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One manifestation of quantum resonances is a large sojourn time, or autocorrelation, for states which are initially localized. We elaborate on Lavines time-energy uncertainty principle and give an estimate on the sojourn time. For the case of perturbed embedded eigenstates the bound is explicit and involves Fermis Golden Rule. It is valid for a very general class of systems. We illustrate the theory by applications to resonances for time dependent systems including the AC Stark effect as well as multistate systems.
Utilizing frameworks developed by Delsarte, Yudin and Levenshtein, we deduce linear programming lower bounds (as $Nto infty$) for the Riesz energy of $N$-point configurations on the $d$-dimensional unit sphere in the so-called hypersingular case; i.e
Even though irreversibility is one of the major hallmarks of any real life process, an actual understanding of irreversible processes remains still mostly semiempirical. In this paper we formulate a thermodynamic uncertainty principle for irreversibl
We construct concrete examples of time operators for both continuous and discrete-time homogeneous quantum walks, and we determine their deficiency indices and spectra. For a discrete-time quantum walk, the time operator can be self-adjoint if the ti
We study a variational model for a diblock-copolymer/homopolymer blend. The energy functional is a sharp-interface limit of a generalisation of the Ohta-Kawasaki energy. In one dimension, on the real line and on the torus, we prove existence of minim
Uncertainty relations play a crucial role in quantum mechanics. A well-defined method exists for deriving such uncertainties for pairs of observables. It does not include, however, an important family of fundamental relations: the time-energy uncerta