A New Approach to Stochastic State selections in Quantum Spin Systems

We propose a new type of Monte Carlo approach in numerical studies of quantum systems. Introducing a probability function which determines whether a state in the vector space survives or not, we can evaluate expectation values of powers of the Hamiltonian from a small portion of the full vector space. This method is free from the negative sign problem because it is not based on importance sampling techniques. In this paper we describe our method and, in order to examine how effective it is, present numerical results on the 4x4, 6x6 and 8x8 Heisenberg spin one-half model. The results indicate that we can perform useful evaluations with limited computer resources. An attempt to estimate the lowest energy eigenvalue is also stated.Comment: 10 pages, 2 figures, 8 table

Stochastic association of neighboring replicons creates replication factories in budding yeast

Peer reviewedPublisher PD

Effect of groundwater flow on forming arsenic contaminated groundwater in Sonargaon, Bangladesh

Three-dimensional groundwater flow in Sonargaon, Bangladesh is numerically simulated in order to evaluate the flow paths of As-contaminated drinking groundwater in the Holocene aquifer of the Ganges-Blamaptra-Meghna delta plain over a recent 30-year period. The model indicates that vertical infiltration of surface groundwater into the shallow Holocene aquifer occurs frequently in the Ganges-Blamaptra-Meghna delta plain. It predicts that the water recharged from ground surface moves approximately 10-20 m vertically downward beneath the flood plain, with a gradually increasing horizontal flow, toward the underlying Pleistocene middle mud layer (aquitard). The model also predicts that groundwaters containing highest As concentrations (>700 mu g/L) are formed on the vertical groundwater flow paths where surface water recharges the Holocene aquifer and not on the horizontal flow paths. Combining with the groundwater chemistry, reducing groundwater condition is not essential for the As-contaminated groundwater of the studied area in the Ganges delta plain.ArticleJOURNAL OF HYDROLOGY. 409(3-4):724-736 (2011)journal articl

Frustrated quantum-spin system on a triangle coupled with ege_g lattice vibrations - Correspondence to Longuet-Higgins et al.'s Jahn-Teller model -

We investigate the quantum three spin model $({\bf S_1},{\bf S_2},{\bf S_3})$ of spin$=1/2$ on a triangle, in which spins are coupled with lattice-vibrational modes through the exchange interaction depending on distances between spin sites. The present model corresponds to the dynamic Jahn-Teller system $E_g\otimes e_g$ proposed by Longuet-Higgins {\it et al.}, Proc.R.Soc.A.{\bf 244},1(1958). This correspondence is revealed by using the transformation to Nakamura-Bishop's bases proposed in Phys.Rev.Lett.{\bf 54},861(1985). Furthermore, we elucidate the relationship between the behavior of a chiral order parameter ${\hat \chi}={\bf S_1\cdot(S_2\times S_3)}$ and that of the electronic orbital angular momentum ${\hat \ell_z}$ in $E_g\otimes e_g$ vibronic model: The regular oscillatory behavior of the expectation value $$for vibronic structures with increasing energy can also be found in that of$$. The increase of the additional anharmonicity(chaoticity) is found to yield a rapidly decaying irregular oscillation of $$

Chaos and its quantization in dynamical Jahn-Teller systems

We investigate the $E_g \otimes e_g$ Jahn-Teller system for the purpose to reveal the nature of quantum chaos in crystals. This system simulates the interaction between the nuclear vibrational modes and the electronic motion in non-Kramers doublets for multiplets of transition-metal ions. Inclusion of the anharmonic potential due to the trigonal symmetry in crystals makes the system nonintegrable and chaotic. Besides the quantal analysis of the transition from Poisson to Wigner level statistics with increasing the strength of anharmonicity, we study the effect of chaos on the electronic orbital angular momentum and explore the magnetic $g$-factor as a function of the system's energy. The regular oscillation of this factor changes to a rapidly-decaying irregular oscillation by increasing the anharmonicity (chaoticity).Comment: 8 pages, 6 figure

Finitely-Generated Projective Modules over the Theta-deformed 4-sphere

We investigate the "theta-deformed spheres" C(S^{3}_{theta}) and C(S^{4}_{theta}), where theta is any real number. We show that all finitely-generated projective modules over C(S^{3}_{theta}) are free, and that C(S^{4}_{theta}) has the cancellation property. We classify and construct all finitely-generated projective modules over C(S^{4}_{\theta}) up to isomorphism. An interesting feature is that if theta is irrational then there are nontrivial "rank-1" modules over C(S^{4}_{\theta}). In that case, every finitely-generated projective module over C(S^{4}_{\theta}) is a sum of a rank-1 module and a free module. If theta is rational, the situation mirrors that for the commutative case theta=0.Comment: 34 page

An Obstruction to Quantization of the Sphere

In the standard example of strict deformation quantization of the symplectic sphere $S^2$, the set of allowed values of the quantization parameter $\hbar$ is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including $S^2$) in which $\hbar$ can take any value in an interval, but these examples are badly behaved. Here, I identify a natural additional axiom for strict deformation quantization and prove that it implies that the parameter set for quantizing $S^2$ is never connected.Comment: 23 page. v2: changed sign conventio

Noncommutative Spheres and Instantons

We report on some recent work on deformation of spaces, notably deformation of spheres, describing two classes of examples. The first class of examples consists of noncommutative manifolds associated with the so called $\theta$-deformations which were introduced out of a simple analysis in terms of cycles in the $(b,B)$-complex of cyclic homology. These examples have non-trivial global features and can be endowed with a structure of noncommutative manifolds, in terms of a spectral triple (\ca, \ch, D). In particular, noncommutative spheres $S^{N}_{\theta}$ are isospectral deformations of usual spherical geometries. For the corresponding spectral triple (\cinf(S^{N}_\theta), \ch, D), both the Hilbert space of spinors \ch= L^2(S^{N},\cs) and the Dirac operator $D$ are the usual ones on the commutative $N$-dimensional sphere $S^{N}$ and only the algebra and its action on $\ch$ are deformed. The second class of examples is made of the so called quantum spheres $S^{N}_q$ which are homogeneous spaces of quantum orthogonal and quantum unitary groups. For these spheres, there is a complete description of $K$-theory, in terms of nontrivial self-adjoint idempotents (projections) and unitaries, and of the $K$-homology, in term of nontrivial Fredholm modules, as well as of the corresponding Chern characters in cyclic homology and cohomology.Comment: Minor changes, list of references expanded and updated. These notes are based on invited lectures given at the ``International Workshop on Quantum Field Theory and Noncommutative Geometry'', November 26-30 2002, Tohoku University, Sendai, Japan. To be published in the workshop proceedings by Springer-Verlag as Lecture Notes in Physic

Electron Spin Resonance in S=1/2 antiferromagnetic chains

A systematic field-theory approach to Electron Spin Resonance (ESR) in the $S=1/2$ quantum antiferromagnetic chain at low temperature $T$ (compared to the exchange coupling $J$) is developed. In particular, effects of a transverse staggered field $h$ and an exchange anisotropy (including a dipolar interaction) $\delta$ on the ESR lineshape are discussed. In the lowest order of perturbation theory, the linewidth is given as $\propto Jh^2/T^2$ and $\propto (\delta/J)^2 T$, respectively. In the case of a transverse staggered field, the perturbative expansion diverges at lower temperature; non-perturbative effects at very low temperature are discussed using exact results on the sine-Gordon field theory. We also compare our field-theory results with the predictions of Kubo-Tomita theory for the high-temperature regime, and discuss the crossover between the two regimes. It is argued that a naive application of the standard Kubo-Tomita theory to the Dzyaloshinskii-Moriya interaction gives an incorrect result. A rigorous and exact identity on the polarization dependence is derived for certain class of anisotropy, and compared with the field-theory results.Comment: 53 pages in REVTEX, 7 figures in EPS included; revised version with missing references and correction