Related papers: Minimum number-phase uncertainty states via weight…
We use spectral projections of time operator in the Liouville space for simple quantum scattering systems in order to define a space of unstable particle states evolving under a contractive semi-group. This space includes purely…
General conditions for the occurrence of mesoscopic phase fluctuations in condensed matter are considered. The description of different thermodynamic phases, which coexist as a mixture of mesoscopically separated regions, is based on the…
We first show that partial transposition for pure and mixed two-particle states in a discrete $N$-dimensional Hilbert space is equivalent to a change in sign of the momentum of one of the particles in the Wigner function for the state. We…
In this paper we give log-convexity properties for solutions to discrete Schr\"odinger equations with different discrete versions of Gaussian decay at two different times. For free evolutions, we use complex analysis arguments to derive…
It has recently been shown that by extending the minimal standard model to include a right-handed partner to $\nu_\tau$, it is possible to gauge the $B - 3 L_\tau$ quantum number consistently. If we add two scalar triplets, one trivial…
The reduced covariant phase space associated with the three-dimensional Euclidean Nambu-Goto action can be identified, via the Enneper-Weierstrass representation of minimal surfaces, with the space of complex analytic functions plus three…
It is shown that fundamental uncertainty relations between photon number and canonical phase of a single-mode optical field can be verified by means of balanced homodyne measurement. All the relevant quantities can be sampled directly from…
Determining the measurement uncertainty region is a difficult problem for generic sets of observables. For this reason the literature on exact measurement uncertainty regions is focused on symmetric sets of observables, where the symmetries…
We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is…
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of…
We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the B\"ottcher-Wenzel inequality. The first relation is mathematically proven, while the second, tighter relation is…
Weak measurements performed between quantum state preparation and post-selection result in complex values for self-adjoint operators, corresponding to complex conditional probabilities for the projections on specific eigenstates. In this…
We consider the cubic Schr\"odinger equation on the euclidean space perturbed by a short-range potential $V$. The presence of a negative simple eigenvalue for $-\Delta+V$ gives rise to a curve of small and localized nonlinear ground states…
It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lema\^itre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy…
The three ways of generalization of canonical coherent states are briefly reviewed and compared with the emphasis laid on the (minimum) uncertainty way. The characteristic uncertainty relations, which include the Schroedinger and Robertson…
We prove a family of $L^p$ uncertainty inequalities on fairly general groups and homogeneous spaces, both in the smooth and in the discrete setting. The crucial point is the proof of the $L^1$ endpoint, which is derived from a general weak…
We present strategies to quantify theoretical uncertainties in modern ab-initio calculations of electromagnetic observables in light and medium-mass nuclei. We discuss how uncertainties build up from various sources, such as the…
We analyze properties of unstable vacuum states from the point of view of the quantum theory. In the literature one can find some suggestions that some of false (unstable) vacuum states may survive up to times when their survival…
We take a modified boundary condition at the dead end of a stub to simulate transmission zeroes being replaced by minima and then the discontinuous phase slip (or decrease) at the transmission zeroes are replaced by a continuous but rapid…
In this paper we describe invariant geometrical ~structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally…