3,076 research outputs found
Propagation of long waves of finite amplitude
We consider the radiation problem for long waves of- small amplitude, caused by an instantaneous disturbance of unit height at the origin. The equations governing this phenomrnon were derived by Long (1964). The asymptotic expressions for the wave front and for large times are obtained. The initial value problem for the non-linear system of equations is also solved, using a perturbation scheme based on the small parameter α, the non-dimensional amplitude of the disturbance. The sofution holds only for t < < I / α as a result of the appearance of a secular term in the fist order solution
Propagation of a bore produced by the sudden break of a dam
In this paper we study the progress of a bore, produced by the sudden break of a dam, when there is a flow of water ahead of the dam and the bed has a mild slope and offers resistance, employing Whitham's rule. We first derive certain interesting results from the general discussion of the differential equation, expressing the variation of the bore strength with the undisturbed Froude number, M0, ratio of bedslope to bed resistance, gα/R = a2 and the bore strength M(x) Ξ {h(x)/h0(x)} where h(x) and h0(x) are the bore height and the undisturbed height of the water immediately ahead of the bore, the horizontal distance x being measured from the dam. The parameters M0 and a2 combine to influence the bore strength in a very special way. We also examine the asymptotic cases when the bore strength M and M 1. The intermediate cases are investigated numerically to bring out the effects of the parameters, α, a2, M0 and the dam height on the strength of the bore, its velocity and the fluid velocity behind it
Numerical evidence for the spin-Peierls state in the frustrated quantum antiferromagnet
We study the spin- Heisenberg antiferromagnet with an
antiferromagnetic (third nearest neighbor) interaction on a square
lattice. We numerically diagonalize this ``-'' model on clusters up
to 32-sites and search for novel ground state properties as the frustration
parameter changes. For ``larger'' we find enhancement of
incommensurate spin order, in agreement with spin-wave, large- expansions,
and other predictions. But for intermediate , the low lying excitation
energy spectrum suggests that this incommensurate order is short-range. In the
same region, the first excited state has the symmetries of the columnar dimer
(spin-Peierls) state. The columnar dimer order parameter suggests the presence
of long-range columnar dimer order. Hence, this spin-Peierls state is the best
candidate for the ground state of the - model in an intermediate
region.Comment: RevTeX file with five postscript figures uuencode
Emergence of coherence in the Mott--superfluid quench of the Bose-Hubbard model
We study the quench from the Mott to the superfluid phase in the Bose-Hubbard
model and investigate the spatial-temporal growth of phase coherence, i.e.,
phase locking between initially uncorrelated sites. To this end, we establish a
hierarchy of correlations via a controlled expansion into inverse powers of the
coordination number . It turns out that the off-diagonal long-range order
spreads with a constant propagation speed, forming local condensate patches,
whereas the phase correlator follows a diffusion-like growth rate.Comment: 4 page
Boundary and impurity effects on entanglement of Heisenberg chains
We study entanglement of a pair of qubits and the bipartite entanglement
between the pair and the rest within open-ended Heisenberg and XY models.
The open boundary condition leads to strong oscillations of entanglements with
a two-site period, and the two kinds of entanglements are 180 degree out of
phase with each other. The mean pairwise entanglement and ground-state energy
per site in the model are found to be proportional to each other. We
study the effects of a single bulk impurity on entanglement, and find that
there exists threshold values of the relative coupling strength between the
impurity and its nearest neighbours, after which the impurity becomes pairwise
entangled with its nearest neighbours.Comment: 6 pages and 6 figure
Magnetic properties of strongly disordered electronic systems
We present a unified, global perspective on the magnetic properties of
strongly disordered electronic systems, with special emphasis on the case where
the ground state is metallic. We review the arguments for the instability of
the disordered Fermi liquid state towards the formation of local magnetic
moments, and argue that their singular low temperature thermodynamics are the
``quantum Griffiths'' precursors of the quantum phase transition to a metallic
spin glass; the local moment formation is therefore not directly related to the
metal-insulator transition. We also review the the mean-field theory of the
disordered Fermi liquid to metallic spin glass transition and describe the
separate regime of ``non-Fermi liquid'' behavior at higher temperatures near
the quantum critical point. The relationship to experimental results on doped
semiconductors and heavy-fermion compounds is noted.Comment: 25 pages; Contribution to the Royal Society Discussion Meeting on
"The Metal-Non Metal Transition in Macroscopic and Microscopic Systems",
March 5-6, 199
Crossover to non-Fermi-liquid spin dynamics in cuprates
The antiferromagnetic spin correlation function , the staggered
spin susceptibility and the energy scale are studied numerically within the t-J model and the Hubbard
model, as relevant to cuprates. It is shown that , related to the
onset of the non-Fermi-liquid spin response at , is very low in
the regime below the 'optimum' hole doping , while it
shows a steep increase in the overdoped regime. A quantitative analysis of NMR
spin-spin relaxation-rate for various cuprates reveals a similar
behavior, indicating on a sharp, but continuous, crossover between a
Fermi-liquid and a non-Fermi-liquid behavior as a function of doping.Comment: 4 pages, 4 figures. Submitted to PR
Thermal melting of density waves on the square lattice
We present the theory of the effect of thermal fluctuations on commensurate
"p x p" density wave ordering on the square lattice (p >= 3, integer). For the
case in which this order is lost by a second order transition, we argue that
the adjacent state is generically an incommensurate striped state, with
commensurate p-periodic long range order along one direction, and
incommensurate quasi-long-range order along the orthogonal direction. We also
present the routes by which the fully disordered high temperature state can be
reached. For p=4, and at special commensurate densities, the "4 x 4"
commensurate state can melt directly into the disordered state via a self-dual
critical point with non-universal exponents.Comment: 12 pages, 5 figure
Schwinger-Keldysh approach to out of equilibrium dynamics of the Bose Hubbard model with time varying hopping
We study the real time dynamics of the Bose Hubbard model in the presence of
time-dependent hopping allowing for a finite temperature initial state. We use
the Schwinger-Keldysh technique to find the real-time strong coupling action
for the problem at both zero and finite temperature. This action allows for the
description of both the superfluid and Mott insulating phases. We use this
action to obtain dynamical equations for the superfluid order parameter as
hopping is tuned in real time so that the system crosses the superfluid phase
boundary. We find that under a quench in the hopping, the system generically
enters a metastable state in which the superfluid order parameter has an
oscillatory time dependence with a finite magnitude, but disappears when
averaged over a period. We relate our results to recent cold atom experiments.Comment: 22 pages, 7 figure
- …