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Takashi Kimura

Publications and source records attributed to Takashi Kimura.

At least 37 records · Page 2Linked to original sources
arXiv2013

Strong-coupling expansion for the spin-1 Bose-Hubbard model

In this study, we perform a strong-coupling expansion up to third order of the hopping parameter $t$ for the spin-1 Bose--Hubbard model with antiferromagnetic interaction. As expected from previous studies, the Mott insulator phase is considerably more stable against the superfluid phase when filling with an even number of bosons than when filling with an odd number of bosons. The phase-boundary curves are consistent with the perturbative mean-field theory in the limit of infinite dimensions. The critical value of the hopping parameter $t_{\rm C}$ at the peak of the Mott lobe depends on the antiferromagnetic interaction. This result indicates the reliability of the strong coupling expansion when $U_2$ possesses large (intermediate) values for Mott lobe with an even (odd) number of bosons. Moreover, in order to improve our results, we apply a few extrapolation methods up to infinite order in $t$. The fitting results of the phase-boundary curves agree better with those of the perturbative mean-field approximation. In addition, the linear fit error of $t_{\rm C}$ is very small for the strong antiferromagnetic interaction.

cond-mat.quant-gas↗
arXiv2013

First-order superfluid-Mott-insulator transition for quantum optical switching in cavity QED arrays with two cavity modes

We theoretically investigated the ground states of coupled arrays of cavity quantum electrodynamical (cavity QED) systems in presence of two photon modes. Within the Gutzwiller-type variational approach, we found the first-order quantum phase transition between Mott insulating and superfluid phases as well as the conventional second-order one. The first-order phase transition was found only for specific types of emitter models, and its physical origin is clarified based on the analytic arguments which are allowed in the perturbative and semiclassical limits. The first-order transition of the correlated photons is accompanied with discontinuous change in the emitter states, not only with the appearance of inter-cavity coherence in the superfluid phase. We also discuss the condition for the first-order transition to occur, which can lead to a strategy for future design of quantum optical switching devices with cavity QED arrays.

cond-mat.quant-gas↗
arXiv2013

Adams operations on the virtual K-theory of P(1,n)

We analyze the structure of the virtual (orbifold) K-theory ring of the complex orbifold P(1,n) and its virtual Adams (or power) operations, by using the non-Abelian localization theorem of Edidin-Graham. In particular, we identify the group of virtual line elements and obtain a natural presentation for the virtual K-theory ring in terms of these virtual line elements. This yields a surjective homomorphism from the virtual K-theory ring of P(1,n) to the ordinary K-theory ring of a crepant resolution of the cotangent bundle of P(1,n) which respects the Adams operations. Furthermore, there is a natural subring of the virtual K-theory ring of P(1,n) which is isomorphic to the ordinary K-theory ring of the resolution. This generalizes the results of Edidin-Jarvis-Kimura who proved the latter for n=2,3.

math.AG↗
arXiv2011

Gutzwiller study of extended Hubbard models with fixed boson densities

We studied all possible ground states, including supersolid (SS) phases and phase separations of hard-core- and soft-core-extended Bose--Hubbard models with fixed boson densities by using the Gutzwiller variational wave function and the linear programming method. We found that the phase diagram of the soft-core model depends strongly on its transfer integral. Furthermore, for a large transfer integral, we showed that an SS phase can be the ground state even below or at half filling against the phase separation. We also found that the density difference between nearest-neighbor sites, which indicates the density order of the SS phase, depends strongly on the boson density and transfer integral.

cond-mat.quant-gas↗
arXiv2011

Dynamics of coupled vortices in a pair of ferromagnetic disks

We here experimentally demonstrate that coupled gyration modes can be resonantly excited primarily by the ac current in a pair of ferromagnetic disks with varied separating distance. The sole gyrotropic mode clearly splits into a higher and a lower frequency modes for different configurations of polarities via dipolar interaction. These experimental results indicate that the magnetostatically coupled pair of vortices behaves similar to a diatomic molecule with bonding and anti-bonding states. These findings lead to the possible extension of designing the magnonic band structure in a chain or an array of vortices.

cond-mat.mes-hall↗
arXiv2009

A representation-valued relative Riemann-Hurwitz theorem and the Hurwitz-Hodge bundle

We provide a formula describing the G-module structure of the Hurwitz-Hodge bundle for admissible G-covers in terms of the Hodge bundle of the base curve, and more generally, for describing the G-module structure of the push-forward to the base of any sheaf on a family of admissible G-covers. This formula can be interpreted as a representation-ring-valued relative Riemann-Hurwitz formula for families of admissible G-covers.

math.AG↗
arXiv2009

Highly crystalline superconducting MgB2 nanowires formed by electrodeposition

Superconducting nanowires can be synthesised in high-throughput chemical routes and hold great promise as a low-dissipative material for superconducting devices. The applicability of superconducting nanowires, however, has been limited due to the lack of an adequate method to fit the nanowires into given electronic circuits. One of the biggest obstacles is to connect metal terminals to superconducting nanowires in order to establish electric contacts. One attractive method to surmount this difficulty is to synthesise superconducting nanowires directly upon metal terminals such that the nanowires electrically contact the metal surface. Here we demonstrate that this can be achieved by electrodeposition in molten salts. The 39-K superconductor magnesium diboride (MgB2) is electrodeposited to metal surfaces in the form of highly crystalline nanowires. The MgB2 nanowires achieve extensive electric contacts with the metal surfaces. The MgB2 nanowires carry high densities of supercurrents that are comparable to bulk materials. This approach to the electrodeposition of MgB2 nanowires provides a solution to one of the major challenges preventing practical applications of superconducting nanowires.

cond-mat.mtrl-sci↗
arXiv2009

Logarithmic trace and orbifold products

We give a purely equivariant construction of orbifold products for quotient Deligne-Mumford stacks [X/G] where G is an arbitrary linear algebraic group (not necessarily finite). The key to our construction is the definition of the "logarithmic trace" of an equivariant vector bundle. We also prove that there is an orbifold Chern character homomorphism which induces an isomorphism of a canonical summand in the orbifold Grothendieck ring with the orbifold Chow ring. As an application we obtain an associative orbifold product on the Grothendieck ring of [X/G] (as opposed to its inerita stack) taken with complex coefficients.

math.AG↗
arXiv2009

The Full Orbifold $K$-theory of Abelian Symplectic Quotients

In their 2007 paper, Jarvis, Kaufmann, and Kimura defined the full orbifold $K$-theory of an orbifold ${\mathfrak X}$, analogous to the Chen-Ruan orbifold cohomology of ${\mathfrak X}$ in that it uses the obstruction bundle as a quantum correction to the multiplicative structure. We give an explicit algorithm for the computation of this orbifold invariant in the case when ${\mathfrak X}$ arises as an abelian symplectic quotient. Our methods are integral $K$-theoretic analogues of those used in the orbifold cohomology case by Goldin, Holm, and Knutson in 2005. We rely on the $K$-theoretic Kirwan surjectivity methods developed by Harada and Landweber. As a worked class of examples, we compute the full orbifold $K$-theory of weighted projective spaces that occur as a symplectic quotient of a complex affine space by a circle. Our computations hold over the integers, and in the particular case of weighted projective spaces, we show that the associated invariant is torsion-free.

math.SG↗
arXiv2008

Tomonaga-Luttinger Liquid Renormalized by a Single Impurity

Effects of a single impurity potential on bulk properties of a spinful Tomonaga-Luttinger (TL) liquid is studied. A boundary bosonization technique is developed to include the impurity potential of {\it arbitrary} strength $V$. Our new bosonization formula for fermion field $ψ$ smoothly connects the two existing expressions in the strong ($V = \infty$) and the weak ($V = 0$) impurity limits. With use of the formula, we found the TL parameters determined from the long-distance correlation functions are renormalized due to the partial transmission through the impurity potential.

cond-mat.mes-hall↗
arXiv2007

Evolution of the spin Hall effect in Pt nanowires: Size and temperature effects

We have studied the evolution of the Spin Hall Effect in the regime where the material size responsible for the spin accumulation is either smaller or larger than the spin diffusion length. Lateral spin valve structures with Pt insertions were successfully used to measure the spin absorption efficiency as well as the spin accumulation in Pt induced through the spin Hall effect. Under a constant applied current the results show a decrease of the spin accumulation signal is more pronounced as the Pt thickness exceeds the spin diffusion length. This implies that the spin accumulation originates from bulk scattering inside the Pt wire and the spin diffusion length limits the SHE. We have also analyzed the temperature variation of the spin hall conductivity to identify the dominant scattering mechanism.

cond-mat.mtrl-sci↗
arXiv2006

Domain Nucleation and Annihilation in Uniformly Magnetized State under Current Pulses in Narrow Ferromagnetic Wires

We investigate the current-driven magnetization dynamics in narrow Permalloy wires by means of Lorentz microscopy and electron holography. Current pulses are found to transform the magnetic structure in the uniformly magnetized state below the Curie temperature. A variety of magnetic states including reversed magnetic domains are randomly obtained in low probability. The dynamics of vortices found in most of observed magnetic states seems to play a key role in triggering the magnetization reversal.

cond-mat.mtrl-sci↗
arXiv2006

Stringy K-theory and the Chern character

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new ring called the full orbifold K-theory of Y. For a global quotient Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra of the full orbifold K-theory of the the stack Y and is linearly isomorphic to the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a different, ``quantum,'' product, which respects the natural group grading. We prove there is a ring isomorphism, the stringy Chern character, from stringy K-theory to stringy cohomology, and a ring homomorphism from full orbifold K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy Grothendieck-Riemann-Roch for etale maps. We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's construction. Since our constructions do not use complex curves, stable maps, admissible covers, or moduli spaces, our results simplify the definitions of Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of Abramovich-Graber-Vistoli's orbifold Chow. We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler Resolution Conjecture holds for symmetric products. Our results hold both in the algebro-geometric category and in the topological category for equivariant almost complex manifolds.

math.AG↗
arXiv2006

Current-excited magnetization dynamics in narrow ferromagnetic wires

We investigate the current-excited magnetization dynamics in a narrow ferromagnetic Permalloy wire by means of Lorentz microscopy, together with the results of simultaneous transport measurements. A detailed structural evolution of the magnetization is presented as a function of the applied current density. Local structural deformation, bidirectional displacement, and magnetization reversal are found below the Curie temperature with increasing the current density. We discuss probable mechanisms of observed features of the current-excited magnetization dynamics.

cond-mat.mtrl-sci↗
arXiv2005

A Genus-3 Topological Recursion Relation

In this paper, we give a new genus-3 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds. This formula also applies to intersection numbers on moduli spaces of spin curves. A by-product of the proof of this formula is a new relation in the tautological ring of the moduli space of 1-pointed genus-3 stable curves.

math.DG↗
arXiv2005

Gutzwiller study of spin-1 bosons in an optical lattice under a magnetic field

We study spin-1 bosons in an optical lattice under a magnetic field by the Gutzwiller approximation. Our results thus obtained join the discontinuous phase boundary curves obtained by perturbative studies through a first-order transition. On the phase boundary curve, we also find a peculiar cusp structure originating from the degeneracy between different spin Mott states under a magnetic field. The magnetic field dependence of both fluctuation in the total number of bosons and the spin magnetization clarifies that the superfluid phase is divided into two regions reflecting the coexisting first- and second-order superfluid transitions.

cond-mat.other↗
arXiv2005

Pointed Admissible G-Covers and G-equivariant Cohomological Field Theories

For any finite group G we define the moduli space of pointed admissible G-covers and the concept of a G-equivariant cohomological field theory (G-CohFT), which, when G is the trivial group, reduce to the moduli space of stable curves and a cohomological field theory (CohFT), respectively. We prove that by taking the "quotient" by G, a G-CohFT reduces to a CohFT. We also prove that a G-CohFT contains a G-Frobenius algebra, a G-equivariant generalization of a Frobenius algebra, and that the "quotient" by G agrees with the obvious Frobenius algebra structure on the space of G-invariants, after rescaling the metric. We also introduce the moduli space of G-stable maps into a smooth, projective variety X with G action. Gromov-Witten-like invariants of these spaces provide the primary source of examples of G-CohFTs. Finally, we explain how these constructions generalize (and unify) the Chen-Ruan orbifold Gromov-Witten invariants of the global quotient [X/G] as well as the ring H*(X,G) of Fantechi and Goettsche.

math.AG↗