Schrödinger and Dirac dynamics on time-dependent quantum graph

Nikiforov, D S; Blinova, Irina V.; Popov, I. Yu.

doi:10.1007/s12648-018-1352-8

Cited by 7 publications

(5 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Taking into account the above theorem, we look for solution of Problem 1 in the following form (14) where:…”

Section: Green's Function Of Problemmentioning

confidence: 99%

“…Taking into account (14) and the conditions (2)-( 4) we get the following conditions for matrix-Green's function:…”

Section: Green's Function Of Problemmentioning

confidence: 99%

“…The Schrödinger equation on the metric graph are well studied (see [11][12][13] and references in them). In [14] the Schrödinger operator on the graph with varying edges was investigated. The Schrödinger equation on the metric graphs was also explored with Fokas unified transformation method in [15].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Green's function method for time-fractional diffusion equation on the star graph with equal bonds

Sobirov¹,

Rakhimov²,

Ergashov³

2021

Nanosystems: Phys. Chem. Math.

View full text Add to dashboard Cite

This work devoted to construction of the matrix-Green's functions of initial-boundary value problems for the time-fractional diffusion equation on the metric star graph with equal bonds. In the case of Dirichlet and mixed boundary conditions we constructed Green's functions explicitly. The uniqueness of the solutions of the considered problems were proved by the method of energy integrals. Some possible applications in branched nanostructures were discussed.

show abstract

“…Taking into account the above theorem, we look for solution of Problem 1 in the following form (14) where:…”

Section: Green's Function Of Problemmentioning

confidence: 99%

“…Taking into account (14) and the conditions (2)-( 4) we get the following conditions for matrix-Green's function:…”

Section: Green's Function Of Problemmentioning

confidence: 99%

See 1 more Smart Citation

Green's function method for time-fractional diffusion equation on the star graph with equal bonds

Sobirov¹,

Rakhimov²,

Ergashov³

2021

Nanosystems: Phys. Chem. Math.

View full text Add to dashboard Cite

show abstract

“…Extension of the dynamical confinement to relativistic case by considering Dirac equation for time-dependent box was done in [33]. Timedependent quantum graphs have been considered in the [34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Quantum particle under dynamical confinement: from quantum fermi acceleration to high harmonic generation

Rakhmanov,

Trunk,

Matrasulov

2024

Phys. Scr.

View full text Add to dashboard Cite

Quantum dynamics of a particle confined in a box with time-dependent wall is revisited by considering some unexplored aspects of the problem. In particular, the case of dynamical confinement in a time-dependent box in the presence of purely time-varying external potential is treated by obtaining exact solution. Also, some external potentials approving separation of space and time variables in the Schrödinger equation with time-dependent boundary conditions are classified. Time-dependence of the average kinetic energy and average quantum force are analyzed. A model for optical high harmonic generation in the presence of dynamical confinement and external monochromatic time-dependent homogeneous electric field is proposed.

show abstract

“…Recently, great attention has been devoted to time-depending metric graphs, i.e. graphs having characteristics (e.g., edge lengths) varying in time [9][10][11][12][13][14][15][16]. This problem is in relation to time-dependent boundary conditions and time dependent potentials [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A time-dependent metric graph with a fourth-order operator on the edges

Blinova

Gnedash

Popov

2021

Theor appl mech (Belgr)

View full text Add to dashboard Cite

The metric graph model is suggested for description of elastic vibration in a network of rods under the assumption that the rod lengths vary in time. A single rod and star-like graph are considered. Influence of the length variation law on the vibration distribution is investigated. For high-frequency length variation one observes a fast transition to high-frequency amplitude distribution

show abstract

Schrödinger and Dirac dynamics on time-dependent quantum graph

Cited by 7 publications

References 27 publications

Green's function method for time-fractional diffusion equation on the star graph with equal bonds

Green's function method for time-fractional diffusion equation on the star graph with equal bonds

Quantum particle under dynamical confinement: from quantum fermi acceleration to high harmonic generation

A time-dependent metric graph with a fourth-order operator on the edges

Contact Info

Product

Resources

About