

December 14, 2023, International conference "Discrete and Continuous Signals: Analysis, Information and Applications". St. Petersburg






On some properties of classical and quantum random walks.СанктПетербург
S. V. Grishin^{} ^{} Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region

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Abstract:
This talk is devoted to homogeneous random walks on a line. In the classical case, the
generating function for the positive halfline ашrst passage time is discussed. It often turns
out to admit an algebraic equation and is useful in statistical computations. Besides, the
corresponding algebraic curve sometimes is rational and has a positive genus which can
be accounted via analyzing singularities.
An open quantum system
$\rho \mapsto \sum_i V_i\rho V_i^*$
where $V_i$ are operators of shift on $a_i$ with coeffcients $\sqrt{p_i}$
is similar to the classical random walk
with increases $a_i$ and their probabilities $p_i$. Some characteristics of it are computed.
Language: English

