Related papers: Minimum number-phase uncertainty states via weight…
Several time-independent methods have been devised for measuring the phase gamma of the Cabibbo-Kobayashi-Maskawa unitarity triangle. It is shown that such measurements generally suffer from discrete ambiguity which is at least 8-fold, not…
We propose a unifying framework for characterizing pure and mixed state phases of matter across equilibrium, non equilibrium, and metastable regimes. We introduce the concept of locally stable states, defined by the operational property…
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…
Necessary and sufficient condition for the existence of a minimum uncertainty state for an arbitrary pair of observables is given.
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
A hierarchy of multimode uncertainty relations on the second moments of n pairs of canonical operators is derived in terms of quantities invariant under linear canonical (i.e. symplectic) transformations. Conditions for the separability of…
Phase-space features of the Wigner flow are examined so to provide a set of continuity equations that describe the flux of quantum information in the phase-space. The reported results suggest that the non-classicality profile of anharmonic…
This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…
Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the…
By a famous result, functions in backward shift invariant subspaces in Hardy spaces are characterized by the fact that they admit a pseudocontinuation a.e. on $\T$. More can be said if the spectrum of the associated inner function has holes…
This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.
Nonminimally coupled free scalar fields may be unstable in the spacetime of compact objects. Such instability can be triggered by classical seeds or, more simply, by quantum fluctuations giving rise to the so-called {\em vacuum awakening…
Let P be a linear, second order, elliptic operator satisfying a Hardy inequality with potential W (i.e. $P-W\geq0$) and best constant $\alpha$. We give conditions so that the spectrum of $W^{-1}P$ is $[\alpha,\infty)$. We apply this to…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…
We give a statistical characterization of states with nonzero winding number in the Phase Turbulence (PT) regime of the one-dimensional Complex Ginzburg-Landau equation. We find that states with winding number larger than a critical one are…
Theoretical predictions need quantified uncertainties for a meaningful comparison to experimental results. This is an idea which presently permeates the field of theoretical nuclear physics. In light of the recent progress in estimating…
The squeezed states are states of minimum uncertainty, but unlike the coherent states, in which the uncertainty in the position and the momentum are the same, these allow to reduce the uncertainty, either in the position or in the momentum,…
Minimum uncertainty states of the conventional Heisenberg uncertainty relation have been extensively studied and are often regarded as the most classical quantum states from the perspective of uncertainty, providing valuable insight into…
We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimetric inequality and of Weissler's inequality for dilations. By contractivity and a standard…
We discuss the relation between density matrices and the uncertainty principle; this allows us to justify and explain a recent statement by Man'ko et al. We thereafter use Hardy's uncertainty principle to prove a new result for Wigner…