680 research outputs found
Scaling properties of noise-induced switching in a bistable tunnel diode circuit
Noise-induced switching between coexisting metastable states occurs in a wide
range of far-from-equilibrium systems including micro-mechanical oscillators,
epidemiological and climate change models, and nonlinear electronic transport
in tunneling structures such as semiconductor superlattices and tunnel diodes.
In the case of tunnel diode circuits, noise-induced switching behavior is
associated with negative differential resistance in the static current-voltage
characteristics and bistability, i.e., the existence of two macroscopic current
states for a given applied voltage. Noise effects are particularly strong near
the onset and offset of bistable current behavior, corresponding to bifurcation
points in the associated dynamical system. In this paper, we show that the
tunnel diode system provides an excellent experimental platform for the
precision measurement of scaling properties of mean switching times versus
applied voltage near bifurcation points. More specifically, experimental data
confirm that the mean switching time scales logarithmically as the 3/2 power of
voltage difference over an exceptionally wide range of time scales and noise
intensities.Comment: 9 pages, 9 figures, accepted manuscript for publication in the
European Physical Journal B, Topical Issue: Non-Linear and Complex Dynamics
in Semiconductors and Related Material
Baryon polarization in low-energy unpolarized meson-baryon scattering
We compute the polarization of the final-state baryon, in its rest frame, in
low-energy meson--baryon scattering with unpolarized initial state, in
Unitarized BChPT. Free parameters are determined by fitting total and
differential cross-section data (and spin-asymmetry or polarization data if
available) for , and scattering. We also compare our
results with those of leading-order BChPT
Computational Difficulty of Global Variations in the Density Matrix Renormalization Group
The density matrix renormalization group (DMRG) approach is arguably the most
successful method to numerically find ground states of quantum spin chains. It
amounts to iteratively locally optimizing matrix-product states, aiming at
better and better approximating the true ground state. To date, both a proof of
convergence to the globally best approximation and an assessment of its
complexity are lacking. Here we establish a result on the computational
complexity of an approximation with matrix-product states: The surprising
result is that when one globally optimizes over several sites of local
Hamiltonians, avoiding local optima, one encounters in the worst case a
computationally difficult NP-hard problem (hard even in approximation). The
proof exploits a novel way of relating it to binary quadratic programming. We
discuss intriguing ramifications on the difficulty of describing quantum
many-body systems.Comment: 5 pages, 1 figure, RevTeX, final versio
Hessian barrier algorithms for linearly constrained optimization problems
In this paper, we propose an interior-point method for linearly constrained
optimization problems (possibly nonconvex). The method - which we call the
Hessian barrier algorithm (HBA) - combines a forward Euler discretization of
Hessian Riemannian gradient flows with an Armijo backtracking step-size policy.
In this way, HBA can be seen as an alternative to mirror descent (MD), and
contains as special cases the affine scaling algorithm, regularized Newton
processes, and several other iterative solution methods. Our main result is
that, modulo a non-degeneracy condition, the algorithm converges to the
problem's set of critical points; hence, in the convex case, the algorithm
converges globally to the problem's minimum set. In the case of linearly
constrained quadratic programs (not necessarily convex), we also show that the
method's convergence rate is for some
that depends only on the choice of kernel function (i.e., not on the problem's
primitives). These theoretical results are validated by numerical experiments
in standard non-convex test functions and large-scale traffic assignment
problems.Comment: 27 pages, 6 figure
New approximations for the cone of copositive matrices and its dual
We provide convergent hierarchies for the cone C of copositive matrices and
its dual, the cone of completely positive matrices. In both cases the
corresponding hierarchy consists of nested spectrahedra and provide outer
(resp. inner) approximations for C (resp. for its dual), thus complementing
previous inner (resp. outer) approximations for C (for the dual). In
particular, both inner and outer approximations have a very simple
interpretation. Finally, extension to K-copositivity and K-complete positivity
for a closed convex cone K, is straightforward.Comment: 8
Detection of non-Gaussian Fluctuations in a Quantum Point Contact
An experimental study of current fluctuations through a tunable transmission
barrier, a quantum point contact, are reported. We measure the probability
distribution function of transmitted charge with precision sufficient to
extract the first three cumulants. To obtain the intrinsic quantities,
corresponding to voltage-biased barrier, we employ a procedure that accounts
for the response of the external circuit and the amplifier. The third cumulant,
obtained with a high precision, is found to agree with the prediction for the
statistics of transport in the non-Poissonian regime.Comment: 4 pages, 4 figures; published versio
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