arXiv subjects

Taksu Cheon

Publications and source records attributed to Taksu Cheon.

At least 55 records · Page 3Linked to original sources

arXiv2010

Fulop-Tsutsui interactions on quantum graphs

We examine scale invariant Fulop-Tsutsui couplings in a quantum vertex of a general degree $n$. We demonstrate that essentially same scattering amplitudes as for the free coupling can be achieved for two $(n-1)$-parameter Fulop-Tsutsui subfamilies if $n$ is odd, and for three $(n-1)$-parameter Fulop-Tsutsui subfamilies if $n$ is even. We also work up an approximation scheme for a general Fulop-Tsutsui vertex, using only $n$ $δ$ function potentials.

math-ph↗

arXiv2010

Short-range interaction in three-dimensional quantum mechanics

We show that it is possible to define shape-independent three-dimensional short-range quantum interactions in two parameter form for non-spherical angular momentum channels through double rescaling of potential strength. Unlike the special case of $l=0$, where the zero range limit of the system is renormalizable, the effective ranges diverge for $l /ne 0$ channels, and the system becomes trivial at zero-size limit. It is also shown that the two-parameter representation with finite interaction range is useful in analyzing phase shifts with accuracy and describing resonances in non-spherical scatterings.

quant-ph↗

arXiv2010

Quantum anholonomies in time-dependent Aharonov-Bohm rings

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, which is described by a non-Abelian connection in the adiabatic limit.

quant-ph↗

arXiv2009

Exotic quantum holonomy in Hamiltonian systems

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.

quant-ph↗

arXiv2009

Spectral filtering in quantum Y-junction

We examine scattering properties of singular vertex of degree $n=2$ and $n=3$, taking advantage of a new form of representing the vertex boundary condition, which has been devised to approximate a singular vertex with finite potentials. We show that proper identification of $δ$ and $δ'$ components in the connection condition between outgoing lines enables the designing of quantum spectral branch-filters.

quant-ph↗

arXiv2009

Approximation of a general singular vertex coupling in quantum graphs

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 $δ$ potential and a vector potential coupled to the "loose" edges by a $δ$ coupling. It is shown that if the lengths of the connecting edges shrink to zero and the potentials are properly scaled, the limit can yield any prescribed singular vertex coupling, and moreover, that such an approximation converges in the norm-resolvent sense.

quant-ph↗

arXiv2009

A Unified Theory of Quantum Holonomies

A periodic change of slow environmental parameters of a quantum system induces quantum holonomy. The phase holonomy is a well-known example. Another is a more exotic kind that exhibits eigenvalue and eigenspace holonomies. We introduce a theoretical formulation that describes the phase and eigenspace holonomies on an equal footing. The building block of the theory is a gauge connection for an ordered basis, which is conceptually distinct from Mead-Truhlar-Berry's connection and its Wilczek-Zee extension. A gauge invariant treatment of eigenspace holonomy based on Fujikawa's formalism is developed. Example of adiabatic quantum holonomy, including the exotic kind with spectral degeneracy, are shown.

quant-ph↗

arXiv2009

Exotic quantum holonomy induced by degeneracy hidden in complex parameter space

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 number, the correspondence of the exotic holonomies and the degeneracy of the non-Hermitian Hamiltonian, or the exceptional points, is revealed. We show that this explains all the known non-trivial characteristics of the exotic holonomies.

quant-ph↗

arXiv2008

New anatomy of quantum holonomy

We present a unified formulation of quantum holonomy which is capable of describing all of its known varieties. The full role of non-Abelian gauge connection is elucidated. As examples, solvable models of quantum kicked spin are analyzed. They are shown to exhibit spiral holonomy, as well as Berry phase and Wilczek-Zee holonomy.

quant-ph↗

arXiv2008

Probabilistic analysis of three-player symmetric quantum games played using the Einstein-Podolsky-Rosen-Bohm setting

This paper extends our probabilistic framework for two-player quantum games to the mutliplayer case, while giving a unified perspective for both classical and quantum games. Considering joint probabilities in the standard Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting for three observers, we use this setting in order to play general three-player non-cooperative symmetric games. We analyze how the peculiar non-factorizable joint probabilities provided by the EPR-Bohm setting can change the outcome of a game, while requiring that the quantum game attains a classical interpretation for factorizable joint probabilities. In this framework, our analysis of the three-player generalized Prisoner's Dilemma (PD) shows that the players can indeed escape from the classical outcome of the game, because of non-factorizable joint probabilities that the EPR setting can provide. This surprising result for three-player PD contrasts strikingly with our earlier result for two-player PD, played in the same framework, in which even non-factorizable joint probabilities do not result in escaping from the classical consequence of the game.

quant-ph↗

arXiv2007

Constructing multi-player quantum games from non-factorizable joint probabilities

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 the generalized three-player game of Prisoner's Dilemma (PD) and show that the players can indeed escape from the classical outcome of the game because of non-factorizable joint probabilities. This result for three-player PD contrasts strikingly with our earlier result for two-player PD for which even non-factorizable joint probabilities are not found to be helpful to escape from the classical outcome of the game.

quant-ph↗

arXiv2007

Anomalous Relativistic Tunneling and Exotic Point Interactions

We examine one-dimensional quantum scattering of a Dirac particle off relativistic potential barriers. With proper considerations of Dirac sea, existence of anomalous tunneling at zero incident-energy is revealed for a particular type of relativistic potential having same magnitudes and opposite signs for scalar and vector components. It is also shown that this leads to an exotic short range limit of the potentials.

quant-ph↗

arXiv2007

Bayesian Nash Equilibria and Bell Inequalities

Games with incomplete information are formulated in a multi-sector probability matrix formalism that can cope with quantum as well as classical strategies. An analysis of classical and quantum strategy in a multi-sector extension of the game of Battle of Sexes clarifies the two distinct roles of nonlocal strategies, and establish the direct link between the true quantum gain of game's payoff and the breaking of Bell inequalities.

quant-ph↗

arXiv2007

Constructing quantum games from non-factorizable joint probabilities

A probabilistic framework is developed that gives a unifying perspective on both the classical and the quantum games. We suggest exploiting peculiar probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to construct quantum games. In our framework a game attains classical interpretation when joint probabilities are factorizable and a quantum game corresponds when these probabilities cannot be factorized. We analyze how non-factorizability changes Nash equilibria in two-player games while considering the games of Prisoner's Dilemma, Stag Hunt, and Chicken. In this framework we find that for the game of Prisoner's Dilemma even non-factorizable EPR joint probabilities cannot be helpful to escape from the classical outcome of the game. For a particular version of the Chicken game, however, we find that the two non-factorizable sets of joint probabilities, that maximally violates the Clauser-Holt-Shimony-Horne (CHSH) sum of correlations, indeed result in new Nash equilibria.

quant-ph↗

arXiv2007

Comment on ``Quasienergy anholonomy and its application to adiabatic quantum state manipulation''

In their Letter [A. Tanaka and M. Miyamoto, Phys. Rev. Lett. 98, 160407 (2007)], Tanaka and Miyamoto introduce a kicked spin model, for which they point out the generic existence of exotic eigenvalue anholonomy. They proceed to show the potential utility of the model for quantum state manipulation and quantum information processing. While we believe their model to be vary useful and their argument to be revealing, In our view, there are three missing elements in the article, without which their discussion seems to be incomplete and the prospect of the application limited. They are on dynamical phase, gauge potential, and on adiabaticity.

quant-ph↗

arXiv2007

Evolutionary stability in quantum games

In evolutionary game theory an Evolutionarily Stable Strategy (ESS) is a refinement of the Nash equilibrium concept that is sometimes also recognized as evolutionary stability. It is a game-theoretic model, well known to mathematical biologists, that was found quite useful in the understanding of evolutionary dynamics of a population. This chapter presents an analysis of evolutionary stability in the emerging field of quantum games.

quant-ph↗

arXiv2006

Game Theory Formulated on Hilbert Space

We present a consistent formulation of quantum game theory that accommodates all possible strategies in Hilbert space. The physical content of the quantum strategy is revealed as a family of classical games representing altruistic game play supplemented by quantum interferences. Crucial role of the entanglement in quantum strategy is illustrated by an example of quantum game representing the Bell's experiment.

quant-ph↗

arXiv2006

Continuous Spectra of Generalized Kronig-Penney Model

The standard Kronig-Penney model with periodic $δ$ potentials is extended to the cases with generalized contact interactions. The eigen equation which determines the dispersion relation for one-dimensional periodic array of the generalized contact interactions is deduced with the transfer matrix formalism. Numerical results are presented which reveal unexpected band spectra with broader band gap in higher energy region for generic model with generalized contact interaction.

quant-ph↗