Generalized Kac's Lemma for Recurrence Time in Iterated Open Quantum Systems

We consider recurrence to the initial state after repeated actions of a quantum channel. After each iteration a projective measurement is applied to check recurrence. The corresponding return time is known to be an integer for the special case of unital channels, including unitary channels. We prove that for a more general class of quantum channels the expected return time can be given as the inverse of the weight of the initial state in the steady state. This statement is a generalization of the Kac lemma for classical Markov chains

Quantized recurrence time in iterated open quantum dynamics

The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of systems that includes classical Markov chains and unitary discrete time quantum walks on networks. Starting from a pure state, the time evolution is induced by repeated applications of a general quantum channel, in each timestep followed by a measurement to detect whether the system has returned to the original state. We prove that if the superoperator is unital in the relevant Hilbert space (the part of the Hilbert space explored by the system), then the expectation value of the return time is an integer, equal to the dimension of this relevant Hilbert space. We illustrate our results on partially coherent quantum walks on finite graphs. Our work connects the previously known quantization of the expected return time for bistochastic Markov chains and for unitary quantum walks, and shows that these are special cases of a more general statement. The expected return time is thus a quantitative measure of the size of the part of the Hilbert space available to the system when the dynamics is started from a certain state

Anomalous Anisotropic Magnetoresistance in Heavy-Fermion PrFe4P12

We have investigated the anisotropy of the magnetoresistance in the Pr-based HF compound PrFe4P12. The large anisotropy of effective mass and its strong field dependence have been confirmed by resistivity measurements. Particularly for H||[111], where the effective mass is most strongly enhanced, the non-Fermi liquid behavior has been observed. Also, we have found the angular dependence of the magnetoresistance sharply enhanced at H||[111], which is evidently correlated with both the non-Fermi liquid behavior and the high-field ordered state (B-phase).Comment: 3 pages, 3 figures. J. Phys. Soc. Jpn. Vol.77, No.8, in pres

Happiness, environmental protection and market economy

The manufacturing sector is leaving the West for Asia’s low wages and good working culture. Europe would be better off keeping these manufacturing activities, slowing down wage inflation and what is more, letting a young, cheaper workforce from the East settle down within their borders. This would aid in preserving the diverse economic structure which has been characteristic for Europe.Beside the economic growth there are two more concepts which have turned into the “holy cows” of economics during the last fifty years. One is the need to constantly improve labor productivity and the other is increasing competitiveness of nations. The high labor productivity of some countries, induces severe unemployment in the globalized world. In the other hand it is high time we understood that it is not competition, but cooperation that brings more happiness to humanity.Should we still opt for “happiness” and “sanity”, it is quite obvious that we all should, in economists’ terms, define our individual welfare functions corresponding to our own set of values, staying free from the influence of media, advertisements and fashion. The cornerstone to all this is the intelligent citizen who prefers local goods and services