The research is dedicated to a detailed theoretical study of dynamic processes that occur during the interaction of a transmon-type qubit connected to a semi-infinite transmission line with two signals: pump and probe. By manipulating the frequencies and amplitudes of the signals it is possible to explore the system behavior. We use the Lindblad equation formalism to make our calculations....
Quantum logic gates applied to qubits are basic elements of the circuit model used for quantum computations. Usually, quantum gates are realized by a resonant excitation, resulting in Rabi oscillations, which lead to a periodic excitation of the qubit. It has certain limitations and complications, like neglecting counter-rotating terms. We investigate an alternative way for quantum control and...
We investigated the electronic processes in a field effect transistor channel using shallow water approximations to obtain the analytical expressions for electron and field distributions, as well as electric fluctuations using the Langevin approach. We considered the current-voltage characteristic of the transistor in the stationary mode. For the non-stationary case, we obtained the spatial...
Motivated by recent experimental observations of unconventional superconductivity in the twisted bilayer and trilayer graphene, we develop a theory of point-contact tunneling into superconductors with arbitrary gap structures and for arbitrary transmission coefficients of the contact. Exploiting the dependence of Andreev reflections on the position of the STM tip relative to lattice symmetry...
We elaborate a systematic way to obtain higher order contributions in the nonlinear steepest descent method for Riemann-Hilbert problem associated with homogeneous Painleve II equation. The problem is reformulated as a matrix factorization problem on two circles and can be solved perturbatively reducing it to finite systems of algebraic linear equations. The method is applied to find...
In our work we consider geodesic equations in Schwarzschild space-time with arbitrary external forces and obtain Gaussian perturbation equations for osculating elements in terms of Weierstrass elliptic functions. As an application, we solve the perturbation equations analytically in linear approximation for forces induced by the presence of the cosmological constant in the Schwarzschild-de...
