arXiv subjects

Koji Kobayashi

Publications and source records attributed to Koji Kobayashi.

33 records · Page 2Linked to original sources

arXiv2015

Modification and Control of Topological Insulator Surface States Using Surface Disorder

We numerically demonstrate a practical means of systematically controlling topological transport on the surface of a three dimensional topological insulator, by introducing strong disorder in a layer of depth $d$ extending inward from the surface of the topological insulator. The dependence on $d$ of the density of states, conductance, scattering time, scattering length, diffusion constant, and mean Fermi velocity are investigated. The proposed control via disorder depth $d$ requires that the disorder strength be near the large value which is necessary to drive the TI into the non-topological phase. If $d$ is patterned using masks, gates, ion implantation, etc., then integrated circuits may be fabricated. This technique will be useful for experiments and for device engineering.

cond-mat.mes-hall↗

arXiv2015

Finite and infinite basis in P and NP

This article provide new approach to solve P vs NP problem by using cardinality of bases function. About NP-Complete problems, we can divide to infinite disjunction of P-Complete problems. These P-Complete problems are independent of each other in disjunction. That is, NP-Complete problem is in infinite dimension function space that bases are P-Complete. The other hand, any P-Complete problem have at most a finite number of P-Complete basis. The reason is that each P problems have at most finite number of Least fixed point operator. Therefore, we cannot describe NP-Complete problems in P. We can also prove this result from incompleteness of P.

cs.CC↗

arXiv2015

The interacting generalized Ricci dark energy model in non-flat universe

We extend our previous analysis and consider the interacting holographic Ricci dark energy (IRDE) model in non-flat universe. We study astrophysical constraints on this model using the recent observations including the type Ia supernovae (SNIa), the baryon acoustic oscillation (BAO), the cosmic microwave background (CMB) anisotropy, and the Hubble parameter. It is shown that the allowed parameter range for the fractional energy density of the curvature is $-0.005$ $\lesssim$ $Ω_{k0}$ $\lesssim$ $0.015$ in the presence of the interactions between dark energy and matter. Without the interaction, the flat universe is observationally disfavored in this model.

astro-ph.CO↗

arXiv2014

Engineering Dirac electrons emergent on the surface of a topological insulator

The concept of topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin-orbit coupled materials, some classes of nodal superconductors and superfluid $^3$He, etc. From a technological point of view, topological insulator is expected to serve as a platform for realizing dissipationless transport in a non-superconducting context. The topological insulator exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context contrast the cases of weak and strong TIs. We study robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new perspective of research in the field.

cond-mat.mes-hall↗

arXiv2014

Small Jump with Negation-UTM Trampoline

This paper divide some complexity class by using fixpoint and fixpointless area of Decidable Universal Turing Machine (UTM). Decidable Deterministic Turing Machine (DTM) have fixpointless combinator that add no extra resources (like Negation), but UTM makes some fixpoint in the combinator. This means that we can jump out of the fixpointless combinator system by making more complex problem from diagonalisation argument of UTM. As a concrete example, we proof L is not P . We can make Polynomial time UTM that emulate all Logarithm space DTM (LDTM). LDTM set close under Negation, therefore UTM does not close under LDTM set. (We can proof this theorem like halting problem and time/space hierarchy theorem, and also we can extend this proof to divide time/space limited DTM set.) In the same way, we proof P is not NP. These are new hierarchy that use UTM and Negation.

cs.CC↗

arXiv2013

Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators

The quantum phase transition between the three dimensional Dirac semimetal and the diffusive metal can be induced by increasing disorder. Taking the system of disordered $\mathbb{Z}_2$ topological insulator as an important example, we compute the single particle density of states by the kernel polynomial method. We focus on three regions: the Dirac semimetal at the phase boundary between two topologically distinct phases, the tricritical point of the two topological insulator phases and the diffusive metal, and the diffusive metal lying at strong disorder. The density of states obeys a novel single parameter scaling, collapsing onto two branches of a universal scaling function, which correspond to the Dirac semimetal and the diffusive metal. The diverging length scale critical exponent $ν$ and the dynamical critical exponent $z$ are estimated, and found to differ significantly from those for the conventional Anderson transition. Critical behavior of experimentally observable quantities near and at the tricritical point is also discussed.

cond-mat.mes-hall↗

arXiv2013

Disordered weak and strong topological insulators

A global phase diagram of disordered weak and strong topological insulators is established numerically. As expected, the location of the phase boundaries is renormalized by disorder, a feature recognized in the study of the so-called topological Anderson insulator. Here, we report unexpected quantization, i.e., robustness against disorder of the conductance peaks on these phase boundaries. Another highlight of the work is on the emergence of two subregions in the weak topological insulator phase under disorder. According to the size dependence of the conductance, the surface states are either robust or "defeated" in the two subregions. The nature of the two distinct types of behavior is further revealed by studying the Lyapunov exponents.

cond-mat.mes-hall↗

arXiv2013

Resolution structure in HornSAT and CNFSAT

This article describes about the difference of resolution structure and size between HornSAT and CNFSAT. We can compute HornSAT by using clauses causality. Therefore we can compute proof diagram by using Log space reduction. But we must compute CNFSAT by using clauses correlation. Therefore we cannot compute proof diagram by using Log space reduction, and reduction of CNFSAT is not P-Complete.

cs.CC↗

arXiv2012

Solvability of HornSAT and CNFSAT

This article describes the solvability of HornSAT and CNFSAT. Unsatisfiable HornCNF have partially ordered set that is made by causation of each clauses. In this partially ordered set, Truth value assignment that is false in each clauses become simply connected space. Therefore, if we reduce CNFSAT to HornSAT, we must make such partially ordered set in HornSAT. But CNFSAT have correlations of each clauses, the partially ordered set is not in polynomial size. Therefore, we cannot reduce CNFSAT to HornSAT in polynomial size.

cs.CC↗

arXiv2012

Topological approach to solve P versus NP

This paper talks about difference between P and NP by using topological space that mean resolution principle. I pay attention to restrictions of antecedent and consequent in resolution, and show what kind of influence the restrictions have for difference of structure between P and NP regarding relations of relation. First, I show the restrictions of antecedent and consequent in resolution principle. Antecedents connect each other, and consequent become a linkage between these antecedents. And we can make consequent as antecedents product by using some resolutions which have same joint variable. We can determine these consequents reducible and irreducible. Second, I introduce RCNF that mean topology of resolution principle in CNF. RCNF is HornCNF and that variable values are presence of restrictions of CNF formula clauses. RCNF is P-Complete. Last, I introduce TCNF that have 3CNF's character which relate 2 variables relations with 1 variable. I show CNF complexity by using CCNF that combine some TCNF. TCNF is NP-Complete and product irreducible. I introduce CCNF that connect TCNF like Moore graph. We cannot reduce CCNF to RCNF with polynomial size. Therefore, TCNF is not in P.

cs.CC↗

arXiv2011

NP is not AL and P is not NC is not NL is not L

This paper talk about that NP is not AL and P, P is not NC, NC is not NL, and NL is not L. The point about this paper is the depend relation of the problem that need other problem's result to compute it. I show the structure of depend relation that could divide each complexity classes.

cs.CC↗

arXiv2011

Connection and Dispersion of Computation

This paper talk about the influence of Connection and Dispersion on Computational Complexity. And talk about the HornCNF's connection and CNF's dispersion, and show the difference between CNFSAT and HornSAT. First, I talk the relation between MUC decision problem and classifying the truth value assignment. Second, I define the two inner products ("inner product" and "inner harmony") and talk about the influence of orthogonal and correlation to MUC. And we can not reduce MUC to Orthogonalization MUC by using HornMUC in polynomial size because HornMUC have high orthogonal of inner harmony and MUC do not. So DP is not P, and NP is not P.

cs.LO↗

arXiv2010

Symmetry and Uncountability of Computation

This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named "testing problem". And I get some condition of the P complete and NP complete by using testing problem. Second, I make two problem "orderly problem" and "chaotic problem". Orderly problem have some order structure. And DTM can limit some possible symbol effectly by using symmetry of each symbol. But chaotic problem must treat some symbol as a set of symbol, so DTM cannot limit some possible symbol. Orderly problem is P complete, and chaotic problem is NP complete. Finally, I clear the computation time of orderly problem and chaotic problem. And P != NP.

cs.CC↗

arXiv2009

Point-Contact Conductance in Asymmetric Chalker-Coddington Network Model

We study the transport properties of disordered two-dimensional electron systems with a perfectly conducting channel. We introduce an asymmetric Chalker-Coddington network model and numerically investigate the point-contact conductance. We find that the behavior of the conductance in this model is completely different from that in the symmetric model. Even in the limit of a large distance between the contacts, we find a broad distribution of conductance and a non-trivial power law dependence of the averaged conductance on the system width. Our results are applicable to systems such as zigzag graphene nano-ribbons where the numbers of left-going and right-going channels are different.

cond-mat.mes-hall↗

arXiv2008

Transport properties in network models with perfectly conducting channels

We study the transport properties of disordered electron systems that contain perfectly conducting channels. Two quantum network models that belong to different universality classes, unitary and symplectic, are simulated numerically. The perfectly conducting channel in the unitary class can be realized in zigzag graphene nano-ribbons and that in the symplectic class is known to appear in metallic carbon nanotubes. The existence of a perfectly conducting channel leads to novel conductance distribution functions and a shortening of the conductance decay length.

cond-mat.mes-hall↗