Related papers: Weak Gibbs measures as Gibbs measures for asymptot…
The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective…
Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. `strong') measurement of the complementary variable. We generalize this method to mixed…
We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the…
An optical analog of the quantum weak measurement scheme proved to be very useful for the observation of optical beam shifts. Here we adapt the weak value amplification method for the observation of the angular Goos-Hanchen shift. We…
With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities)…
The variance of an observable in a pre-selected quantum system, which is always real and non-negative, appears as an increase in the probe wave packet width in indirect measurements. Extending this framework to pre- and post-selected…
It is well known from quantum mechanics that weak measurements offer a means of amplifying and detecting very small phenomena. We present here the first experimental observation of the Goos-Hanchen shift via a weak measurement approach.
If $(X,d)$ is a metric space then the map $f\colon X\to X$ is defined to be a weak contraction if $d(f(x),f(y))<d(x,y)$ for all $x,y\in X$, $x\neq y$. We determine the simplest non-closed sets $X\subseteq \mathbb{R}^n$ in the sense of…
Gibbs random fields corresponding to systems of real-valued spins (e.g. systems of interacting anharmonic oscillators) indexed by the vertices of unbounded degree graphs with a certain summability property are constructed. It is proven that…
It is proved that every normalized weakly null \sq\ has a sub\sq\ which is convexly unconditional. Further, an Hierarchy of summability methods is introduced and with this we give a complete classification of the complexity of weakly null…
In order to illustrate a recently derived covariant formalism for computing asymptotic symmetries and asymptotically conserved superpotentials in gauge theories, the case of gravity with minimally coupled scalar fields is considered and the…
This work demonstrates that repeated weak measurements together with post-selection can produce sharp dynamical discontinuities in meter observables, even in minimal quantum systems. The discontinuous behavior is governed by the polar angle…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
The weak value, the average result of a weak measurement, has proven useful for probing quantum and classical systems. Examples include the amplification of small signals, investigating quantum paradoxes, and elucidating fundamental quantum…
We consider Gibbs measures relative to Brownian motion of Feynman-Kac type, with single site potential V. We show that for a large class of V, including the Coulomb potential, there exist infinitely many infinite volume Gibbs measures.
We consider the action of Mandelbrot multiplicative cascades on probability measures supported on a symbolic space. For general probability measures, we obtain almost a sharp criterion of non-degeneracy of the limiting measure; it relies on…
We prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable…
Weak measurements with imaginary weak values are reexamined in light of recent experimental results. The shift of the meter, due to the imaginary part of the weak value, is derived via the probability of postselection, which allows…
Chatterjee's correlation coefficient has recently been proposed as a new association measure for bivariate random vectors that satisfies a number of desirable properties. Among these properties is the feature that the coefficient equals one…