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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

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

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

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

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

A localization marker from many-body quantum geometry measurementsApr 26 2019In condensed matter, the quantum geometric tensor characterizes the geometry of single-particle Bloch states. Here, we generalize this notion by introducing a many-body geometric tensor, which is defined in the parameter space of twist angles associated ... 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

Topological PhotonicsFeb 12 2018Apr 02 2019Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators ... 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

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

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

T-systems, Y-systems, and cluster algebras: Tamely laced caseMar 05 2010Jun 08 2010The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently they were generalized to quantum affinizations of quantum Kac-Moody algebras associated with a wide class of generalized ... More

Symmetry and Conservation Laws in Semiclassical Wave Packet DynamicsOct 29 2014Mar 23 2015We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noether's theorem. We consider two slightly different formulations of Gaussian ... 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

On Tate Acyclicity and Uniformity of Berkovich Spectra and Adic SpectraMar 31 2014Mar 23 2017We construct a non-sheafy uniform Banach algebra such that a rational localisation of the Berkovich spectrum does not preserve the uniformity. We also construct uniform affinoid rings in the sense of Roland Huber such that rational localisations of the ... 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

Contact Geometry of the Pontryagin Maximum PrincipleJan 30 2015Mar 09 2015This paper gives a brief contact-geometric account of the Pontryagin maximum principle. We show that key notions in the Pontryagin maximum principle---such as the separating hyperplanes, costate, necessary condition, and normal/abnormal minimizers---have ... 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

Investigation of the rotation effects on high--density matter in hybrid starsNov 03 2014The equation of state (EOS) of high-density matter is still not clear and several recent observations indicate restrictions to EOSs. Theoretical studies should thus elucidate EOSs at high density and/or high temperature. Many theoretical studies have ... More

Rogers dilogarithms of higher degree and generalized cluster algebrasMay 16 2016Sep 27 2016In connection with generalized cluster algebras we introduce a certain generalization of the celebrated Rogers dilogarithm, which we call the Rogers dilogarithms of higher degree. We show that there is an identity of these generalized Rogers dilogarithms ... 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

Note on dilogarithm identities from nilpotent double affine Hecke algebrasSep 30 2012Dec 25 2012Recently Cherednik and Feigin obtained several Rogers-Ramanujan type identities via the nilpotent double affine Hecke algebras (Nil-DAHA). These identities further led to a series of dilogarithm identities, some of which are known, while some are left ... More

Geometric Kinematic Control of a Spherical Rolling RobotAug 30 2018We give a geometric account of kinematic control of a spherical rolling robot controlled by two internal wheels just like the toy robot Sphero. Particularly, we introduce the notion of shape space and fibers to the system by exploiting its symmetry and ... 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

A proof of simultaneous linearization with a polylog estimateSep 06 2006Dec 26 2006We give an alternative proof of simultaneous linearization recently shown by T.Ueda, which connects the Schr\"oder equation and the Abel equation analytically. Indeed, we generalize Ueda's original result so that we may apply it to the parabolic fixed ... More

Rogers dilogarithms of higher degree and generalized cluster algebrasMay 16 2016Mar 19 2017In connection with generalized cluster algebras we introduce a certain generalization of the celebrated Rogers dilogarithm, which we call the Rogers dilogarithms of higher degree. We show that there is an identity of these generalized Rogers dilogarithms ... 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

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

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

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

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

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

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

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

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

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

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

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

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

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)].

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

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

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

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

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

Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum Theory (Extended Abstract)Dec 30 2014The 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 relation ... More

Universal Uncertainty Principle, Simultaneous Measurability, and Weak ValuesJun 24 2011Aug 03 2011In the conventional formulation, it is broadly accepted that simultaneous measurability and commutativity of observables are equivalent. However, several objections have been claimed that there are cases in which even nowhere commuting observables can ... More

Conservation laws, uncertainty relations, and quantum limits of measurementsDec 24 2001The uncertainty relation between the noise operator and the conserved quantity leads to a bound for the accuracy of general measurements. The bound extends the assertion by Wigner, Araki, and Yanase that conservation laws limit the accuracy of ``repeatable'', ... More

Operations, Disturbance, and Simultaneous MeasurabilityMay 15 2000May 16 2000Quantum mechanics predicts the joint probability distributions of the outcomes of simultaneous measurements of commuting observables, but the current formulation lacks the operational definition of simultaneous measurements. In order to provide foundations ... More

Phase Operator Problem and Macroscopic Extension of Quantum MechanicsMay 19 1997To find the Hermitian phase operatorof a single-mode electromagnetic field in quantum mechanics, the Schroedinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The Hermitian ... More

Quantum Measurement, Information, and Completely Positive MapsJul 18 2001Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.

An Operational Approach to Quantum State ReductionJun 13 1997An operational approach to quantum state reduction, the state change of the measured system caused by a measurement of an observable conditional upon the outcome of measurement, is founded without assuming the projection postulate in any stages of the ... More

Quantum State Reduction and the Quantum Bayes PrincipleMay 16 1997This paper gives new foundations of quantum state reduction without appealing to the projection postulate for the probe measurement. For this purpose, the quantum Bayes principle is formulated as the most fundamental principle for determining the state ... More

Orthomodular-Valued Models for Quantum Set TheoryAug 04 2009May 14 2017In 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed ... More

Classical weight one forms in Hida families: Hilbert modular caseJun 21 2016Jun 24 2016The purpose of this paper is to investigate the number of classical weight one specializations of a non-CM ordinary Hida family of parallel weight Hilbert cusp forms. It is known that a specialization of a primitive ordinary Hida family at any arithmetic ... More

Continuous Distributions on $(0,\,\infty)$ Giving Benford's Law ExactlyMay 03 2019Benford's law is a famous law in statistics which states that the leading digits of random variables in diverse data sets appear not uniformly from 1 to 9; the probability that d (d=1,...,9) appears as a leading digit is given by \log_{10}(1+1/d). This ... More

Metric spaces with subexponential asymptotic dimension growthAug 16 2011We prove that a metric space with subexponential asymptotic dimension growth has Yu's property A.

A functional analysis proof of Gromov's polynomial growth theoremOct 14 2015Oct 27 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

Solid von Neumann AlgebrasFeb 10 2003Feb 24 2003We prove that the relative commutant of a diffuse von Neumann subalgebra in a hyperbolic group von Neumann algebra is always injective. It follows that any non-injective subfactor in a hyperbolic group von Neumann algebra is non-Gamma and prime. The proof ... More

A note on non-amenability of B(\ell_p) for p=1,2Jan 12 2004This is an expository note on non-amenabilty of the Banach algebra B(\ell_p) for p=1,2. These were proved respectively by Connes (p=2) and Read (p=1) via very different methods. We give a single proof which reproves both.

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

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

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

A Kurosh type theorem for type II_1 factorsJan 12 2004Dec 21 2007We prove a Kurosh type theorem for free-product type II_1 factors. In particular, if M = LF_2 \otimes R, then the free-product type II_1 factors M*...*M are all prime and pairwise non-isomorphic. This paper is a continuation of [N. Ozawa, Solid von Neumann ... 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

Constant terms of Eisenstein series over a totally real fieldOct 27 2014In this paper, we compute constant terms of Eisenstein series defined over a totally real field, at various cusps. In his paper published in 2003, M. Ohta computed the constant terms of Eisenstein series of weight two over the field of rational numbers, ... More

About the Connes Embedding Conjecture---Algebraic approaches---Dec 07 2012Feb 18 2013This is an expanded lecture note for "Masterclass on sofic groups and applications to operator algebras" (University of Copenhagen, 5-9 November 2012). It is about algebraic aspects of the Connes Embedding Conjecture. It contains new proofs of equivalence ... 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

Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three DimensionsDec 15 2016Mar 15 2017Three-dimensional random electron systems undergo quantum phase transitions and show rich phase diagrams. Examples of the phases are the band gap insulator, Anderson insulator, strong and weak topological insulators, Weyl semimetal, and diffusive metal. ... More

Topology of the regular part for infinitely renormalizable quadratic polynomialsJun 28 2007In this paper we describe the well studied process of renormalization of quadratic polynomials from the point of view of their natural extensions. In particular, we describe the topology of the inverse limit of infinitely renormalizable quadratic polynomials ... More

Comment on "Proof of Heisenberg's error-disturbance principle"May 19 2015Recently, Kosugi [arXiv:1504.03779v2 [quant-ph]] argued that Heisenberg's error-disturbance relation (EDR) must be interpreted as being between the resolution, the preparational error for the post-measurement observable, and the disturbance. He further ... More

Error-disturbance relations in mixed statesApr 13 2014Heisenberg's uncertainty principle was originally formulated in 1927 as a quantitative relation between the "mean error" of a measurement of one observable and the disturbance thereby caused on another observable. Heisenberg derived this famous relation ... More

Quantum Reality and Measurement: A Quantum Logical ApproachNov 05 2009May 03 2010The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring apparatus can ... More

Uncertainty principle for quantum instruments and computingOct 11 2003Aug 11 2004Recently, universally valid uncertainty relations have been established to set a precision limit for any instruments given a disturbance constraint in a form more general than the one originally proposed by Heisenberg. One of them leads to a quantitative ... More

Closed incompressible surfaces in the complements of positive knotsApr 24 2001We show that any closed incompressible surface in the complement of a positive knot is algebraically non-split from the knot, positive knots cannot bound non-free incompressible Seifert surfaces and that the splitability and the primeness of positive ... More

Measurability and ComputabilitySep 16 1998The conceptual relation between the measurability of quantum mechanical observables and the computability of numerical functions is re-examined. A new formulation is given for the notion of measurability with finite precision in order to reconcile the ... More