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Miki Wadati

Publications and source records attributed to Miki Wadati.

At least 19 recordsLinked to original sources
arXiv2007

Multicomponent Bright Solitons in F = 2 Spinor Bose-Einstein Condensates

We study soliton solutions for the Gross--Pitaevskii equation of the spinor Bose--Einstein condensates with hyperfine spin F=2 in one-dimension. Analyses are made in two ways: by assuming single-mode amplitudes and by generalizing Hirota's direct method for multi-components. We obtain one-solitons of single-peak type in the ferromagnetic, polar and cyclic states, respectively. Moreover, twin-peak type solitons both in the ferromagnetic and the polar state are found.

cond-mat.other↗
arXiv2007

Matter-Wave Bright Solitons with a Finite Background in Spinor Bose-Einstein Condensates

We investigate dynamical properties of bright solitons with a finite background in the F=1 spinor Bose-Einstein condensate (BEC), based on an integrable spinor model which is equivalent to the matrix nonlinear Schrödinger equation with a self-focusing nonlineality. We apply the inverse scattering method formulated for nonvanishing boundary conditions. The resulting soliton solutions can be regarded as a generalization of those under vanishing boundary conditions. One-soliton solutions are derived in an explicit manner. According to the behaviors at the infinity, they are classified into two kinds, domain-wall (DW) type and phase-shift (PS) type. The DW-type implies the ferromagnetic state with nonzero total spin and the PS-type implies the polar state, where the total spin amounts to zero. We also discuss two-soliton collisions. In particular, the spin-mixing phenomenon is confirmed in a collision involving the DW-type. The results are consistent with those of the previous studies for bright solitons under vanishing boundary conditions and dark solitons. As a result, we establish the robustness and the usefulness of the multiple matter-wave solitons in the spinor BECs.

cond-mat.other↗
arXiv2006

Dark solitons in F=1 spinor Bose--Einstein condensate

We study dark soliton solutions of a multi-component Gross--Pitaevskii equation for hyperfine spin F=1 spinor Bose--Einstein condensate. The interactions are supposed to be inter-atomic repulsive and anti-ferromagnetic ones of equal magnitude. The solutions are obtained from those of an integrable $2\times 2$ matrix nonlinear Schrödinger equation with nonvanishing boundary conditions. We investigate the one-soliton and two-soliton solutions in detail. One-soliton is classified into two kinds. The ferromagnetic state has wavefunctions of domain-wall shape and its total spin is nonzero. The polar state provides a hole soliton and its total spin is zero. These two states are selected by choosing the type of the boundary conditions. In two-soliton collisions, we observe the spin-mixing or spin-transfer. It is found that, as "magnetic" carriers, solitons in the ferromagnetic state are operative for the spin-mixing while those in the polar are passive.

cond-mat.other↗
arXiv2005

Exact Analysis of Delta-Function Attractive Fermions and Repulsive Bosons in One-Dimension

The Gaudin integral equation for the ground state of a one-dimensional delta-function attractive spin-1/2 fermions is solved in the form of power series. The first few terms of the asymptotic expansions for both strong and weak coupling cases are calculated analytically. The physical quantities such as the ground state energy are expressed in terms of a single dimensionless parameter gamma =c/D, where c is the coupling constant and D is the number density. The results agree with those obtained from the perturbation calculations, which include the one in the classical electrostatics originally by Kirchhoff. In the strong coupling limit, the connection to the solutions of the Lieb-Liniger integral equation for the ground state of a one-dimensional delta-function repulsive bose gas is shown explicitly.

cond-mat.stat-mech↗
arXiv2004

Exact Analysis of Soliton Dynamics in Spinor Bose-Einstein Condensates

We propose an integrable model of a multicomponent spinor Bose-Einstein condensate in one dimension, which allows an exact description of the dynamics of bright solitons with spin degrees of freedom. We consider specifically an atomic condensate in the F=1 hyperfine state confined by an optical dipole trap. When the mean-field interaction is attractive (c_0 < 0) and the spin-exchange interaction of a spinor condensate is ferromagnetic (c_2 < 0), we prove that the system possesses a completely integrable point leading to the existence of multiple bright solitons. By applying results from the inverse scattering method, we analyze a collision law for two-soliton solutions and find that the dynamics can be explained in terms of the spin precession.

cond-mat.stat-mech↗
arXiv2004

Matter-Wave Solitons in an F=1 Spinor Bose-Einstein Condensate

Following our previous work [J. Ieda, T. Miyakawa, M. Wadati, cond-mat/0404569] on a novel integrable model describing soliton dynamics of an F=1 spinor Bose--Einstein condensate, we discuss in detail the properties of the multi-component system with spin-exchange interactions. The exact multiple bright soliton solutions are obtained for the system where the mean-field interaction is attractive (c_0 < 0) and the spin-exchange interaction is ferromagnetic (c_2 < 0). A complete classification of the one-soliton solution with respect to the spin states and an explicit formula of the two-soliton solution are presented. For solitons in polar state, there exists a variety of different shaped solutions including twin peaks. We show that a "singlet pair" density can be used to distinguish those energetically degenerate solitons. We also analyze collisional effects between solitons in the same or different spin state(s) by computing the asymptotic forms of their initial and final states. The result reveals that it is possible to manipulate the spin dynamics by controlling the parameters of colliding solitons.

cond-mat.mes-hall↗
arXiv2004

Correlation Function of Asymmetric Simple Exclusion Process with Open Boundaries

We investigate the correlation functions of the one-dimensional Asymmetric Simple Exclusion Process (ASEP) with open boundaries. The conditions for the boundaries are made most general. The correlation function is expressed in a multifold integral whose behavior we study in detail. We present a phase diagram of the correlation length. For the case the correlation length diverges, we further give the leading terms of the finite-size correction.

cond-mat.stat-mech↗
arXiv2004

WDVV equation and Triple-product Relation

We study the relation between the WDVV equations and the $τ$-function of the noncommutative KP (NCKP) hierarchy. WDVV-like equations (Hirota triple-product relation) in the noncommutative context appear as a consequence of the non-trivial equation for $τ$-function of the NC KP hierarchy, while the prepotential in the Seiberg-Witten (SW) theory has been identified to the $τ$-function of the Whitham hierarchy. We show that the spectral curve for the SW theory is the same as the Toda-chain hierarchy. We also show that Whitham hierarchy includes commutative Toda/KP hierarchy as a construction. Further, we comment on the origin of the Hirota triple-product relation in the context of the SW theory.

hep-th↗
arXiv2003

Asymmetric Simple Exclusion Process with Open Boundaries and Askey-Wilson Polynomials

We study the one-dimensional asymmetric simple exclusion process (ASEP) with open boundary conditions. Particles are injected and ejected at both boundaries. It is clarified that the steady state of the model is intimately related to the Askey-Wilson polynomials. The partition function and the $n$-point functions are obtained in the integral form with four boundary parameters. The thermodynamic current is evaluated to confirm the conjectured phase diagram.

cond-mat.stat-mech↗
arXiv2002

Multipartite Entanglement and Hyperdeterminants

We classify multipartite entanglement in a unified manner, focusing on a duality between the set of separable states and that of entangled states. Hyperdeterminants, derived from the duality, are natural generalizations of entanglement measures, the concurrence, 3-tangle for 2, 3 qubits respectively. Our approach reveals how inequivalent multipartite entangled classes of pure states constitute a partially ordered structure under local actions, significantly different from a totally ordered one in the bipartite case. Moreover, the generic entangled class of the maximal dimension, given by the nonzero hyperdeterminant, does not include the maximally entangled states in Bell's inequalities in general (e.g., in the 4 or more qubits), contrary to the widely known bipartite or 3-qubit cases. It suggests that not only are they never locally interconvertible with the majority of multipartite entangled states, but they would have no grounds for the canonical n-partite entangled states. Our classification is also useful for that of mixed states.

quant-ph↗
arXiv2002

Graphical representation of the partition function for a 1-D delta-function Bose gas

One-dimensional repulsive delta-function bose system is studied. By only using the Bethe ansatz equation, n-particle partition functions are exactly calculated. From this expression for the n-particle partition function, the n-particle cluster integral is derived. The results completely agree with those of the thermal Bethe ansatz (TBA). This directly proves the validity of the TBA. The theory of partitions and graphs is used to simplify the discussion.

cond-mat.stat-mech↗
arXiv2002

Direct Calculation of Thermodynamic Quantities for Heisenberg Model

The XXX Heisenberg model is studied at finite temperature. The free energy is derived without recourse to Thermal Bethe Ansatz method and Quantum Transfer Matrix method. The result perfectly agrees with the free energy derived by Thermal Bethe Ansatz method. An explicit expression of the cluster expansion coefficient in arbitrary order is presented for the first time.

cond-mat.stat-mech↗
arXiv2002

A direct calculation of the free energy from the Bethe ansatz equation for the Heisenberg model

Thermodynamics of the XXX Heisenberg model is studied. The trace of the Boltzmann weight with respect to the Hilbert space is taken in the thermodynamic limit with the number of up-spins being fixed. The expression of the trace gives an explanation why the correct thermodynamic quantities are derived from the string hypothesis. Combining this with the previous result, we conclude that the free energy can be calculated only by assuming the Bethe ansatz equation. The method is more direct than other known methods which were used to derive the free energy.

cond-mat.stat-mech↗
arXiv2002

Partition Function for a 1-D delta-function Bose Gas

The N-particle partition function of a one-dimensional $δ$-function bose gas is calculated explicitly using only the periodic boundary condition (the Bethe ansatz equation). The N-particles cluster integrals are shown to be the same as those by the thermal Bethe ansatz method.

cond-mat.stat-mech↗
arXiv2002

Universal Transport Properties of Disordered Quantum Wires

For disordered quantum wires which belong to all ten universality classes, the universal quantities of transport properties are obtained through DMPK approach. Calculated are the universal parts of one- and two-point correlation functions for probability distribution functions of transmission eigenvalues. In this analysis, the asymptotic solution of DMPK equation is used. Transport properties for new universality classes(chiral and Bogoliubov-de Gennes classes) are discussed comparing with those for standard class.

cond-mat.mes-hall↗
arXiv2001

Geometric Strategy for the Optimal Quantum Search

We explore quantum search from the geometric viewpoint of a complex projective space $CP$, a space of rays. First, we show that the optimal quantum search can be geometrically identified with the shortest path along the geodesic joining a target state, an element of the computational basis, and such an initial state as overlaps equally, up to phases, with all the elements of the computational basis. Second, we calculate the entanglement through the algorithm for any number of qubits $n$ as the minimum Fubini-Study distance to the submanifold formed by separable states in Segre embedding, and find that entanglement is used almost maximally for large $n$. The computational time seems to be optimized by the dynamics as the geodesic, running across entangled states away from the submanifold of separable states, rather than the amount of entanglement itself.

quant-ph↗
arXiv2001

Quantum cloning machines for equatorial qubits

Quantum cloning machines for equatorial qubits are studied. For the case of 1 to 2 phase-covariant quantum cloning machine, we present the networks consisting of quantum gates to realize the quantum cloning transformations. The copied equatorial qubits are shown to be separable by using Peres-Horodecki criterion. The optimal 1 to M phase-covariant quantum cloning transformations are given.

quant-ph↗