically analyzed. In particular, we point out that the effect of triviality is already important at the two-loop level for a heavy Higgs (600 GeV < MH < 1 TeV) even when the top mass is below 200 GeV. © 1994.

We calculate the twisted supersymmetric determinants that are necessary for the study of the propagation of spinning strings on arbitrary orbifolds. We calculate the degeneration behaviour of multiloop amplitudes for twisted internal sectors. We use this to derive the spectrum of dimensions of twist fields. © 1989 Springer-Verlag.

The scattering amplitudes for the covariant formulation of closed Type II and heterotic superstrings are shown to be equivalent, order-by-order in string perturbation theory, to those of the light-cone interacting string picture. This establishes the unitarity of covariant superstring perturbation theory and the Lorentz invariance of the light-cone superstring. © 1990.

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.

We generalize the Lax pair and Bäcklund transformations for Toda and N = 1 super Toda equations to the case of arbitrary world-sheet background geometry. We use the fact that the Toda equations express constant curvature conditions, which arise naturally from flatness conditions equivalent to the W-gravity equation of motion. © 1992.

We quantitatively investigate the behavior of momentum cumulants in the φ{symbol}4 theory under thermal gradients, using stochastic thermostats. We relate this to the violations of local equilibrium. The non-equilibrium behavior is found to be quite well described by a dependence ∼ (∇ T)2, on the temperature gradient. Dependence of the quantities on the thermostat type is analyzed and its physical implications are discussed. © 2007 Elsevier B.V. All rights reserved.

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. © Springer Science+Business Media, LLC 2006.

© 2018 Author(s). In the investigations of inhomogeneous media, availability of methods to study the interior of the material without affecting it is valuable. Optical coherence tomography provides such a functionality by providing depth resolved images of semi-transparent objects non-invasively. This is especially useful in medicine and is used not only in research but also in clinical practice. Optical coherence tomography characterizes each cross section by its reflectance. The basic physics principle underlying optical coherence tomography is low-coherence interferometry, which is combined with lateral scanning to produce cross sections. It is clearly desirable to obtain more detailed information regarding each cross section, if available. We have developed a system which measures the fluctuation spectra at all depths in low-coherence interferometry. By providing more information for each cross section, this can in principle be effective in tissue characterization and pathological diagnosis. The system uses the time dependence of the low-coherence interferometry data to obtain the fluctuation spectrum at each depth. Additionally, noise reduction is applied to obtain the spectra without unwanted noise, such as shot-noise, which can swamp the signal. The measurement system is applied to samples with no external stimuli, and depth resolved thermal fluctuation spectra of the samples are obtained. These spectra are compared with their corresponding theoretical expectations and are found to agree. The measurement system requires dualizing the detectors in the low-coherence interferometer but otherwise requires little additional equipment. The measurements were performed in ten to a hundred seconds.

© 2019 American Physical Society. Water is ubiquitous, and the surface properties of ice have been studied for some time, due to their importance. A liquidlike layer (LLL) is known to exist on ice, below the melting point. We use surface thermal fluctuation spectroscopy to study the LLL, including its thickness, for pure ice, and for ice with impurities. We find that the properties of the LLL are experimentally those of liquid water, with thickness much smaller than previous results. We also find that impurities cause the LLL to be thicker, and quite inhomogeneous, with properties depending on the dopant.