729 research outputs found
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
Chaos and its quantization in dynamical Jahn-Teller systems
We investigate the 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 -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
Frustrated quantum-spin system on a triangle coupled with lattice vibrations - Correspondence to Longuet-Higgins et al.'s Jahn-Teller model -
We investigate the quantum three spin model
of spin 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 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 and
that of the electronic orbital angular momentum in vibronic model: The regular oscillatory behavior of the expectation value
. The increase of the additional
anharmonicity(chaoticity) is found to yield a rapidly decaying irregular
oscillation of
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 , the set of allowed values of the quantization parameter
is not connected; indeed, it is almost discrete. Li recently constructed a
class of examples (including ) in which 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 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
-deformations which were introduced out of a simple analysis in terms
of cycles in the -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 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 are the usual ones on the
commutative -dimensional sphere and only the algebra and its action
on are deformed. The second class of examples is made of the so called
quantum spheres which are homogeneous spaces of quantum orthogonal
and quantum unitary groups. For these spheres, there is a complete description
of -theory, in terms of nontrivial self-adjoint idempotents (projections)
and unitaries, and of the -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
quantum antiferromagnetic chain at low temperature (compared to the
exchange coupling ) is developed. In particular, effects of a transverse
staggered field and an exchange anisotropy (including a dipolar
interaction) on the ESR lineshape are discussed. In the lowest order
of perturbation theory, the linewidth is given as and
, 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
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