Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1206.5890 · Nanosystems Physics Chemistry Mathematics

Time-dependent quantum graph

Davron U. Matrasulov, Jambul Yusupov, K.K. Sabirov, Zarifboy A. Sobirov

Published Apr 16, 2015• 18 citations
arXivHTMLPDF

Abstract

In this paper, we study quantum star graphs with time-dependent bond lengths.Quantum dynamics are treated by solving Schrodinger equation with time-dependent boundary conditions given on graphs.The time-dependence of the average kinetic energy is analyzed.The space-time evolution of a Gaussian wave packet is treated for an harmonically breathing star graph.

DOI
10.17586/2220-8054-2015-6-2-173-181

Related papers

Kicked particle dynamics in quantum graphs

Jambul Yusupov, Valijon Eshniyozov, O. Karpova +1 more

The quantum dynamics of a delta-kicked driven particle in a star-shaped network is studied by obtaining an exact solution for the time-dependent Schrödinger equation within a single kicking period.The timedependence of the average kinetic energy and the Gaussian wave packet evolution are analyzed.

Nanosystems Physics Chemistry Mathematics•Dec 21, 2015•1 citation

Time evolution and the Schrödinger equation on time dependent quantum graphs *

Uzy Smilansky, Gilad Sofer

Abstract The purpose of the present paper is to discuss the time dependent Schrödinger equation on a metric graph with time-dependent edge lengths, and the proper way to pose the problem so that the corresponding time evolution is unitary. We show that the well posedness of the Schrödinger equation can be guaranteed by replacing the standard Kirchhoff Laplacian with a magnetic Schrödinger operator with a harmonic potential. We then generalize the result to time dependent families of vertex conditions. We also apply the theory to show the existence of a geometric phase associated with a slowly changing quantum graph.

arXiv:2210.14652•Journal of Physics A Mathematical and Theoretical•Jan 17, 2024•1 citation

Particle transport in a network of quantum harmonic oscillators

Jambul Yusupov, Kh. Sh. Matyokubov, K.K. Sabirov

In this paper, we address the problem of a particle dynamics in a network of quantum harmonic oscillators by solving the stationary Schrödinger equation on metric graphs in the presence of harmonic oscillator potential with bond-dependent frequency.Particle transport is analyzed by considering wave packet dynamics in such a system modeled in terms of quantum graph.

Nanosystems Physics Chemistry Mathematics•Apr 25, 2020•3 citations

Time dependent quantum graph with loop

Еремин Дмитрий Александрович, E.N. Grishanov, O. G. Kostrov +2 more

A quantum graph, consisting of a ring and segment is considered.We deal with the free Schrödinger ooperator at the edges and Kirchhoff conditions at the internal vertex.The lengths of the graph edges varies in time.Time evolution of wave packet is studied for different parameters of length varying law.

Nanosystems Physics Chemistry Mathematics•Aug 25, 2017•4 citations

Time-dependent metric graph: Wave dynamics

Антон Юрьевич Попов, I. Yu. Popov, D S Nikiforov +1 more

We consider a metric graph under the assumption that lengths of its edges vary in time. The dynamics of waves of different nature on the graph is compared. We investigate classical waves governed by wave equation, non-relativistic quantum (Schrödinger) particles and relativistic (Dirac) particles. Star like graph and graph with a loop are considered.

AIP conference proceedings•Jan 1, 2019•1 citation

Quantum Dynamics

Uri Peskin

Explicitly time-dependent Hamiltonians are ubiquitous in applications of quantum theory. It is therefore necessary to solve the time-dependent Schrödinger equation directly. The system’s dynamics is associated with a unitary time-evolution operator (a propagator), formally given as an infinite Dyson series. Time-dependent observables are invariant under unitary time-dependent transformations, where it is sometimes useful to transform the time-evolution from the states into the corresponding operators. This is carried out in part (in full) by transforming to the interaction (Heisenberg) picture. The corresponding equations of motion for the time-dependent operators are introduced. For quadratic potential energy functions, the time evolution of quantum expectation values coincides with the corresponding classical dynamics. This is demonstrated and analyzed in detail for Gaussian wave packets and a coherent state. Finally, we derive exact and approximate expressions for time-dependent transition probabilities and transition rates between quantum states. The validity of time-dependent perturbation theory is analyzed by comparison to exact dynamics.

Cambridge University Press eBooks•May 11, 2023•0 citations
In this paper, we study quantum star graphs with time-dependent bond lengths.Quantum dynamics are treated by solving Schrodinger equation with time-dependent boundary conditions given on graphs.The time-dependence of the average kinetic energy is analyzed.The space-time evolution of a Gaussian wave packet is treated for an harmonically breathing star graph.
Abstract The purpose of the present paper is to discuss the time dependent Schrödinger equation on a metric graph with time-dependent edge lengths, and the proper way to pose the problem so that the corresponding time evolution is unitary. We show that the well posedness of the Schrödinger equation can be guaranteed by replacing the standard Kirchhoff Laplacian with a magnetic Schrödinger operator with a harmonic potential. We then generalize the result to time dependent families of vertex conditions. We also apply the theory to show the existence of a geometric phase associated with a slowly changing quantum graph.
Explicitly time-dependent Hamiltonians are ubiquitous in applications of quantum theory. It is therefore necessary to solve the time-dependent Schrödinger equation directly. The system’s dynamics is associated with a unitary time-evolution operator (a propagator), formally given as an infinite Dyson series. Time-dependent observables are invariant under unitary time-dependent transformations, where it is sometimes useful to transform the time-evolution from the states into the corresponding operators. This is carried out in part (in full) by transforming to the interaction (Heisenberg) picture. The corresponding equations of motion for the time-dependent operators are introduced. For quadratic potential energy functions, the time evolution of quantum expectation values coincides with the corresponding classical dynamics. This is demonstrated and analyzed in detail for Gaussian wave packets and a coherent state. Finally, we derive exact and approximate expressions for time-dependent transition probabilities and transition rates between quantum states. The validity of time-dependent perturbation theory is analyzed by comparison to exact dynamics.