Related papers: A Simple Derivation of Schroedinger Uncertainty Re…
We consider the Cauchy problem for the fourth order nonlinear Schr\"{o}dinger equation with derivative nonlinearity $(i\partial _t + \Delta ^2) u= \pm \partial (|u|^2u)$ on $\mathbb{R} ^d$, $d \ge 3$, with random initial data, where…
We consider the Schr\"{o}dinger equation $(i\partial_t+\Delta)u=0$ on an $n$-dimensional simplex with Dirichlet boundary conditions. We use a commutator argument along with integration by parts to obtain an observability asymptotic for any…
The duality symmetric but not manifestly covariant action proposed by Schwarz-Sen is canonically quantized in the Coulomb gauge. The resulting theory turns out to be, nevertheless, relativistically invariant. It is shown, afterwards, that…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
For the wave and the Schr\"odinger equations we show how observability can be deduced from the observability of solutions localized in frequency according to a dyadic scale.
The problem of inferring the outcome of a simultaneous measurement of two non-commuting observables is addressed. We show that for certain pairs with dense spectra, precise inferences of the measurement outcomes are possible in pre-and…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=exp[i phi] VU. Its most important application is to constrain how much a quantum state can be localised simultaneously in two…
We establish observability inequalities for various problems involving fractional Schr\"odinger operators $(-\Delta)^{\alpha/2}+V$, $\alpha>0$, on a compact Riemannian manifold. Observability from an open set for the corresponding…
We consider the inverse problem of determining the coupling coefficients in a two-state Schr\"odinger system. We prove a Lipschitz stability inequality for the zeroth and first order coupling terms by finitely many partial lateral…
We prove a logarithmic convexity result for exponentially weighted $L^2$-norms of solutions to electromagnetic Schr\"odinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique…
In this work we derive a matrix formulation of a noise-disturbance uncertainty relation, which is akin to the Robertson-Schr\"odinger uncertainty principle. Our inequality is stronger than Ozawa's uncertainty principle and takes…
Time-reversal symmetry plays an essential role in the thermodynamic uncertainty relations, which bound the fluctuations of observables in terms of the associated dissipation. In fact, thermodynamic uncertainty relations are typically…
The quantification of the "measurement uncertainty" aspect of Heisenberg's Uncertainty Principle---that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two…
We give an exceptionally short derivation of Schroedinger's equation by replacing the idealization of a point particle by a density distribution.
Based on mixedness definition as M=1-tr(\r{ho}^2), we obtain a new variance-based uncertainty equality along with an inequality for Hermitian operators of a single-qubit system. The obtained uncertainty equality can be used as a measure of…
Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of…
We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and…
An explicit two-soliton solution for the derivative nonlinear Schr\"odinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one…
We propose a nonlinear modification of the Schr\"{o}dinger equation that possesses the main properties of this equation such as the Galilean invariance, the weak separability of composite systems, and the homogeneity in the wave function.…