arXiv subjects

Fumihiko Nakamura

Publications and source records attributed to Fumihiko Nakamura.

At least 19 recordsLinked to original sources

arXiv2026

Longest increasing subsequences of dyadic-type chaotic orbits

This paper studies the longest increasing subsequence (LIS) problem for sequences generated by dyadic-type chaotic interval maps. Starting from a single point $x\in[0,1)$ chosen uniformly at random, we form the order pattern of the first $N$ points of its orbit, with the doubling map as the basic model. Let $λ_1^{(N)}$ be the LIS length, equivalently the length of the first row of the Young diagram obtained by Schensted's insertion. We show that $\mathbb E[λ_1^{(N)}]/\sqrt N\to 2$, matching the leading asymptotics in the classical Ulam--Hammersley problem for uniform random permutations.

math.DS↗

arXiv2025

Finitude of physical measures for Markovian random maps

We study the finiteness of physical measures for skew-product transformations $F$ associated with discrete-time random dynamical systems driven by ergodic Markov chains. We develop a framework, using an independent and identically distributed (i.i.d.) representation of the Markov process, that facilitates transferring results from the well-studied Bernoulli (i.i.d.) setting to the Markovian context. Specifically, we establish conditions for the existence of finitely many ergodic, $F$-invariant measures, absolutely continuous with respect to a reference measure, such that their statistical basins of attraction for measurable bounded observables cover the phase space almost everywhere. Furthermore, we investigate a weaker notion, which demands finitely many physical measures (not necessarily absolutely continuous) whose weak$^*$ basins of attraction cover the phase space almost everywhere. We show that for random maps on compact metric spaces driven by Markov chains on finite state spaces, this property holds if the system is mostly contracting, i.e., if all the Markovian invariant measures have negative maximal Lyapunov exponents. This result is applied to random $C^1$ diffeomorphisms of the circle and the interval under conditions based on the absence of invariant probability measures or finite invariant sets, respectively. We also connect our result to the quasi-compactness of the Koopman operator on the space of Hölder continuous functions.

math.DS↗

arXiv2025

Metallisation of the Mott Insulator Ca$_{2}$RuO$_{4}$ using Electric Double-Layer Gating

To verify whether the Mott insulator Ca2RuO4 can be switched by applying electric-field alone, regardless of current flow, we employ metallisation using electric double-layer gating (EDLG). The resistance change due to EDLG occurs only when positive gate-voltage above +3 V is applied. The amplitude of the reduction, reaching ~97% of the initial value, is difficult to interpret as surface metallisation and is likely related to structural change in bulk.

cond-mat.str-el↗

arXiv2024

Finitude of physical measures for random maps

For random compositions of independent and identically distributed measurable maps on a Polish space, we study the existence and finitude of absolutely continuous ergodic stationary probability measures (which are, in particular, physical measures) whose basins of attraction cover the whole space almost everywhere. We characterize and hierarchize such random maps in terms of their associated Markov operators, as well as show the difference between classes in the hierarchy by plenty of examples, including additive noise, multiplicative noise, and iterated function systems. We also provide sufficient practical conditions for a random map to belong to these classes. For instance, we establish that any continuous random map on a compact Riemannian manifold with absolutely continuous transition probability has finitely many physical measures whose basins of attraction cover Lebesgue almost all the manifold.

math.DS↗

arXiv2024

Challenges in extracting nonlinear current-induced phenomena in Ca2RuO4

An appealing direction to change the properties of strongly correlated materials is to induce nonequilibrium steady states by the application of a direct current. While access to these novel states is of high scientific interest, Joule heating due to current flow often constitutes a hurdle to identify nonthermal effects. The biggest challenge usually resides in measuring accurately the temperature of a sample subjected to direct current, and to use probes that give direct information of the material. In this work, we exploit the simultaneous measurement of electrical transport and magnetisation to probe non-equilibrium steady states in Ca2RuO4. In order to reveal non-thermal current-induced effects, we employ a simple model of Joule self-heating to remove the effects of heating and discuss the importance of temperature inhomogeneity within the sample. Our approach provides a solid basis for investigating current-induced phenomena in highly resistive materials.

cond-mat.str-el↗

arXiv2023

Unique Itinerant Ferromagnetism in 4d-electron System Ca2RuO4

We have studied the magnetic properties of pressure-induced ferromagnet Ca2RuO4 to reveal the uniqueness of the 4d-electron ferromagnetism in the quasi-two-dimensional conductor. The magnetic parameters have been estimated from the paramagnetic susceptibility and the magnetisation process under pressure up to 2 GPa. The parameters can well be interpreted on the basis of the self-consistent renormalization theory of spin fluctuation for 3D-itinerant ferromagnet. Nevertheless, the metallic Ca2RuO4 shows quite strong anisotropy not only in the conductivity but also in the magnetisation process. Such the strong anisotropy is rare for an itinerant ferromagnet and is a unique characteristic of the 4d electron system Ca2RuO4.

cond-mat.str-el↗

arXiv2023

Arcsine law for random dynamics with a core

In their recent paper [8], G.Hata and the fourth author first gave an example of random iterations of two piecewise linear interval maps without (deterministic) indifferent periodic points for which the arcsine law -- a characterization of intermittent dynamics in infinite ergodic theory -- holds. The key in the proof of the result is the existence of a Markov partition preserved by each interval maps. In the present paper, we give a class of random iterations of two interval maps without indifferent periodic points but satisfying the arcsine law, by introducing a concept of core random dynamics. As applications, we show that the generalized arcsine law holds for generalized Hata-Yano maps and piecewise linear versions of Gharaei-Homburg maps, both of which do not have a Markov partition in general.

math.DS↗

arXiv2022

Random invariant densities for Markov operator cocycles and random mean ergodic theorem

In the present paper, we consider random invariant densities and the mean ergodic theorem for Markov operator cocycles which are applicable to quenched type random dynamical systems. We give necessary and sufficient conditions for the existence of random invariant densities for Markov operator cocycles and establish the mean ergodic theorem for generalized linear operator cocycles over a weakly sequentially complete Banach space. The advantage of the result is that we show the implication of weak precompactness for almost every environment to strong convergence in the global sense.

math.DS↗

arXiv2022

Keldysh space control of charge dynamics in a strongly driven Mott insulator

The fate of a Mott insulator under strong low frequency optical driving conditions is a fundamental problem in quantum many-body dynamics. Using ultrafast broadband optical spectroscopy, we measured the transient electronic structure and charge dynamics of an off-resonantly pumped Mott insulator Ca$_2$RuO$_4$. We observe coherent bandwidth renormalization and nonlinear doublon-holon pair production occurring in rapid succession within a sub-100 femtosecond pump pulse duration. By sweeping the electric field amplitude, we demonstrate continuous bandwidth tuning and a Keldysh cross-over from a multi-photon absorption to quantum tunneling dominated pair production regime. Our results provide a procedure to control coherent and nonlinear heating processes in Mott insulators, facilitating the discovery of novel out-of-equilibrium phenomena in strongly correlated systems.

cond-mat.str-el↗

arXiv2022

Lyapunov exponents for random maps

It has been recently realized that for abundant dynamical systems on a compact manifold, the set of points for which Lyapunov exponents fail to exist, called the Lyapunov irregular set, has positive Lebesgue measure. In the present paper, we show that under any physical noise, the Lyapunov irregular set has zero Lebesgue measure and the number of such Lyapunov exponents is finite. This result is a Lyapunov exponent version of Araújo's theorem on the existence and finitude of time averages. Furthermore, we numerically compute the Lyapunov exponents for a surface flow with an attracting heteroclinic connection, which enjoys the Lyapunov irregular set of positive Lebesgue measure, under a physical noise. This paper also contains the proof of the disappearance of Lyapunov irregular behavior on a positive Lebesgue measure set for a surface flow with an attracting homoclinic/heteroclinic connection under a non-physical noise.

math.DS↗

arXiv2021

Mixing and observation for Markov operator cocycles

We consider generalized definitions of mixing and exactness for random dynamical systems in terms of Markov operator cocycles. We first give six fundamental definitions of mixing for Markov operator cocycles in view of observations of the randomness in environments, and show that they can be reduced into two different groups. Secondly, we give the definition of exactness for Markov operator cocycles and show that Lin's criterion for exactness can be naturally extended to the case of Markov operator cocycles. Finally, in the class of asymptotically periodic Markov operator cocycles, we show the Lasota-Mackey type equivalence between mixing, exactness and asymptotic stability.

math.DS↗

arXiv2021

Asymptotic (statistical) periodicity in two-dimensional maps

In this paper we give a new sufficient condition for asymptotic periodicity of Frobenius-Perron operator corresponding to two--dimensional maps. The result of the asymptotic periodicity for strictly expanding systems, that is, all eigenvalues of the system are greater than one, in a high-dimensional dynamical systems was already known. Our new theorem enables to apply for the system having an eigenvalue smaller than one. The key idea for the proof is a function of bounded variation defined by line integration. Finally, we introduce a new two-dimensional dynamical system exhibiting the asymptotic periodicity with different periods depending on parameter values, and discuss to apply our theorem to the model.

math.DS↗

arXiv2021

Emergence of low-energy electronic states in oxygen-controlled Mott insulator Ca$_{2}$RuO$_{4+δ}$

Insulator-to-metal transition in Ca$_{2}$RuO$_{4}$ has drawn keen attention because of its sensitivity to various stimulation and its potential controllability. Here, we report a direct observation of Fermi surface, which emerges upon introducing excess oxygen into an insulating Ca$_{2}$RuO$_{4}$, by using angle-resolved photoemission spectroscopy. Comparison between energy distribution curves shows that the Mott insulating gap is closed by eV-scale spectral-weight transfer with excess oxygen. Momentum-space mapping exhibits two square-shaped sheets of the Fermi surface. One is a hole-like $α$ sheet around the corner of a tetragonal Brillouin zone, and the other is an electron-like $β$ sheet around the $Γ$ point. The electron occupancies of the $α$ and $β$ bands are determined to be $n_α=1.6$ and $n_β=0.6$, respectively. Our result indicates that the insulator-to-metal transition occurs selectively in $d_{xz}$ and $d_{yz}$ bands and not yet in $d_{xy}$ band. This orbital selectivity is most likely explained in terms of the energy level of $d_{xy}$, which is deeper for Ca$_{2}$RuO$_{4+δ}$ than for Ca$_{1.8}$Sr$_{0.2}$RuO$_{4}$. Consequently, we found substantial differences from the Fermi surface of other ruthenates, shedding light on a unique role of excess oxygen among the metallization methods of Ca$_{2}$RuO$_{4}$.

cond-mat.str-el↗

arXiv2020

Role of local temperature in the current-driven metal-insulator transition of Ca2RuO4

It was recently reported that a continuous electric current is a powerful control parameter to trigger changes in the electronic structure and metal-insulator transitions (MITs) in Ca2RuO4. However, the spatial evolution of the MIT and the implications of the unavoidable Joule heating have not been clarified yet, often hindered by the difficulty to asses the local sample temperature. In this work, we perform infrared thermal imaging on single-crystal Ca2RuO4 while controlling the MIT by electric current. The change in emissivity at the phase transition allows us to monitor the gradual formation and expansion of metallic phase upon increasing current. Our local temperature measurements indicate that, within our experimental resolution, the MIT always occurs at the same local transition temperatures, irrespectively if driven by temperature or by current. Our results highlight the importance of local heating, phase coexistence, and microscale inhomogeneity when studying strongly correlated materials under the flow of electric current.

cond-mat.mtrl-sci↗

arXiv2020

Periodic structures for nonlinear piecewise contracting maps

In this paper, we first show that any nonlinear monotonic increasing contracting maps with one discontinuous point on a unit interval which has an unique periodic point with period $n$ conjugates to a piecewise linear contracting map which has periodic point with same period. Second, we consider one parameter family of monotonic increasing contracting maps, and show that the family has the periodic structure called Arnold tongue for the parameter which is associated with the Farey series. This implies that there exist a parameter set with a positive Lebesgue measure such that the map has a periodic point with an arbitrary period. Moreover, the parameter set with period $(m+n)$ exists between the parameter set with period $m$ and $n$.

math.DS↗

arXiv2020

Asymptotically stable control problems by infinite horizon optimal control with negative discounting

In the paper, for the system which possesses both an attractor and a stable fixed point, we first formulate new stable control problems to find the asymptotically stable control function which realizes to transit a state moving around the attractor to the stable fixed point. Then by using the ordinary differential equation based on the infinite horizon optimal control model with negative discounts, we give one of answers for the stable control problem in a two-dimensional case. Furthermore, under some conditions, we verify that the phase space can be separated to some open connected components depending on the asymptotic behavior of the orbit starting from the initial point in their components. This classification of initial points suggests that it is enable to robustly achieve a stable control. Moreover, we illustrate some numerical results for the stable control obtained by applying our focused system for the Bonhoeffer-van der Pol model.

math.OC↗

arXiv2017

Anomalous Thermoelectric Response in an Orbital-Ordered Oxide Near and Far from Equilibrium

We report the thermoelectric transport properties in the orbital-ordered Mott insulating phase of Ca$_2$RuO$_4$ close to and far from equilibrium. Near equilibrium conditions where the temperature gradient is only applied to the sample, an insulating but non-monotonic temperature variation of the Seebeck coefficient is observed, which is accounted for in terms of a temperature-induced suppression of the orbital order. In non-equilibrium conditions where we have applied high electrical currents, we find that the Seebeck coefficient is anomalously increased in magnitude with increasing external current. The present result clearly demonstrates a non-thermal effect since the heating simply causes a decrease of the Seebeck coefficient, implying a non-trivial non-equilibrium effect such as a modification of the spin and orbital state in currents.

cond-mat.str-el↗

arXiv2016

Current-induced giant diamagnetism in the Mott insulator Ca2RuO4

Mott insulators have surprised us many times by hosting new and diverse quantum phenomena when the frozen electrons are perturbed by various stimuli. Superconductivity, metal-insulator transition, and colossal magnetoresistance induced by element substitution, pressure, and magnetic field are prominent examples. Here we report a novel phenomenon, namely giant diamagnetism, in the Mott insulator Ca2RuO4 induced by electric current. With application of 1 A/cm2 current, the strongest diamagnetism among all nonsuperconducting materials is induced as the system is tuned to a semimetallic state. The origin lies in the emergence of indirect Dirac cones in the many-body spectrum and associated monopole-like anomaly in the momentum dependent susceptibility. This record-breaking and switchable diamagnetism is a new class of non-equilibrium quantum phenomena on the verge of Mott insulating states.

cond-mat.str-el↗