27,051 research outputs found
Exact ground state of finite Bose-Einstein condensates on a ring
The exact ground state of the many-body Schr\"odinger equation for bosons
on a one-dimensional ring interacting via pairwise -function
interaction is presented for up to fifty particles. The solutions are obtained
by solving Lieb and Liniger's system of coupled transcendental equations for
finite . The ground state energies for repulsive and attractive interaction
are shown to be smoothly connected at the point of zero interaction strength,
implying that the \emph{Bethe-ansatz} can be used also for attractive
interaction for all cases studied. For repulsive interaction the exact energies
are compared to (i) Lieb and Liniger's thermodynamic limit solution and (ii)
the Tonks-Girardeau gas limit. It is found that the energy of the thermodynamic
limit solution can differ substantially from that of the exact solution for
finite when the interaction is weak or when is small. A simple relation
between the Tonks-Girardeau gas limit and the solution for finite interaction
strength is revealed. For attractive interaction we find that the true ground
state energy is given to a good approximation by the energy of the system of
attractive bosons on an infinite line, provided the interaction is stronger
than the critical interaction strength of mean-field theory.Comment: 28 pages, 11 figure
Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial
Applying a method developed by Takamura and Takano for the nonsymmetric Jack
polynomial, we present the Rodrigues formula for the nonsymmetric multivariable
Hermite polynomial.Comment: 5 pages, LaTe
Cyclic fatigue resistance tests of Nickel-Titanium rotary files using simulated canal and weight loading conditions
published_or_final_versio
Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial
Extending a method developed by Takamura and Takano, we present the Rodrigues
formula for the nonsymmetric multivariable Laguerre polynomials which form the
orthogonal basis for the -type Calogero model with distinguishable
particles. Our construction makes it possible for the first time to
algebraically generate all the nonsymmetric multivariable Laguerre polynomials
with different parities for each variable.Comment: 6 pages, LaTe
Diffusion-limited loop formation of semiflexible polymers: Kramers theory and the intertwined time scales of chain relaxation and closing
We show that Kramers rate theory gives a straightforward, accurate estimate
of the closing time of a semiflexible polymer that is valid in cases
of physical interest. The calculation also reveals how the time scales of chain
relaxation and closing are intertwined, illuminating an apparent conflict
between two ways of calculating in the flexible limit.Comment: Europhys. Lett., 2003 (in press). 8 pages, 3 figures. See also,
physics/0101087 for physicist's approach to and the importance of
semiflexible polymer looping, in DNA replicatio
Kinetics of macroion coagulation induced by multivalent counterions
Due to the strong correlations between multivalent counterions condensed on a
macroion, the net macroion charge changes sign at some critical counterion
concentration. This effect is known as the charge inversion. Near this critical
concentration the macroion net charge is small. Therefore, short range
attractive forces between macroions dominate Coulomb repulsion and lead to
their coagulation. The kinetics of macroion coagulation in this range of
counterion concentrations is studied. We calculate the Coulomb barrier between
two approaching like charged macroions at a given counterion concentration. Two
different macroion shapes (spherical and rod-like) are considered. A new
"self-regulated" regime of coagulation is found. As the size of aggregates
increases, their charge and Coulomb barrier also grow and diminish the sticking
probability of aggregates. This leads to a slow, logarithmic increase of the
aggregate size with time.Comment: Some formulas correcte
Assessing moisture in porous traditional building materials
Historic England is often asked for advice on damp problems in historic and traditional buildings. Whilst many different methods are commonly used to assess damp problems in walls, all have some drawbacks. There is lack of agreement over how they should be used and little information about how they compare one with another. This project developed a common methodology in the laboratory to compare the performance of a range of invasive and non-invasive moisture measurement methods used to assess moisture in porous masonry. The findings suggested that most of the measurement techniques can provide good semi-quantitative estimates of moisture levels in porous traditional building materials
Interference Effects Due to Commensurate Electron Trajectories and Topological Crossovers in (TMTSF)2ClO4
We report angle-dependent magnetoresistance measurements on (TMTSF)2ClO4 that
provide strong support for a new macroscopic quantum phenomenon, the
interference commensurate (IC) effect, in quasi-one dimensional metals. In
addition to observing rich magnetoresistance oscillations, and fitting them
with one-electron calculations, we observe a clear demarcation of
field-dependent behavior at local resistance minima and maxima (versus field
angle). Anticipated by a theoretical treatment of the IC effect in terms of
Bragg reflections in the extended Brillouin zone, this behavior results from
1D-2D topological crossovers of electron wave functions as a function of field
orientation.Comment: 14 page
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