16,643 research outputs found
Averaging approximation to singularly perturbed nonlinear stochastic wave equations
An averaging method is applied to derive effective approximation to the
following singularly perturbed nonlinear stochastic damped wave equation \nu
u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain
\,, \,. Here is a small parameter
characterising the singular perturbation, and \,, \,, parametrises the strength of the noise. Some scaling transformations
and the martingale representation theorem yield the following effective
approximation for small , u_t=\D u+f(u)+\nu^\alpha\dot{W} to an error of
\ord{\nu^\alpha}\,.Comment: 16 pages. Submitte
Ricci flows with unbounded curvature
We show that any noncompact Riemann surface admits a complete Ricci flow
g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).Comment: 12 pages, 1 figure; updated reference
Running-phase state in a Josephson washboard potential
We investigate the dynamics of the phase variable of an ideal underdamped
Josephson junction in switching current experiments. These experiments have
provided the first evidence for macroscopic quantum tunneling in large
Josephson junctions and are currently used for state read-out of
superconducting qubits. We calculate the shape of the resulting macroscopic
wavepacket and find that the propagation of the wavepacket long enough after a
switching event leads to an average voltage increasing linearly with time.Comment: 6 pages, 3 figure
An Exact Conformal Symmetry Ansatz on Kaluza-Klein Reduced TMG
Using a Kaluza-Klein dimensional reduction, and further imposing a conformal
Killing symmetry on the reduced metric generated by the dilaton, we show an
Ansatz that yields many of the known stationary axisymmetric solutions to TMG.Comment: 20 pages, 1 figure, v3: postprint, added one re
Single-charge rotating black holes in four-dimensional gauged supergravity
We consider four-dimensional U(1)^4 gauged supergravity, and obtain
asymptotically AdS_4, non-extremal, charged, rotating black holes with one
non-zero U(1) charge. The thermodynamic quantities are computed. We obtain a
generalization that includes a NUT parameter. The general solution has a
discrete symmetry involving inversion of the rotation parameter, and has a
string frame metric that admits a rank-2 Killing-Stackel tensor.Comment: 9 page
Non-local nuclear spin quieting in quantum dot molecules: Optically-induced extended two-electron spin coherence time
We demonstrate the extension of coherence between all four two-electron spin
ground states of an InAs quantum dot molecule (QDM) via non-local suppression
of nuclear spin fluctuations in both constituent quantum dots (QDs), while
optically addressing only the upper QD transitions. Long coherence times are
revealed through dark-state spectroscopy as resulting from nuclear spin locking
mediated by the exchange interaction between the QDs. Lineshape analysis
provides the first measurement of the quieting of the Overhauser field
distribution correlating with reduced nuclear spin fluctuations.Comment: Supplementary materials can be found on the publication page of our
website. http://research.physics.lsa.umich.edu/dst/Publications.htm
Charge sensing in carbon nanotube quantum dots on microsecond timescales
We report fast, simultaneous charge sensing and transport measurements of
gate-defined carbon nanotube quantum dots. Aluminum radio frequency single
electron transistors (rf-SETs) capacitively coupled to the nanotube dot provide
single-electron charge sensing on microsecond timescales. Simultaneously, rf
reflectometry allows fast measurement of transport through the nanotube dot.
Charge stability diagrams for the nanotube dot in the Coulomb blockade regime
show extended Coulomb diamonds into the high-bias regime, as well as even-odd
filling effects, revealed in charge sensing data.Comment: 4 pages, 4 figure
Hydrodynamics of the Kuramoto-Sivashinsky Equation in Two Dimensions
The large scale properties of spatiotemporal chaos in the 2d
Kuramoto-Sivashinsky equation are studied using an explicit coarse graining
scheme. A set of intermediate equations are obtained. They describe
interactions between the small scale (e.g., cellular) structures and the
hydrodynamic degrees of freedom. Possible forms of the effective large scale
hydrodynamics are constructed and examined. Although a number of different
universality classes are allowed by symmetry, numerical results support the
simplest scenario, that being the KPZ universality class.Comment: 4 pages, 3 figure
Remarks on the extension of the Ricci flow
We present two new conditions to extend the Ricci flow on a compact manifold
over a finite time, which are improvements of some known extension theorems.Comment: 9 pages, to appear in Journal of Geometric Analysi
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