arXiv subjects

Daisuke Takahashi

Publications and source records attributed to Daisuke Takahashi.

26 records · Page 2Linked to original sources

arXiv2009

Exact Results for Tunneling Problems of Bogoliubov Excitations in the Critical Supercurrent State

We show the exact solution of Bogoliubov equations at zero-energy in the critical supercurrent state for arbitrary shape of potential barrier. With use of this solution, we prove the absence of perfect transmission of excitations in the low-energy limit by giving the explicit expression of transmission coefficient. The origin of disappearance of perfect transmission is the emergence of zero-energy density fluctuation near the potential barrier.

cond-mat.quant-gas↗

arXiv2009

Exact Solution of Bogoliubov Equations for Bosons in One-Dimensional Piecewise Constant Potential

We show that Bogoliubov equations in one-dimensional systems with piecewise constant potentials can be always solved. In particular, we analyze in detail the case where the condensate wavefunction is a real-valued function, and give the explicit expressions for wavefunctions of Bogoliubov excitations. By means of these solutions, we consider transmission and reflection properties of Bogoliubov excitations for two types of potential, namely, a rectangular barrier and a potential step. The results yield simple and exact examples of anomalous tunneling effect and quantum evaporation.

cond-mat.quant-gas↗

arXiv2009

Absence of Anomalous Tunneling of Bogoliubov Excitations for Arbitrary Potential Barrier under the Critical Condensate Current

We derive the exact solution of low energy limit of Bogoliubov equations for excitations of Bose-Einstein condensate in the presence of arbitrary potential barrier and maximum current of condensate. Using this solution, we give the explicit expression for the transmission coefficient against the potential barrier, which shows partial transmission in the low energy limit. The wavefunctions of excitations in the low energy limit do not coincide with that of the condensate. The absence of the perfect transmission in the critical current state originates from local enhancement of density fluctuations around the potential barrier.

cond-mat.other↗

arXiv2008

On a discrete optimal velocity model and its continuous and ultradiscrete relatives

We propose a discrete traffic flow model with discrete time. Continuum limit of this model is equivalent to the optimal velocity model. It has also an ultradiscrete limit and a piecewise-linear type of traffic flow model is obtained. Both models show phase transition from free flow to jam in a fundamental diagram. Moreover, the ultradiscrete model includes the Fukui-Ishibashi model in a special case.

nlin.AO↗

arXiv2006

Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings

We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-Roberts-Thompson (QRT) mapping, and a discrete Lyapunov function of the mappings is identical to an explicit conserved quantity of the QRT mapping. Moreover we can obtain a differential and an ultradiscrete limit of the mappings preserving the existence of Lyapunov function. We also give applications of a mapping with an adjusted parameter, a probabilistic mapping and coupled mappings.

nlin.SI↗

arXiv2005

Third-order integrable difference equations generated by a pair of second-order equations

We show that the third-order difference equations proposed by Hirota, Kimura and Yahagi are generated by a pair of second-order difference equations. In some cases, the pair of the second-order equations are equivalent to the Quispel-Robert-Thomson(QRT) system, but in the other cases, they are irrelevant to the QRT system. We also discuss an ultradiscretization of the equations.

nlin.SI↗

arXiv2000

A family of multi-value cellular automaton model for traffic flow

A family of multi-value cellular automaton (CA) associated with traffic flow is presented in this paper. The family is obtained by extending the rule-184 CA, which is an ultradiscrete analogue to the Burgers equation. CA models in the family show both metastable states and stop-and-go waves, which are often observed in real traffic flow. Metastable states in the models exist not only on a prominent part of a free phase but also in a congested phase.

nlin.AO↗

arXiv1999

On integrability test for ultradiscrete equations

We consider an integrability test for ultradiscrete equations based on the singularity confinement analysis for discrete equations. We show how singularity pattern of the test is transformed into that of ultradiscrete equation. The ultradiscrete solution pattern can be interpreted as a perturbed solution. We can also check an integrability of a given equation by a perturbation growth of a solution, namely Lyapunov exponent. Therefore, singularity confinement test and Lyapunov exponent are related each other in ultradiscrete equations and we propose an integrability test from this point of view.

solv-int↗