The Structure on Invariant Measures of C1C^1 generic diffeomorphisms

Let $\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism f\in\Diff(M). We show that the space of invariant measures supported on $\Lambda$ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in $\Lambda$ (which implies the set of irregular$^+$ points is also residual in $\Lambda$). As an application, we show that the non-uniform hyperbolicity of irregular$^+$ points in $\Lambda$ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in $\Lambda$) determines the uniform hyperbolicity of $\Lambda$

Near-Infrared Coronagraphic Observations of the T Tauri Binary System UY Aur

We present a near-infrared image of UY Aur, a 0.9" separated binary system, using the Coronagraphic Imager with Adaptive Optics on the Subaru Telescope. Thanks to adaptive optics, the spatial resolution of our image was ~0.1" in the full width at half maximum of the point spread function, the highest achieved. By comparison with previous measurements, we estimated that the orbital period is ~1640 yrs and the total mass of the binary is ~1.73 solar mass. The observed H-band magnitude of the secondary varies by as much as 1.3 mag within a decade, while that of the primary is rather stable. This inconstancy may arise from photospheric variability caused by an uneven accretion rate or from the rotation of the secondary. We detected a half-ring shaped circumbinary disk around the binary with a bright southwest part but a barely detectable northeast portion. The brightness ratio is ~57. Its inner radius and inclination are about 520 AU and 42, respectively. The disk is not uniform but has remarkable features, including a clumpy structure along the disk, circumstellar material inside the inner cavity, and an extended armlike structure. The circumstellar material inside the cavity probably corresponds to a clump or material accreting from the disk onto the binary. The armlike structure is a part of the disk, created by the accretion from the outer region of the disk or encounters with other stellar systems.Comment: 16 pages, 6 figures; accepted for publication in A

Relation between Vortex core charge and Vortex Bound States

Spatially inhomogeneous electron distribution around a single vortex is discussed on the basis of the Bogoliubov-de Gennes theory. The spatial structure and temperature dependence of the electron density around the vortex are presented. A relation between the vortex core charge and the vortex bound states (or the Caroli-de Gennes-Matricon states) is pointed out. Using the scanning tunneling microscope, information on the vortex core charge can be extracted through this relation.Comment: 5 pages, 3 figures; minor changes; Version to appear in JPSJ 67, No.10, 199

Quantum-secure message authentication via blind-unforgeability

Formulating and designing unforgeable authentication of classical messages in the presence of quantum adversaries has been a challenge, as the familiar classical notions of unforgeability do not directly translate into meaningful notions in the quantum setting. A particular difficulty is how to fairly capture the notion of "predicting an unqueried value" when the adversary can query in quantum superposition. In this work, we uncover serious shortcomings in existing approaches, and propose a new definition. We then support its viability by a number of constructions and characterizations. Specifically, we demonstrate a function which is secure according to the existing definition by Boneh and Zhandry, but is clearly vulnerable to a quantum forgery attack, whereby a query supported only on inputs that start with 0 divulges the value of the function on an input that starts with 1. We then propose a new definition, which we call "blind-unforgeability" (or BU.) This notion matches "intuitive unpredictability" in all examples studied thus far. It defines a function to be predictable if there exists an adversary which can use "partially blinded" oracle access to predict values in the blinded region. Our definition (BU) coincides with standard unpredictability (EUF-CMA) in the classical-query setting. We show that quantum-secure pseudorandom functions are BU-secure MACs. In addition, we show that BU satisfies a composition property (Hash-and-MAC) using "Bernoulli-preserving" hash functions, a new notion which may be of independent interest. Finally, we show that BU is amenable to security reductions by giving a precise bound on the extent to which quantum algorithms can deviate from their usual behavior due to the blinding in the BU security experiment.Comment: 23+9 pages, v3: published version, with one theorem statement in the summary of results correcte

Site-selective nuclear magnetic relaxation time in a superconducting vortex state

The temperature and field dependences of the site-selective nuclear spin relaxation time T_1 around vortices are studied comparatively both for s-wave and d-wave superconductors, based on the microscopic Bogoliubov-de Gennes theory. Reflecting low energy electronic excitations associated with the vortex core, the site selective temperature dependences deviate from those of the zero-field case, and T_1 becomes faster with approaching the vortex core. In the core region, T_1^{-1} has a new peak below the superconducting transition temperature T_c. The field dependence of the overall T_1(T) behaviors for s-wave and d-wave superconductors is investigated and analyzed in terms of the local density of states. The NMR study by the resonance field dependence may be a new method to probe the spatial resolved vortex core structure in various conventional and unconventional superconductors.Comment: 14Pages, 26 figures, revte

Local density of states in the vortex lattice in a type II superconductor

Local density of states (LDOS) in the triangular vortex lattice is investigated based on the quasi-classical Eilenberger theory. We consider the case of an isotropic s-wave superconductor with the material parameter appropriate to NbSe_2. At a weak magnetic field, the spatial variation of the LDOS shows cylindrical structure around a vortex core. On the other hand, at a high field where the core regions substantially overlap each other, the LDOS is sixfold star-shaped structure due to the vortex lattice effect. The orientation of the star coincides with the experimental data of the scanning tunneling microscopy. That is, the ray of the star extends toward the nearest-neighbor (next nearest-neighbor) vortex direction at higher (lower) energy.Comment: 10 pages, RevTex, 32 figure

On centralizer algebras for spin representations

We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be described in terms of non-standard q-deformations of orthogonal Lie algebras; in the odd-dimensional case only a certain subalgebra will appear. In the classical case q = 1 the relations boil down to Lie algebra relations

Attacks on quantum key distribution protocols that employ non-ITS authentication

We demonstrate how adversaries with unbounded computing resources can break Quantum Key Distribution (QKD) protocols which employ a particular message authentication code suggested previously. This authentication code, featuring low key consumption, is not Information-Theoretically Secure (ITS) since for each message the eavesdropper has intercepted she is able to send a different message from a set of messages that she can calculate by finding collisions of a cryptographic hash function. However, when this authentication code was introduced it was shown to prevent straightforward Man-In-The-Middle (MITM) attacks against QKD protocols. In this paper, we prove that the set of messages that collide with any given message under this authentication code contains with high probability a message that has small Hamming distance to any other given message. Based on this fact we present extended MITM attacks against different versions of BB84 QKD protocols using the addressed authentication code; for three protocols we describe every single action taken by the adversary. For all protocols the adversary can obtain complete knowledge of the key, and for most protocols her success probability in doing so approaches unity. Since the attacks work against all authentication methods which allow to calculate colliding messages, the underlying building blocks of the presented attacks expose the potential pitfalls arising as a consequence of non-ITS authentication in QKD-postprocessing. We propose countermeasures, increasing the eavesdroppers demand for computational power, and also prove necessary and sufficient conditions for upgrading the discussed authentication code to the ITS level.Comment: 34 page