Polynuclear growth model, GOE2^2 and random matrix with deterministic source

We present a random matrix interpretation of the distribution functions which have appeared in the study of the one-dimensional polynuclear growth (PNG) model with external sources. It is shown that the distribution, GOE$^2$, which is defined as the square of the GOE Tracy-Widom distribution, can be obtained as the scaled largest eigenvalue distribution of a special case of a random matrix model with a deterministic source, which have been studied in a different context previously. Compared to the original interpretation of the GOE$^2$ as ``the square of GOE'', ours has an advantage that it can also describe the transition from the GUE Tracy-Widom distribution to the GOE$^2$. We further demonstrate that our random matrix interpretation can be obtained naturally by noting the similarity of the topology between a certain non-colliding Brownian motion model and the multi-layer PNG model with an external source. This provides us with a multi-matrix model interpretation of the multi-point height distributions of the PNG model with an external source.Comment: 27pages, 4 figure

Exact solution for the stationary Kardar-Parisi-Zhang equation

We obtain the first exact solution for the stationary one-dimensional Kardar-Parisi-Zhang equation. A formula for the distribution of the height is given in terms of a Fredholm determinant, which is valid for any finite time $t$. The expression is explicit and compact enough so that it can be evaluated numerically. Furthermore, by extending the same scheme, we find an exact formula for the stationary two-point correlation function.Comment: 9 pages, 3 figure

Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion

On a multi-assets Black-Scholes economy, we introduce a class of barrier options. In this model we apply a generalized reflection principle in a context of the finite reflection group acting on a Euclidean space to give a valuation formula and the semi-static hedge.Comment: Asia-Pacific Financial Markets, online firs

Vertically coupled double quantum dots in magnetic fields

Ground-state and excited-state properties of vertically coupled double quantum dots are studied by exact diagonalization. Magic-number total angular momenta that minimize the total energy are found to reflect a crossover between electron configurations dominated by intra-layer correlation and ones dominated by inter-layer correlation. The position of the crossover is governed by the strength of the inter-layer electron tunneling and magnetic field. The magic numbers should have an observable effect on the far infra-red optical absorption spectrum, since Kohn's theorem does not hold when the confinement potential is different for two dots. This is indeed confirmed here from a numerical calculation that includes Landau level mixing. Our results take full account of the effect of spin degrees of freedom. A key feature is that the total spin, $S$, of the system and the magic-number angular momentum are intimately linked because of strong electron correlation. Thus $S$ jumps hand in hand with the total angular momentum as the magnetic field is varied. One important consequence of this is that the spin blockade (an inhibition of single-electron tunneling) should occur in some magnetic field regions because of a spin selection rule. Owing to the flexibility arising from the presence of both intra-layer and inter-layer correlations, the spin blockade is easier to realize in double dots than in single dots.Comment: to be published in Phys. Rev. B1

Spin-Blockade in Single and Double Quantum Dots in Magnetic Fields: a Correlation Effect

The total spin of correlated electrons in a quantum dot changes with magnetic field and this effect is generally linked to the change in the total angular momentum from one magic number to another, which can be understood in terms of an `electron molecule' picture for strong fields. Here we propose to exploit this fact to realize a spin blockade, i.e., electrons are prohibited to tunnel at specific values of the magnetic field. The spin-blockade regions have been obtained by calculating both the ground and excited states. In double dots the spin-blockade condition is found to be less stringent than in single dots.Comment: 4pages, to be published in Phys. Rev. B (Rapid Communication

Difference in radiocarbon ages of carbonized material from the inner and outer surfaces of pottery from a wetland archaeological site

AMS (Accelerator Mass Spectrometry) radiocarbon dates for eight potsherds from a single piece of pottery from a wetland archaeological site indicated that charred material from the inner pottery surfaces (5052 ± 12 BP; N = 5) is about 90 14C years older than that from the outer surfaces (4961 ± 22 BP; N = 7). We considered three possible causes of this difference: the old wood effect, reservoir effects, and diagenesis. We concluded that differences in the radiocarbon ages between materials from the inner and outer surfaces of the same pot were caused either by the freshwater reservoir effect or by diagenesis. Moreover, we found that the radiocarbon ages of carbonized material on outer surfaces (soot) of pottery from other wetland archaeological sites were the same as the ages of material on inner surfaces (charred food) of the same pot within error, suggesting absence of freshwater reservoir effect or diagenesis

Classical double-layer atoms: artificial molecules

The groundstate configuration and the eigenmodes of two parallel two-dimensional classical atoms are obtained as function of the inter-atomic distance (d). The classical particles are confined by identical harmonic wells and repel each other through a Coulomb potential. As function of d we find several structural transitions which are of first or second order. For first (second) order transitions the first (second) derivative of the energy with respect to d is discontinuous, the radial position of the particles changes discontinuously (continuously) and the frequency of the eigenmodes exhibit a jump (one mode becomes soft, i.e. its frequency becomes zero).Comment: 4 pages, RevTex, 5 ps figures, to appear in Phys.Rev.Let

Wall Crossing As Seen By Matrix Models

The number of BPS bound states of D-branes on a Calabi-Yau manifold depends on two sets of data, the BPS charges and the stability conditions. For D0 and D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold X, both are naturally related to the Kahler moduli space M(X). We construct unitary one-matrix models which count such BPS states for a class of toric Calabi-Yau manifolds at infinite 't Hooft coupling. The matrix model for the BPS counting on X turns out to give the topological string partition function for another Calabi-Yau manifold Y, whose Kahler moduli space M(Y) contains two copies of M(X), one related to the BPS charges and another to the stability conditions. The two sets of data are unified in M(Y). The matrix models have a number of other interesting features. They compute spectral curves and mirror maps relevant to the remodeling conjecture. For finite 't Hooft coupling they give rise to yet more general geometry \widetilde{Y} containing Y.Comment: 44 pages, 9 figures, published versio

Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.Comment: 48 pages, 8 figure

Conductance Quantization and Magnetoresistance in Magnetic Point Contacts

We theoretically study the electron transport through a magnetic point contact (PC) with special attention to the effect of an atomic scale domain wall (DW). The spin precession of a conduction electron is forbidden in such an atomic scale DW and the sequence of quantized conductances depends on the relative orientation of magnetizations between left and right electrodes. The magnetoresistance is strongly enhanced for the narrow PC and oscillates with the conductance.Comment: 4 pages, 4 figures, revised version with new figure