Related papers: Minimum number-phase uncertainty states via weight…
We present a least squares method for estimating parameters from measurements of event yields in the presence of background and crossfeed. We adopt a unified approach to incorporating the statistical and systematic uncertainties on the…
We present new estimate for Hardy-type inequality in variable exponent Lebesgue spaces. More precisely, by imposing regularity assumptions on the exponent, we prove that the estimations can be reduced to the fixed exponents.
We generalize Hardy's proof of nonlocality to the case of bipartite mixed statistical operators, and we exhibit a necessary condition which has to be satisfied by any given mixed state $\sigma$ in order that a local and realistic hidden…
Choosing four entangled stets to form an orthogonal and complete basis for a two-particle system, we argue that a local hidden variable model should give the probability of each entangled state if the two-particle system is described by a…
We determine a positive normalised phase space probability distribution $P$ with minimum mean square fractional deviation from the Wigner distribution $W$ .The minimum deviation, an invariant under phase space rotations, is a quantitative…
We investigate the geometric phases and the Bargmann invariants associated with a multi-level quantum systems. In particular, we show that a full set of `gauge-invariant' objects for an $n$-level system consists of $n$ geometric phases and…
Completeness is proved for some subsystems of a system of coherent states. The linear dependence of states is investigated for the von Neumann type subsystems. A detailed study is made of the case when a regular lattice on the complex…
This study explores the link between Modified Gravity and modifications of phase space volume. Analyzing Fermi gas modifications {in the non-relativistic limit of the} Ricci-based gravities, we derive a generalized partition function in the…
By analyzing the survival probability amplitude of an unstable state we show that the energy corrections to this state in the long ($t \to \infty$) and relatively short (lifetime of the state) time regions, are different. It is shown that…
The uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The situation is different if one can build a…
We study the Complex Ginzburg--Landau initial value problem $\partial_t u=(1+i\alpha) \partial_x^2 u + u - (1+i\beta) u |u|^2$, $u(x,0)=u_0(x)$ for a complex field $u\in{\bf C}$, with $\alpha,\beta\in{\bf R}$. We consider the Benjamin--Feir…
We introduce two extensions of the space of Bridgeland stability conditions of a triangulated category. First we consider lax stability conditions where semistable objects are allowed to have mass zero but still have a phase. The…
A systematic analysis of the Eckhaus instability in the one-dimensional Ginzburg-Landau equation is presented. The analysis is based on numerical integration of the equation in a large (xt)-domain. The initial conditions correspond to a…
We introduce a quantifier of phase-space complexity for discrete-variable (DV) quantum systems. Motivated by a recent framework developed for continuous-variable systems, we construct a complexity measure of quantum states based on the…
We obtain Fourier inequalities in the weighted $L_p$ spaces for any $1<p<\infty$ involving the Hardy-Ces\`aro and Hardy-Bellman operators. We extend these results to product Hardy spaces for $p\le 1$. Moreover, boundedness of the…
We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^\infty$…
We provide necessary and sufficient conditions for states to have an arbitrarily small uncertainty product of the azimuthal angle $\phi $ and its canonical moment $L_{z}$. We illustrate our results with analytical examples.
In this paper, we completely give the solution of the problem of Littlewood-type randomization in the Hardy and Bergman spaces of Dirichlet series. The Littlewood-type theorem for Bergman spaces of Dirichlet series is very different from…
In a recent paper, Buniy et al. have argued that a possible discretization of spacetime leads to an unavoidable discretization of the state space of quantum mechanics. In this paper, we show that this conclusion is not limited to quantum…
Uncertainty relations for mixed quantum states (precisely, purity-bounded position-momentum relations, developed by Bastiaans and then by Man'ko and Dodonov) are studied in general multi-dimensional case. An expression for family of mixed…