We examine scale invariant Fulop-Tsutsui couplings in a quantum vertex of a general degree . A particular attention is paid to the free coupling. We consider the free coupling in a vertex of degree and determine its scattering amplitudes. We demonstrate that essentially same scattering amplitudes as for the free coupling can be achieved for two -parameter Fulop-Tsutsui subfami...
Anholonomies in eigenstates are studied through time-dependent variations of a magnetic flux in an Aharonov-Bohm ring. The anholonomies in the eigenenergy and the expectation values of eigenstates are shown to persist beyond the adiabatic regime. The choice of the gauge of the magnetic flux is shown to be crucial to clarify the relationship of these anholonomies to the eigenspace anholonomy, wh...
An adiabatic change of a bound state along a closed circuit in the parameter space can induces holonomies not only in the phase of the state, but also in the associated eigenspace and eigenvalue. The former is the well-known Berry phase while the latter, namely the exotic holonomy, is found a decade ago and its origin has not been understood yet. By extending the parameter into the complex numb...
The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a potential and a vector potential coupled to the "loose" edges by a coupling. It is shown that if the lengths of the connecting edges shrin...
We study the evolution of quantum eigenstates in the presence of level crossing under adiabatic cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic evolution, can arise from non-Abelian gauge potentials among non-degenerate levels. We illustrate our arguments with solvable two and three level models.
We use the standard three-party Einstein-Podolsky-Rosen (EPR) setting in order to play general three-player non-cooperative symmetric games. We analyze how the peculiar non-factorizable joint probabilities that may emerge in the EPR setting can change outcome of the game. Our setup requires that the quantum game attains classical interpretation for factorizable joint probabilities. We analyze t...
This electronic lecture covers the theory of "quantum graph", which is one of the main subject under current research at the Mathematical Engineering Laboratory/ Theoretical Physics Group at Kochi University of Technology. The lecture is based on various review articles by the author which have appeared on Scientific journals in Japanese. The original audience of this web lecture was...
This electronic lecture note on the cellular automaton models of traffic flow is an outgrowth of the materials pepared for the seminars and study meetings of the Mathematical Engineering Laboratory (aka, Theoretical Physics Group) at the Graduate School of Kochi University of Technology. It has been made accessible to KUT students who might be interested in joining us. Now it is open to gener...
