Anna Vershynina

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Abstract. In this article, we define the transport dimension of probability measures on Rm using ramified optimal transportation theory. We show that the transport dimension of a probability measure is bounded above by the Minkowski dimension and below by the Hausdorff dimension of the measure. Moreover, we introduce a metric, called “the dimensional(More)
We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our(More)
We prove upper bounds on the rate, called ”mixing rate”, at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under nonlocal unitary evolution. For an ensemble consisting of two states, with probabilities of p and 1 − p, we prove that the mixing rate is bounded above by 4 √ p(1− p) for any Hamiltonian of(More)
We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking(More)
Cordipin-retard is one of the new highly effective slow-releasing hypotensive drugs from the calcium antagonists family. Single intake of the drug is equal to that of corinfar while prolonged treatment with cordipin-retard surpasses corinfar in hypotensive influence and duration of effect. No adverse effect of the drug on conductive system of the heart and(More)
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