arXiv subjects

V. V. Shamshutdinova

Publications and source records attributed to V. V. Shamshutdinova.

5 recordsLinked to original sources

arXiv2010

Equivalent Hermitian operator from supersymmetric quantum mechanics

Diagonalizable pseudo-Hermitian Hamiltonians with real and discrete spectra, which are superpartners of Hermitian Hamiltonians, must be $η$-pseudo-Hermitian with Hermitian, positive-definite and non-singular $η$ operators. We show that despite the fact that an $η$ operator produced by a supersymmetric transformation, corresponding to the exact supersymmetry, is singular, it can be used to find the eigenfunctions of a Hermitian operator equivalent to the given pseudo-Hermitian Hamiltonian. Once the eigenfunctions of the Hermitian operator are found the operator may be reconstructed with the help of the spectral decomposition.

math-ph↗

arXiv2009

Dynamics of Josephson-junction qubits with exactly solvable time-dependent bias pulses

The quantum dynamics of a two-state system (qubit) can be governed by means of external control parameters present in time-dependent bias pulses of special forms. We consider the class of biases for which the time evolution equation without a dissipation can be solved exactly. Concentrating for definiteness on the flux qubit we calculate the probability of the definite direction of the current in the loop and its time-averaged values as functions of the qubit's control parameters both analytically and solving numerically the equation of motion for the density matrix in the presence of relaxation and decoherence. It is shown that there exist such time-dependent biases that the definite current direction probability with no dissipation taken into account becomes a monotonously growing function of time tending to a value which may exceed 1/2. We also calculate the probability to find the system in the excited state and show the possibility of the inverse population in a properly driven two-state system provided the relaxation and dephasing rates are small enough.

quant-ph↗

arXiv2009

Towards Dynamical Qubit Controlling with Time-Dependent External Fields

For a flux qubit described by a two-level system of equations we propose a special time dependent external control field. We show that for a qubit placed in this field there exists a critical value of tunnel frequency. When the tunnel frequency is close to its critical value, the probability value of a definite direction of the current circulating in a Josephson-junction circuit may be kept above 1/2 during a desirable time interval. We also show that such a behavior is not much affected by a sufficiently small dissipation.

quant-ph↗

arXiv2006

Two-level systems: exact solutions and underlying pseudo-supersymmetry

Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a olynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final Hamiltonian of a chain and for solutions of the spin equation are derived. Applications are intended for a two-level atom in an electromagnetic field with a possible time-dependence of the field frequency. For a specific form of this dependence, the time oscillations of the probability to populate the excited level disappear. Under certain conditions this probability becomes a function tending monotonously to a constant value which can exceed 1/2.

quant-ph↗

arXiv2004

Darboux transformation for two-level systems

We develop the Darboux procedure for the case of the two-level system. In particular, it is demonstrated that one can construct the Darboux intertwining operator that does not violate the specific structure of the equations of the two-level system, transforming only one real potential into another real potential. We apply the obtained Darboux transformation to known exact solutions of the two-level system. Thus, we find three classes of new solutions for the two-level system and the corresponding new potentials that allow such solutions.

math-ph↗