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B. F. Samsonov

Publications and source records attributed to B. F. Samsonov.

10 recordsLinked to original sources
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↗
arXiv2006

Exact propagators for complex SUSY partners of real potentials

A method for calculating exact propagators for those complex potentials with a real spectrum which are SUSY partners of real potentials is presented. It is illustrated by examples of propagators for some complex SUSY partners of the harmonic oscillator and zero potentials.

quant-ph↗
arXiv2006

Irreducible second order SUSY transformations between real and complex potentials

Second order SUSY transformations between real and complex potentials for three important from physical point of view Sturm-Liouville problems, namely, problems with the Dirichlet boundary conditions for a finite interval, for a half axis and for the whole real line are analyzed. For every problem conditions on transformation functions are formulated when transformations are irreducible, i.e. when either the intermediate Hamiltonian is not well defined in the same Hilbert space as the initial and final Hamiltonians or its eigenfunctions cannot be obtained by applying transformation operator either on eigenfunctions of the initial Hamiltonian or on these of the final Hamiltonian. Obtained results are illustrated by numerous simple examples.

quant-ph↗
arXiv2006

Multichannel coupling with supersymmetric quantum mechanics and exactly-solvable model for Feshbach resonance

A new type of supersymmetric transformations of the coupled-channel radial Schroedinger equation is introduced, which do not conserve the vanishing behavior of solutions at the origin. Contrary to usual transformations, these ``non-conservative'' transformations allow, in the presence of thresholds, the construction of potentials with coupled scattering matrices from uncoupled potentials. As an example, an exactly-solvable potential matrix is obtained which provides a very simple model of Feshbach-resonance phenomenon.

quant-ph↗
arXiv2004

Supersymmetry approach to nuclear-spin-polarization-induced quantum dot structure calculations

In nuclear-spin-polarization-induced quantum dots the electrons are confined through local nuclear spin polarization. The model electron confinement potential is time-dependent due to the nuclear spin diffusion and relaxation processes. It can be well-approximated by a Gaussian curve which is not an exactly solvable potential. We demonstrate that it can also be approximated by multisoliton potentials for the zero value of the angular momentum and by their singular analogues for other values of momentum without any loss of calculational accuracy. We obtain these potentials by supersymmetric (or equivalently Darboux) transformations from the zero potential. The main advantage of such potentials is that they are exactly solvable. Time-dependence of the nuclear-spin-polarization-induced quantum dot energy levels is found.

cond-mat.mes-hall↗
arXiv2003

New exactly solvable periodic potentials for the Dirac equation

A new exactly solvable relativistic periodic potential is obtained by the periodic extension of a well-known transparent scalar potential. It is found that the energy band edges are determined by a transcendental equation which is very similar to the corresponding equation for the Dirac Kronig-Penney model. The solutions of the Dirac equation are expressed in terms of elementary functions.

quant-ph↗
arXiv2003

Supersymmetric manipulation of quasienergy states. Application to the Berry phase

Time-dependent supersymmetry allows one to delete quasienergy levels for time-periodic Hamiltonians and to create new ones. We illustrate this by examining an exactly solvable model related to the simple harmonic oscillator with a time-varying frequency. For an interesting nonharmonic example we present the change of the Berry phase due to a supersymmetry transformation.

quant-ph↗
arXiv2001

Darboux transformations and hidden quadratic supersymmetry of the one-dimensional stationary Dirac equation

A matricial Darboux operator intertwining two one-dimensional stationary Dirac Hamiltonians is constructed. This operator is such that the potential of the second Dirac Hamiltonian as well as the corresponding eigenfunctions are determined through the knowledge of only two eigenfunctions of the first Dirac Hamiltonian. Moreover this operator together with its adjoint and the two Hamiltonians generate a quadratic deformation of the superalgebra subtending the usual supersymmetric quantum mechanics. Our developments are illustrated on the free particle case and the generalized Coulomb interaction. In the latter case, a relativistic counterpart of shape-invariance is observed.

quant-ph↗
arXiv1998

Darboux transformation of coherent states

It is proved that the Darboux transformation of the system of coherent states of a free particle leads to the states that may be treated as coherent states of soliton-like potentials.

math-ph↗