16,511 research outputs found
Finite-size scaling of out-of-time-ordered correlators at late times
Chaotic dynamics in quantum many-body systems scrambles local information so
that at late times it can no longer be accessed locally. This is reflected
quantitatively in the out-of-time-ordered correlator of local operators, which
is expected to decay to zero with time. However, for systems of finite size,
out-of-time-ordered correlators do not decay exactly to zero and in this paper
we show that the residual value can provide useful insights into the chaotic
dynamics. When energy is conserved, the late-time saturation value of the
out-of-time-ordered correlator of generic traceless local operators scales as
an inverse polynomial in the system size. This is in contrast to the inverse
exponential scaling expected for chaotic dynamics without energy conservation.
We provide both analytical arguments and numerical simulations to support this
conclusion.Comment: improved presentatio
S-Lemma with Equality and Its Applications
Let and be two quadratic functions
having symmetric matrices and . The S-lemma with equality asks when the
unsolvability of the system implies the existence of a real
number such that . The
problem is much harder than the inequality version which asserts that, under
Slater condition, is unsolvable if and only if for some . In this paper, we
show that the S-lemma with equality does not hold only when the matrix has
exactly one negative eigenvalue and is a non-constant linear function
(). As an application, we can globally solve as well as the two-sided generalized trust region subproblem
without any condition. Moreover, the
convexity of the joint numerical range where is a (possibly non-convex) quadratic
function and are affine functions can be characterized
using the newly developed S-lemma with equality.Comment: 34 page
A generalized structure of Bell inequalities for bipartite arbitrary dimensional systems
We propose a generalized structure of Bell inequalities for arbitrary
d-dimensional bipartite systems, which includes the existing two types of Bell
inequalities introduced by Collins-Gisin-Linden-Massar-Popescu [Phys. Rev.
Lett. 88, 040404 (2002)] and Son-Lee-Kim [Phys. Rev. Lett. 96, 060406 (2006)].
We analyze Bell inequalities in terms of correlation functions and joint
probabilities, and show that the coefficients of correlation functions and
those of joint probabilities are in Fourier transform relations. We finally
show that the coefficients in the generalized structure determine the
characteristics of quantum violation and tightness.Comment: 6 pages, 1 figur
Extracellular signal-regulated kinases mediate the enhancing effects of inflammatory mediators on resurgent currents in dorsal root ganglion neurons
Previously we reported that a group of inflammatory mediators significantly enhanced resurgent currents in dorsal root ganglion neurons. To understand the underlying intracellular signaling mechanism, we investigated the effects of inhibition of extracellular signal-regulated kinases and protein kinase C on the enhancing effects of inflammatory mediators on resurgent currents in rat dorsal root ganglion neurons. We found that the extracellular signal-regulated kinases inhibitor U0126 completely prevented the enhancing effects of the inflammatory mediators on both Tetrodotoxin-sensitive and Tetrodotoxin-resistant resurgent currents in both small and medium dorsal root ganglion neurons. U0126 substantially reduced repetitive firing in small dorsal root ganglion neurons exposed to inflammatory mediators, consistent with prevention of resurgent current amplitude increases. The protein kinase C inhibitor Bisindolylmaleimide I also showed attenuating effects on resurgent currents, although to a lesser extent compared to extracellular signal-regulated kinases inhibition. These results indicate a critical role of extracellular signal-regulated kinases signaling in modulating resurgent currents and membrane excitability in dorsal root ganglion neurons treated with inflammatory mediators. It is also suggested that targeting extracellular signal-regulated kinases-resurgent currents might be a useful strategy to reduce inflammatory pain
A linear theory for control of non-linear stochastic systems
We address the role of noise and the issue of efficient computation in
stochastic optimal control problems. We consider a class of non-linear control
problems that can be formulated as a path integral and where the noise plays
the role of temperature. The path integral displays symmetry breaking and there
exist a critical noise value that separates regimes where optimal control
yields qualitatively different solutions. The path integral can be computed
efficiently by Monte Carlo integration or by Laplace approximation, and can
therefore be used to solve high dimensional stochastic control problems.Comment: 5 pages, 3 figures. Accepted to PR
Rates of Neutrino Absorption on Nucleons and the Reverse Processes in Strong Magnetic Fields
The rates of electron neutrino capture on neutron, electron anti-neutrino
capture on proton, and their reverse processes are important for understanding
the production of heavy elements in the supernova environment above the
protoneutron star. Observations and theoretical considerations suggest that
some protoneutron stars may be born with strong magnetic fields. We develop a
numerical method to calculate the above rates in supernova environments with
magnetic fields up to 10^16 G. This method is accurate to the order of one over
nucleon mass. We show that our results have the correct behavior in the limit
of high neutrino energy or small magnetic field. Based on comparison of our
results with various approximations, we recommend efficient estimates of the
above rates for use in models of supernova nucleosynthesis in the presence of
strong magnetic fields.Comment: 21 pages, 4 figures. Some explaination and references are added in
the second versio
Nonequilibrium quantum criticality in open electronic systems
A theory is presented of quantum criticality in open (coupled to reservoirs)
itinerant electron magnets, with nonequilibrium drive provided by current flow
across the system. Both departures from equilibrium at conventional
(equilibrium) quantum critical points and the physics of phase transitions
induced by the nonequilibrium drive are treated. Nonequilibrium-induced phase
transitions are found to have the same leading critical behavior as
conventional thermal phase transitions.Comment: 5 pages, 1 figur
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