Related papers: Full characterization of modular values for two-di…
Recently, weak value $\rm A_w$ derived in the pre- and post-selected weak measurement has been shown to be powerful in measuring minute physical effects. In principle, the decrease in the post-selection probability will increase the…
We generalize the concept of a weak value of a quantum observable to cover arbitrary real positive operator measures. We show that the definition is operationally meaningful in the sense that it can be understood within the quantum theory…
We show that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topologiclal results are con- sequences of the modular invariance of elliptic operators on loop spaces. Previously we…
We study the discrete eigenvalues emerging from the threshold of the essential spectrum of one or two-dimensional Schr\"odinger operators with complex-valued $ L^p $-potentials in a weak coupling regime. We derive necessary and sufficient…
Weak values arise in quantum theory when the result of a weak measurement is conditioned on a subsequent strong measurement. The majority of the trials are discarded, leaving only very few successful events. Intriguingly those can display a…
This paper deals mainly with some aspects of the adjointable operators on Hilbert $C^*$-modules. A new tool called the generalized polar decomposition for each adjointable operator is introduced and clarified. As an application, the general…
I show that the application of the quantum-mechanical (QM) which-way weak measurement scheme of Vaidman may lead to logical inconsistencies. To this end, I study weak values of projection operators. Weak values are (normalized) amplitudes,…
We establish a new regularity property for weak solutions of parabolic systems with coefficients depending measurably on time as well as on all spatial variables. Namely, weak solutions are locally H{\"o}lder continuous Lp valued functions…
It has been proposed that the ability to perform joint weak measurements on post-selected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the…
Weak values are traditionally obtained using a weak interaction between the measured system and a pointer state. It has, however, been pointed out that weak coupling can be replaced by a carefully tailored strong interaction. This paper…
We investigate inexact proximity operators for weakly convex functions. To this aim, we derive sum rules for proximal {\epsilon}-subdifferentials, by incorporating the moduli of weak convexity of the functions into the respective formulas.…
The extraordinary concept of weak value amplification has attracted considerable attention for addressing foundational questions in quantum mechanics and for metrological applications in high precision measurement of small physical…
Weak measurement has been shown to play important roles in the investigation of both fundamental and practical problems. Anomalous weak values are generally believed to be observed only when post-selection is performed, i.e, only a…
The time evolution of the two-time conditional probability of the classical stochastic process is described in an analogous form of the quantum mechanical wave equations. By using it, we emulate the same strange behaviors as those of the…
We present a complex probability measure relevant for double (pairs of) states in quantum mechanics, as an extension of the standard probability measure for single states that underlies Born's statistical rule. When the double states are…
In a weak measurement the real and imaginary parts of a weak value participate in the shifts of the complementary variables of a pointer. While the real part represents the value of an observable in the limit of zero measurement strength,…
The quantum theoretical concepts of modular momentum and dynamical non-locality, which were introduced four decades ago, have recently been used to explain single particle quantum interference phenomena. Although the non-local exchange of…
Modular symmetries are known to be powerful and have various remarkable properties. We point out that the structure of vector-valued modular forms (VVMFs) space leads to the absence of couplings which cannot be explained in terms of the…
Recent string theory tests of swampland ideas like the distance or the dS conjectures have been performed at weak coupling. Testing these ideas beyond the weak coupling regime remains challenging. We propose to exploit the modular…
We establish the existence of global weak solutions of the 2D incompressible Euler equation, for a large class of non-smooth open sets. These open sets are the complements (in a simply connected domain) of a finite number of connected…