Decay Law Regularity

Igor V. Zozoulenko, Torbjörn Blomquist

We perform numerical studies of wave packet propagation through open quantum billiards whose classical counterparts exhibit regular and chaotic dynamics. We show that for $t\ensuremath{\lesssim}{\ensuremath{\tau}}_{H}({\ensuremath{\tau}}_{H}$ being the Heisenberg time), the features in the transmitted and reflected currents are directly related to specific classical trajectories connecting the billiard leads. When $t\ensuremath{\gtrsim}{\ensuremath{\tau}}_{H},$ the calculated quantum-mechanical current starts to deviate from its classical counterpart, with the decay rate obeying a power law that depends on the number of decay channels. In a striking contrast to the classical escape from chaotic and regular systems (exponentially fast ${e}^{\ensuremath{-}\ensuremath{\gamma}t}$ for the former versus power-law ${t}^{\ensuremath{-}\ensuremath{\xi}}$ for the latter), the asymptotic decay of the corresponding quantum systems does not show a qualitative difference.

John P. Losee

In the early years of the twentieth century, Ernest Rutherford undertook pioneering studies of radioactive decay sequences. Kinetic molecular theory and the theory of radioactive decay both are based on statistical considerations. On the regularity-between-states view of causality, each stage of the decay process is in a cause-effect relation to its successor stage. The decay of thorium, qua ensemble of atoms, qualifies as a causal process on the regularity-between-states view. Regularities had been established that link the heating of elements and the occurrence of lines in their spectra. The causal relations at stake are regularities of transition between electron states, and to establish these regularities is to enable explanatory arguments to be given of atomic spectra. The correspondence principle provided a link between discontinuous transitions within the atom to continuous motions adequately described by classical physics. However, Neils Bohr's theory of the atom retained both quantum and classical aspects. Quantum mechanics and classical mechanics both feature causal laws.

Asher Peres

Jean-Paul Marchand

Jinzhao Wang, Yuxiang Yang

We prove that the regularized, stabilized sandwiched Rényi divergence of finite-dimensional quantum channels converges to their regularized relative entropy as the Rényi order tends to one. The key tool is the channel hockey-stick divergence: Gour's Stinespring approximation bound and a Schatten norm estimate amplify an asymptotic bound below one into exponential decay at higher threshold rates. For channel pairs with finite max-relative entropy, known operational connections then give exponential strong converses for parallel and adaptive discrimination, a sharp zero--one testing law, and the subchannel asymptotic equipartition property.