Evolution of Trapped vs. Main Liquids during Crystallization of Northwest Africa 773 Olivine Cumulate.

第2回極域科学シンポジウム/第34回南極隕石シンポジウム 11月18日（金） 国立国語研究所 2階講

Power-law behavior in the power spectrum induced by Brownian motion of a domain wall

We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a $\omega^{-3/2}$ power spectrum. This is successfully applied to the totally asymmetric simple exclusion process (TASEP) with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and discreteness of the system is not effective.Comment: 4 pages, 4 figure

Construction of a matrix product stationary state from solutions of finite size system

Stationary states of stochastic models, which have $N$ states per site, in matrix product form are considered. First we give a necessary condition for the existence of a finite $M$-dimensional matrix product state for any ${N,M}$. Second, we give a method to construct the matrices from the stationary states of small size system when the above condition and $N\le M$ are satisfied. Third, the method by which one can check that the obtained matrices are valid for any system size is presented for the case where $M=N$ is satisfied. The application of our methods is explained using three examples: the asymmetric exclusion process, a model studied in [F. H. Jafarpour: J. Phys. A: Math. Gen. 36 (2003) 7497] and a hybrid of both of the models.Comment: 22 pages, no figure. Major changes: sec.3 was shortened; the list of references were changed. This is the final version, which will appear in J.Phys.

The One-dimensional KPZ Equation and the Airy Process

Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an n-point generating function and write it in terms of a Fredholm determinant. For long times the generating function converges to a limit, which is established to be equivalent to the standard expression of the n-point distribution of the Airy process.Comment: 15 page

Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra

We study the partially asymmetric exclusion process with open boundaries. We generalise the matrix approach previously used to solve the special case of total asymmetry and derive exact expressions for the partition sum and currents valid for all values of the asymmetry parameter q. Due to the relationship between the matrix algebra and the q-deformed quantum harmonic oscillator algebra we find that q-Hermite polynomials, along with their orthogonality properties and generating functions, are of great utility. We employ two distinct sets of q-Hermite polynomials, one for q1. It turns out that these correspond to two distinct regimes: the previously studied case of forward bias (q1) where the boundaries support a current opposite in direction to the bulk bias. For the forward bias case we confirm the previously proposed phase diagram whereas the case of reverse bias produces a new phase in which the current decreases exponentially with system size.Comment: 27 pages LaTeX2e, 3 figures, includes new references and further comparison with related work. To appear in J. Phys.

Will jams get worse when slow cars move over?

Motivated by an analogy with traffic, we simulate two species of particles (`vehicles'), moving stochastically in opposite directions on a two-lane ring road. Each species prefers one lane over the other, controlled by a parameter $0 \leq b \leq 1$ such that $b=0$ corresponds to random lane choice and $b=1$ to perfect `laning'. We find that the system displays one large cluster (`jam') whose size increases with $b$, contrary to intuition. Even more remarkably, the lane `charge' (a measure for the number of particles in their preferred lane) exhibits a region of negative response: even though vehicles experience a stronger preference for the `right' lane, more of them find themselves in the `wrong' one! For $b$ very close to 1, a sharp transition restores a homogeneous state. Various characteristics of the system are computed analytically, in good agreement with simulation data.Comment: 7 pages, 3 figures; to appear in Europhysics Letters (2005

From interacting particle systems to random matrices

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuation laws were first discovered in random matrix models. Moreover, the limit process for curved limit shape turned out to show up in a dynamical version of hermitian random matrices, but this analogy does not extend to the case of symmetric matrices. Therefore the connections between growth models and random matrices is only partial.Comment: 18 pages, 8 figures; Contribution to StatPhys24 special issue; minor corrections in scaling of section 2.

Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries

The one-dimensional partially asymmetric simple exclusion process with open boundaries is considered. The stationary state, which is known to be constructed in a matrix product form, is studied by applying the theory of q-orthogonal polynomials. Using a formula of the q-Hermite polynomials, the average density profile is computed in the thermodynamic limit. The phase diagram for the correlation length, which was conjectured in the previous work[J. Phys. A {\bf 32} (1999) 7109], is confirmed.Comment: 24 pages, 6 figure

Universal exit probabilities in the TASEP

We study the joint exit probabilities of particles in the totally asymmetric simple exclusion process (TASEP) from space-time sets of given form. We extend previous results on the space-time correlation functions of the TASEP, which correspond to exits from the sets bounded by straight vertical or horizontal lines. In particular, our approach allows us to remove ordering of time moments used in previous studies so that only a natural space-like ordering of particle coordinates remains. We consider sequences of general staircase-like boundaries going from the northeast to southwest in the space-time plane. The exit probabilities from the given sets are derived in the form of Fredholm determinant defined on the boundaries of the sets. In the scaling limit, the staircase-like boundaries are treated as approximations of continuous differentiable curves. The exit probabilities with respect to points of these curves belonging to arbitrary space-like path are shown to converge to the universal Airy$_2$ process.Comment: 46 pages, 7 figure

A multi-layer extension of the stochastic heat equation

Motivated by recent developments on solvable directed polymer models, we define a 'multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions.Comment: v4: substantially extended and revised versio