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Stability of ultracold atomic Bose condensates with Rashba spin-orbit coupling against quantum and thermal fluctuationsMar 28 2012Apr 06 2012We study the stability of Bose condensates with Rashba-Dresselhaus spin-orbit coupling in three dimensions against quantum and thermal fluctuations. The ground state depletion of the plane-wave condensate due to quantum fluctuations is, as we show, finite, ... More

Synthetic dimensions with magnetic fields and local interactions in photonic latticesJul 01 2016We discuss how one can realize a photonic device that combines synthetic dimensions and synthetic magnetic fields with spatially local interactions. Using an array of ring resonators, the angular coordinate around each resonator spans the synthetic dimension ... More

Condensation transition of ultracold Bose gases with Rashba spin-orbit couplingJul 22 2012Feb 27 2013We study the Bose-Einstein condensate phase transition of three-dimensional ultracold bosons with isotropic Rashba spin-orbit coupling. Investigating the structure of Ginzburg-Landau free energy as a function of the condensate density, we show, within ... More

Striped states in weakly trapped ultracold Bose gases with Rashba spin-orbit couplingApr 30 2012Jul 12 2012The striped state of ultracold bosons with Rashba spin-orbit coupling in a homogeneous infinite system has, as we show, a constant particle flow, which in a finite-size system would accumulate particles at the boundaries; it is thus not a physical steady ... More

Renormalization of interactions of ultracold atoms in simulated Rashba gauge fieldsJul 15 2011Oct 13 2011Interactions of ultracold atoms with Rashba spin-orbit coupling, currently being studied with simulated (artificial) gauge fields, have nontrivial ultraviolet and infrared behavior. Examining the ultraviolet structure of the Bethe-Salpeter equation, we ... More

Two-slit diffraction with highly charged particles: Niels Bohr's consistency argument that the electromagnetic field must be quantizedFeb 16 2009We analyze Niels Bohr's proposed two-slit interference experiment with highly charged particles that argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's ... More

Anomalous and Quantum Hall Effects in Lossy Photonic LatticesJul 25 2013Apr 01 2014We theoretically discuss analogues of the anomalous and the integer quantum Hall effect in driven-dissipative two-dimensional photonic lattices in the presence of a synthetic gauge field. Photons are coherently injected by a spatially localized pump, ... More

Discontinuities in the First and Second Sound Velocities at the Berezinskii-Kosterlitz-Thouless TransitionOct 14 2013Jan 19 2014We calculate the temperature dependence of the first and second sound velocities in the superfluid phase of a 2D dilute Bose gas by solving Landau's two fluid hydrodynamic equations. We predict the occurrence of a significant discontinuity in both velocities ... More

Ground-state phases of ultracold bosons with Rashba-Dresselhaus spin-orbit couplingSep 22 2011Jan 09 2012We study ultracold bosons in three dimensions with an anisotropic Rashba-Dresselhaus spin-orbit coupling. We first carry out the exact summation of ladder diagrams for the two-boson t-matrix at zero energy. Then, with the t-matrix as the effective interaction, ... More

Population imbalance and pairing in the BCS-BEC crossover of three-component ultracold fermionsNov 01 2010Dec 14 2010We investigate the phase diagram and the BCS-BEC crossover of a homogeneous three-component ultracold Fermi gas with a U(3) invariant attractive interaction. We show that the system at sufficiently low temperatures exhibits population imbalance, as well ... More

Supercurrent and dynamical instability of spin-orbit-coupled ultracold Bose gasesMay 03 2013Jun 11 2013We investigate the stability of supercurrents in a Bose-Einstein condensate with one-dimensional spin-orbit and Raman couplings. The consequence of the lack of Galilean invariance is explicitly discussed. We show that in the plane-wave phase, characterized ... More

Quantum Hall effect in momentum spaceFeb 24 2016May 04 2016We theoretically discuss a momentum-space analog of the quantum Hall effect, which could be observed in topologically nontrivial lattice models subject to an external harmonic trapping potential. In our proposal, the Niu-Thouless-Wu formulation of the ... More

Synthetic Dimensions for Cold Atoms from Shaking a Harmonic TrapMay 30 2016Jun 23 2016We introduce a simple scheme to implement synthetic dimensions and gauge fields in ultracold atomic gases, which only requires two basic and ubiquitous ingredients: the harmonic trap, which confines the atoms, combined with a periodic shaking. In our ... More

Orbital edge states in a photonic honeycomb latticeSep 21 2016We experimentally reveal the emergence of edge states in a photonic lattice with orbital bands. We use a two-dimensional honeycomb lattice of coupled micropillars whose bulk spectrum shows four gapless bands arising from the coupling of $p$-like photonic ... More

Quantum Mechanics with a Momentum-Space Artificial Magnetic FieldMar 24 2014Nov 19 2014The Berry curvature is a geometrical property of an energy band which acts as a momentum space magnetic field in the effective Hamiltonian describing single-particle quantum dynamics. We show how this perspective may be exploited to study systems directly ... More

Momentum-space Harper-Hofstadter modelNov 05 2014Aug 14 2015We show how the weakly trapped Harper-Hofstadter model can be mapped onto a Harper-Hofstadter model in momentum space. In this momentum-space model, the band dispersion plays the role of the periodic potential, the Berry curvature plays the role of an ... More

Hadronic matter phases and their application to rapidly rotating neutron starsDec 28 2015Neutron stars are commonly considered as astronomical objects having highdensity interiors and an inner core region in which various hadronic matter phases are expected. Several studies show that the inner structures affect macroscopic phenomena of the ... More

Appearance of a quark matter phase in hybrid starsOct 03 2013The appearance of quark matter in the core of hybrid stars is a fundamental issue in such compact stars. The central density of these stars is sufficiently high such that nuclear matter undergoes a further change into other exotic phases that consist ... More

Tessellation and Lyubich-Minsky laminations associated with quadratic maps I: Pinching semiconjugaciesSep 11 2006We introduce tessellation of the filled Julia sets for hyperbolic and parabolic quadratic maps. Then the dynamics inside their Julia sets are organized by tiles which work like external rays outside. We also construct continuous families of pinching semiconjugacies ... More

Set Theory and p-adic AlgebrasMar 11 2013We verified that the existence of a maximal ideal of height 0 in a p-adic algebra in a certain class is independent of the axiom of ZFC. We established the theory on a P-point in the boundary of a topological space in the universal totally disconnected ... More

Periodicities in cluster algebras and dilogarithm identitiesJun 03 2010Aug 04 2011We consider two kinds of periodicities of mutations in cluster algebras. For any sequence of mutations under which exchange matrices are periodic, we define the associated T- and Y-systems. When the sequence is `regular', they are particularly natural ... More

Symplectic Group, Ladder Operators, and the Hagedorn Wave PacketsOct 04 2015We develop an alternative view of the semiclassical wave packets of Hagedorn---often called the Hagedorn wave packets---stressing the roles of the symplectic and metaplectic groups along with the Heisenberg--Weyl group. Our point of view clarifies the ... More

Characterisation of the Berkovich Spectrum of the Banach Algebra of Bounded Continuous FunctionsMar 02 2013Jul 14 2014For a complete valuation field k and a topological space X, we prove the universality of the underlying topological space of the Berkovich spectrum of the Banach k-algebra Cbd(X,k) of bounded continuous k-valued functions on X. This result yields three ... More

The Riemann hypothesis and holomorphic index in complex dynamicsFeb 22 2016We give an interpretation of the Riemann hypothesis in terms of complex and topological dynamics. For example, the Riemann hypothesis is affirmative and all zeros of the Riemann zeta function are simple if and only if a certain meromorphic function has ... More

Tessellation and Lyubich-Minsky laminations associated with quadratic maps II: Topological structures of 3-laminationsSep 29 2006Jun 24 2008According to an analogy to quasi-Fuchsian groups, we investigate topological and combinatorial structures of Lyubich and Minsky's affine and hyperbolic 3-laminations associated with the hyperbolic and parabolic quadratic maps. We begin by showing that ... More

Statistical test for detecting community structure in real-valued edge-weighted graphsOct 13 2016We propose a novel method to test the existence of community structure of undirected real-valued edge-weighted graph. The method is based on Wigner semicircular law on the asymptotic behavior of the random distribution for eigenvalues of a real symmetric ... More

Hahn--Banach Theorem and Duality Theory on non-Archimedean Locally Convex SpacesApr 17 2015Mar 21 2016Let $k$ be a local field with valuation ring $O_k$ and residue field $\overline{k}$. We extend Hahn--Banach theorem for the class of seminormed $k$-vector spaces to several classes of locally convex spaces and subspaces over $k$, $O_k$, and $\overline{k}$. ... More

Region of hadron-quark mixed phase in hybrid starsMay 12 2011Hadron--quark mixed phase is expected in a wide region of the inner structure of hybrid stars. However, we show that the hadron--quark mixed phase should be restricted to a narrower region to because of the charge screening effect. The narrow region of ... More

The Siegel Upper Half Space is a Marsden-Weinstein Quotient: Symplectic Reduction and Gaussian Wave PacketsApr 15 2015Aug 07 2015We show that the Siegel upper half space $\Sigma_{d}$ is identified with the Marsden-Weinstein quotient obtained by symplectic reduction of the cotangent bundle $T^{*}\mathbb{R}^{2d^{2}}$ with $\mathsf{O}(2d)$-symmetry. The reduced symplectic form on ... More

Chandrasekhar-Clogston limit and critical polarization in a Fermi-Bose superfluid mixtureMay 28 2014Sep 20 2014We study mixtures of a population-imbalanced strongly-interacting Fermi gas and of a Bose-Einstein condensed gas at zero temperature. In the homogeneous case, we find that the Chandrasekhar-Clogston critical polarization for the onset of instability of ... More

How to directly observe Landau levels in driven-dissipative strained honeycomb latticesApr 15 2015Sep 24 2015We study the driven-dissipative steady-state of a coherently-driven Bose field in a honeycomb lattice geometry. In the presence of a suitable spatial modulation of the hopping amplitudes, a valley-dependent artificial magnetic field appears and the low-energy ... More

Artificial Magnetic Fields in Momentum Space in Spin-Orbit Coupled SystemsDec 11 2014Apr 01 2015The Berry curvature is a geometrical property of an energy band which can act as a momentum space magnetic field in the effective Hamiltonian of a wide range of systems. We apply the effective Hamiltonian to a spin-1/2 particle in two dimensions with ... More

Floquet topological system based on frequency-modulated classical coupled harmonic oscillatorsOct 15 2015Feb 03 2016We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use ... More

Momentum-space Landau levels in driven-dissipative cavity arraysOct 11 2015Jan 21 2016We theoretically study the driven-dissipative Harper-Hofstadter model on a 2D square lattice in the presence of a weak harmonic trap. Without pumping and loss, the eigenstates of this system can be understood, in certain limits, as momentum-space toroidal ... More

Optical-lattice-assisted magnetic phase transition in a spin-orbit-coupled Bose-Einstein condensateMay 06 2016Oct 14 2016We investigate the effect of a periodic potential generated by a one-dimensional optical lattice on the magnetic properties of an $S=1/2$ spin-orbit-coupled Bose gas. By increasing the lattice strength one can achieve a magnetic phase transition between ... More

Noncommutative real algebraic geometry of Kazhdan's property (T)Dec 19 2013Jan 26 2015It is well-known that a finitely generated group $\Gamma$ has Kazhdan's property (T) if and only if the Laplacian element $\Delta$ in ${\mathbb R}[\Gamma]$ has a spectral gap. In this paper, we prove that this phenomenon is witnessed in ${\mathbb R}[\Gamma]$. ... More

Amenable actions and exactness for discrete groupsFeb 22 2000Feb 26 2000It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Cech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete groups.

Homotopy invariance of AF-embeddabilityJan 21 2002We prove that AF-embeddability is a homotopy invariant in the class of separable exact $C^*$-algebras. This work was inspired by Spielberg's work on homotopy invariance of AF-embeddability and Dadarlat's serial works on AF-embeddability of residually ... More

A remark on contractible Banach algebrasOct 27 2011It is a longstanding problem whether every contractible Banach algebra is necessarily finite-dimensional. In this note, we confirm this for Banach algebras acting on Banach spaces with the uniform approximation property. This generalizes a result of Paulsen ... More

A functional analysis proof of Gromov's polynomial growth theoremOct 14 2015Mar 12 2016The celebrated theorem of Gromov asserts that any finitely generated group with polynomial growth contains a nilpotent subgroup of finite index. Alternative proofs have been given by Kleiner and others. In this note, we give yet another proof of Gromov's ... More

Examples of groups which are not weakly amenableDec 03 2010Aug 22 2011We prove that weak amenability of a locally compact group imposes a strong condition on its amenable closed normal subgroups. This extends non weak amenability results of Haagerup (1988) and Ozawa--Popa (2010). A von Neumann algebra analogue is also obtained. ... More

A remark on amenable von Neumann subalgebras in a tracial free productJan 26 2015Jan 27 2015Let $M=M_1*M_2$ be a nontrivial tracial free product of finite von Neumann algebras. We prove that any amenable subalgebra of $M$ that has a diffuse intersection with $M_1$ is in fact contained in $M_1$. This has been proved by C. Houdayer under more ... More

Heisenberg's original derivation of the uncertainty principle and its universally valid reformulationsJul 08 2015Jul 23 2015Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the constraint that ... More

Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum TheoryApr 26 2015Nov 09 2015The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of equality between ... More

Disproving Heisenberg's error-disturbance relationAug 16 2013Recently, Busch, Lahti, and Werner (arXiv:1306.1565v1 [quant-ph]) claimed that Heisenberg's error-disturbance relation can be proved in its original form with new formulations of error and disturbance, in contrast to the theory proposed by the present ... More

Uncertainty Relations for Noise and Disturbance in Generalized Quantum MeasurementsJul 08 2003Heisenberg's uncertainty relation for measurement noise and disturbance states that any position measurement with noise epsilon brings the momentum disturbance not less than hbar/2epsilon. This relation holds only for restricted class of measuring apparatuses. ... More

Quantum Limits of Measurement and Computing Induced by Conservation Laws and Uncertainty RelationsOct 08 2002A quantitative extension of the Wigner-Araki-Yanase theorem is obtained on the limitation on precise, non-disturbing measurements of observables which do not commute with additive conserved quantities, and applied to obtaining a limitation on the accuracy ... More

Physical content of Heisenberg's uncertainty relation: Limitation and reformulationOct 07 2002Jul 08 2003Heisenberg's reciprocal relation between position measurement error and momentum disturbance is rigorously proven under the assumption that those error and disturbance are independent of the state of the measured object. A generalization of Heisenberg's ... More

On the Concept of Quantum State Reduction: Inconsistency of the Orthodox ViewFeb 09 1998The argument is re-examined that the program of deriving the rule of state reduction from the Schroedinger equation holding for the object-apparatus composite system falls into a vicious circle or an infinite regress called the von Neumann chain. It is ... More

Knots and surfacesMar 30 2016This article is an English translation of Japanese article "Musubime to Kyokumen", Math. Soc. Japan, Sugaku Vol. 67, No. 4 (2015) 403--423. It surveys a specific area in Knot Theory concerning surfaces in knot exteriors.

Mathematical foundations of quantum information: Measurement and foundationsJan 25 2012Sep 21 2014The purpose of this paper is to survey some topics on mathematical foundations of quantum information developed mainly by the present author and co-workers for the last three decades. The topics include an axiomatic construction of quantum measurement ... More

Orthomodular-valued models for quantum set theoryAug 04 2009Orthomodular logic represented by a complete orthomodular lattice has been studied as a pertinent generalization of the two-valued logic, Boolean-valued logic, and quantum logic. In this paper, we introduce orthomodular logic valued models for set theory ... More

Quantum perfect correlationsJan 16 2005Aug 17 2005The notion of perfect correlations between arbitrary observables, or more generally arbitrary POVMs, is introduced in the standard formulation of quantum mechanics, and characterized by several well-established statistical conditions. The transitivity ... More

Universal uncertainty principle and quantum state control under conservation lawsNov 10 2004Heisenberg's uncertainty principle, exemplified by the gamma ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement contradicts the ... More

Impossibility of obtaining split links from split links via twistingsApr 24 2001We show that if a split link is obtained from a split link $L$ in $S^3$ by $1/n$-Dehn surgery along a trivial knot $C$, then the link $L\cup C$ is splittable. That is to say, it is impossible to obtain a split link from a split link via a non-trivial ... More

Entanglement measures and the Hilbert-Schmidt distanceFeb 13 2000In order to construct a measure of entanglement on the basis of a ``distance'' between two states, it is one of desirable properties that the ``distance'' is nonincreasing under every completely positive trace preserving map. Contrary to a recent claim, ... More

Boundary Amenability of Relatively Hyperbolic GroupsJan 31 2005Jun 05 2005Let K be a fine hyperbolic graph and G be a group acting on K with finite quotient. We prove that G is exact provided that all vertex stabilizers are exact. In particular, a relatively hyperbolic group is exact if all its peripheral groups are exact. ... More

Quasi-homomorphism rigidity with noncommutative targetsNov 20 2009Aug 01 2010As a strengthening of Kazhdan's property (T) for locally compact groups, property (TT) was introduced by Burger and Monod. In this paper, we add more rigidity and introduce property (TTT). This property is suited for the study of rigidity phenomena for ... More

Rate and G- matrices of a non-negative block tri-diagonal matrix and application to a 3-dimensional skip-free Markov modulated random walkNov 08 2016First, we extend matrix analytic methods to the case of nonnegative block tri-diagonal matrices with countably many phase states, where rate matrices and so-called G-matrices are redefined and some properties of them are clarified. Second, we apply the ... More

Stability of multidimensional skip-free Markov modulated reflecting random walks: Revisit to Malyshev and Menshikov's results and application to queueing networksAug 15 2012Feb 16 2015Let $\{\boldsymbol{X}_n\}$ be a discrete-time $d$-dimensional process on $\mathbb{Z}_+^d$ with a supplemental (background) process $\{J_n\}$ on a finite set and assume the joint process $\{\boldsymbol{Y}_n\}=\{(\boldsymbol{X}_n,J_n)\}$ to be Markovian. ... More

Tsirelson's Problem and Asymptotically Commuting Unitary MatricesNov 12 2012Mar 23 2013In this note, we consider quantum correlations of bipartite systems having a slight interaction, and reinterpret Tsirelson's problem (and hence Kirchberg's and Connes's conjectures) in terms of finite-dimensional asymptotically commuting positive operator ... More

Weak Amenability of Hyperbolic GroupsApr 12 2007Dec 21 2007We prove that hyperbolic groups are weakly amenable. This partially extends the result of Cowling and Haagerup showing that lattices in simple Lie groups of real rank one are weakly amenable. We take a combinatorial approach in the spirit of Haagerup ... More

An Application of Expanders to $B(H) \otimes B(H)$Oct 15 2001Oct 27 2002With the help of Kirchberg's and Selberg's theorems, we prove that the minimal tensor product of $B(H)$ with itself does not have the WEP (weak expectation property) of Lance.

Unknotting submanifolds of the 3-sphere by twistingsSep 21 2016Dec 01 2016By the Fox's re-embedding theorem, any compact submanifold of the 3-sphere can be re-embedded in the 3-sphere so that it is unknotted. It is unknown whether the Fox's re-embedding can be replaced with twistings. In this paper, we will show that any closed ... More

Non-minimal bridge positions of torus knots are stabilizedJun 05 2010We show that any non-minimal bridge decomposition of a torus knot is stabilized and that $n$-bridge decompositions of a torus knot are unique for any integer $n$. This implies that a knot in a bridge position is a torus knot if and only if there exists ... More

Additivity of free genus of knotsNov 08 1998We show that free genus of knots is additive under connected sum.

Quantum State Reduction: An Operational ApproachNov 07 1997A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle relative to the ... More

Quantum Limits of Measurements and Uncertainty PrincipleMay 19 2015In this paper, we show how the Robertson uncertainty relation gives certain intrinsic quantum limits of measurements in the most general and rigorous mathematical treatment. A general lower bound for the product of the root-mean-square measurement errors ... More

Realization of Measurement and the Standard Quantum LimitMay 05 2015This paper, following [M. Ozawa, Phys. Rev. Lett. 60, 385 (1988)], reports a refutation of the claim that for monitoring the position of a free mass such as gravitational-wave interferometers the sensitivity is limited by the so called standard quantum ... More

Waist and trunk of knotsMay 27 2009Jun 01 2009We introduce two numerical invariants, the waist and the trunk of knots. The waist of a closed incompressible surface in the complement of a knot is defined as the minimal intersection number of all compressing disks for the surface in the 3-sphere and ... More

Defense of "Impossibility of distant indirect measurement of the quantum Zeno effect"Mar 04 2006Apr 01 2006Recently, Wallentowitz and Toschek [Phys. Rev. A 69, 046101 (2005)] criticized the assertion made by Hotta and Morikawa [Phys. Rev. A 69, 052114 (2004)] that distant indirect measurements do not cause the quantum Zeno effect, and claimed that their proof ... More

Universal Uncertainty Principle in the Measurement Operator FormalismOct 12 2005Oct 27 2005Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation. Recently, a new relation ... More

Perfect correlations between noncommuting observablesOct 11 2003Dec 10 2004The problem as to when two noncommuting observables are considered to have the same value arises commonly, but shows a nontrivial difficulty. Here, an answer is given by establishing the notion of perfect correlations between noncommuting observables, ... More

Uncertainty Relations for Joint Measurements of Noncommuting ObservablesOct 11 2003Universally valid uncertainty relations are proven in a model independent formulation for inherent and unavoidable extra noises in arbitrary joint measurements on single systems, from which Heisenber's original uncertainty relation is proven valid for ... More

Conservative Quantum ComputingDec 31 2001Jun 21 2002Conservation laws limit the accuracy of physical implementations of elementary quantum logic gates. If the computational basis is represented by a component of spin and physical implementations obey the angular momentum conservation law, any physically ... More

Position measuring interactions and the Heisenberg uncertainty principleJun 30 2001Jun 02 2002An indirect measurement model is constructed for an approximately repeatable, precise position measuring apparatus that violates the assertion, sometimes called the Heisenberg uncertainty principle, that any position measuring apparatus with noise epsilon ... More

Controlling Quantum State ReductionMay 12 1998Every measurement leaves the object in a family of states indexed by the possible outcomes. This family, called the posterior states, is usually a family of the eigenstates of the measured observable, but it can be an arbitrary family of states by controlling ... More

Quantum Nondemolition Monitoring of Universal Quantum ComputersApr 15 1997Nov 18 1997The halt scheme for quantum Turing machines, originally proposed by Deutsch, is reformulated precisely and is proved to work without spoiling the computation. The ``conflict'' pointed out recently by Myers in the definition of a universal quantum computer ... More

A remark on fullness of some group measure space von Neumann algebrasFeb 08 2016Oct 27 2016Recently C. Houdayer and Y. Isono have proved among other things that every biexact group $\Gamma$ has the property that for any non-singular strongly ergodic action $\Gamma\curvearrowright (X,\mu)$ on a standard measure space the group measure space ... More

An example of a solid von Neumann algebraApr 02 2008We prove that the group-measure-space von Neumann algebra $L^\infty(T^2) \rtimes SL(2,Z)$ is solid. The proof uses topological amenability of the action of $SL(2,Z)$ on the Higson corona of $Z^2$.

A remark on fullness of some group measure space von Neumann algebrasFeb 08 2016Mar 12 2016Recently C. Houdayer and Y. Isono have proved among other things that every biexact group $\Gamma$ has the property that for any non-singular strongly ergodic action $\Gamma\curvearrowright (X,\mu)$ on a standard measure space the group measure space ... More

Unknotting submanifolds of the 3-sphere by twistingsSep 21 2016By the Fox's re-embedding theorem, any compact submanifold of the 3-sphere can be re-embedded in the 3-sphere so that it is unknotted. It is unknown whether the Fox's re-embedding can be replaced with twistings. In this paper, we will show that any closed ... More

Dixmier approximation and symmetric amenability for C*-algebrasApr 12 2013Jan 26 2015We study some general properties of tracial C*-algebras. In the first part, we consider Dixmier type approximation theorem and characterize symmetric amenability for C*-algebras. In the second part, we consider continuous bundles of tracial von Neumann ... More

Boundaries of Reduced Free Group C*-AlgebrasNov 22 2004Dec 21 2007We prove that the crossed product $C^*$-algebra $C^*_r(\Gamma,\partial\Gamma)$ of a free group $\Gamma$ with its boundary $\partial\Gamma$ naturally sits between the reduced group $C^*$-algebra $C^*_r\Gamma$ and its injective envelope $I(C^*_r\Gamma)$. ... More

About the QWEP conjectureJun 03 2003May 10 2004This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].

Rational structure on algebraic tangles and closed incompressible surfaces in the complements of algebraically alternating knots and linksMar 09 2008May 07 2009Let $F$ be an incompressible, meridionally incompressible and not boundary-parallel surface with boundary in the complement of an algebraic tangle $(B,T)$. Then $F$ separates the strings of $T$ in $B$ and the boundary slope of $F$ is uniquely determined ... More

Ascending number of knots and linksMay 23 2007We introduce a new numerical invariant of knots and links from the descending diagrams. It is considered to live between the unknotting number and the bridge number.

Essential state surfaces for knots and linksSep 06 2006Nov 17 2010We study a canonical spanning surface obtained from a knot or link diagram depending on a given Kauffman state, and give a sufficient condition for the surface to be essential. By using the essential surface, we can see the triviality and splittability ... More

Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurementJul 19 2002The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant, hbar/2, as demonstrated by Heisenberg's ... More

Heisenberg's uncertainty relation: Violation and reformulationFeb 23 2014The uncertainty relation formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable so that their product should be no less than a limit set ... More

Coexistence of coiled surfaces and spanning surfaces for knots and linksNov 26 2012It is a well-known procedure for constructing a torus knot or link that first we prepare an unknotted torus and meridian disks in the complementary solid tori of it, and second smooth the intersections of the boundary of meridian disks uniformly. Then ... More

The representativity of pretzel knotsNov 16 2009In the present paper, we will show that a $(p,q,r)$-pretzel knot has the representativity 3 if and only if $(p,q,r)$ is either $\pm(-2,3,3)$ or $\pm(-2,3,5)$. We also show that a large algebraic knot has the representativity less than or equal to 3.

Bridge position and the representativity of spatial graphsSep 07 2009Nov 17 2010First, we extend Otal's result for the trivial knot to trivial spatial graphs, namely, we show that for any bridge tangle decomposing sphere $S^2$ for a trivial spatial graph $\Gamma$, there exists a 2-sphere $F$ such that $F$ contains $\Gamma$ and $F$ ... More

Transfer principle in quantum set theoryApr 15 2006Oct 03 2006In 1981, Takeuti introduced quantum set theory as the quantum counterpart of Boolean valued models of set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed subspaces in a Hilbert space and showed ... More

Measurements of Nondegenerate Discrete ObservablesMar 09 2000Every measurement on a quantum system causes a state change from the system state just before the measurement to the system state just after the measurement conditional upon the outcome of measurement. This paper determines all the possible conditional ... More

The Problem of Measurement and the Theory of Quantum State ReductionOct 07 1997Nov 06 1997A new approach to the problem of measurement in quantum mechanics is proposed. In this approach, the process of measurement is described in the Heisenberg picture and divided into two stages. The first stage is to transduce the measured observable to ... More

Operational Characterization of Simultaneous Measurements in Quantum MechanicsFeb 13 1998Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The question is answered ... More

Stability condition of a two-dimensional QBD process and its application to estimation of efficiency for two-queue modelsAug 20 2018In order to analyze stability of a two-queue model, we consider a two-dimensional quasi-birth-and-death process (2d-QBD process), denoted by $\{\boldsymbol{Y}(t)\}=\{((L_1(t),L_2(t)),J(t))\}$. The two-dimensional process $\{(L_1(t),L_2(t))\}$ on $\mathbb{Z}_+^2$ ... More

Positive recurrence and transience of a two-station network with server statesAug 28 2013We study positive recurrence and transience of a two-station network in which the behavior of the server in each station is governed by a Markov chain with a finite number of server states; this service process can represent various service disciplines ... More

Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas ApproachJul 16 2014Aug 14 2014We study the partition function of three-dimensional ${\mathcal N}=4$ superconformal Chern-Simons theories of the circular quiver type, which are natural generalizations of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was ... More