Evgeny Yarevsky

Quantum Zeno and anti-Zeno effects in the Friedrichs model

We analyze the short-time behavior of the survival probability in the frame of the Friedrichs model for different formfactors. We have shown that this probability is not necessary analytic at the time origin. The time when the quantum Zeno effect could be observed is found to be much smaller than usually estimated. We have also studied the anti-Zeno era and have estimated its duration.

Integral-difference collision operators: Analytical and numerical spectral analysis

We analyze spectral properties of a class of integral-difference collision operators arising in some nonequilibrium statistical physics models. We present analytical estimates and numerical results for the operators defined on finite intervals and corresponding to the truncated Gaussian equilibrium distribution function. Some conclusions are drawn about the spectrum of operators on whole axis. Physical limitations for these kinds of models are discussed.

The connection between the rigged Hilbert space and the complex scaling approaches for resonances. The Friedrichs model

Abstract The rigged Hilbert space approach and the complex scaling method are compared for the Friedrichs model. It is shown that they define the same resonance pole. The choice of the test space for the rigged Hilbert space approach is discussed.

Eigen energies and the statistical distributions of the rovibrational levels of the bosonic van der Waals argon trimer.

The eigen energies and the statistical distributions of the rovibrational levels (J = 0-2) of the bosonic van der Waals argon trimer were calculated using a full angular momentum three-dimensional finite element method. The influence of interatomic potentials on the vibrational levels and statistical properties of the trimer was discussed.

Decoherence and Zeno time in quantum computations

Abstract We analyze the short-time behaviour of the survival probability in the frame of the Friedrichs model for different formfactors. We have shown that the probability may not be quadratic for the short times while the quantum Zeno effect (QZE) still exists in this case. We have found that the time when the QZE could be observed is much smaller than usually assumed. We have studied the anti-Zeno era and have estimated its duration. Related decoherence processes are also discussed.

Resonances of the cusp family

We study a family of chaotic maps with limit cases—the tent map and the cusp map (the cusp family). We discuss the spectral properties of the corresponding Frobenius–Perron operator in different function spaces including spaces of analytical functions and study numerically the eigenvalues and eigenfunctions.

The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius–Perron operator U of the cusp map F:[−1,1]→[−1,1], F(x)=1−2|x| (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any q∈(0,1) the spectrum of U in the Hardy space in the disk {z∈C:|z−q|<1+q} is the union of the segment [0,1] and some finite or countably infinite set of isolated eigenvalues of finite multiplicity.