Response functions of an artificial Anderson atom in the atomic limit

We consider the spin and pseudospin (charge) response functions of the exactly soluble Anderson atom model. We demonstrate, in particular, that a deviation from the magnetic Curie-law behaviour, appropriate for a free spin one-half, increases with increasing asymmetry and temperature. In general, oscillator strength is transferred from the spin degrees of freedom to the pseudospin modes. We also consider the negative-U Anderson atom and demonstrate that the pseudospin modes are the relevant low-energy excitations in this case. Especially, the roles of the spin and charge excitations are interchanged upon reversal of the intrasite Coulomb repulsion, U.Comment: 23 pages, 12 figures. Accepted for publication in J. Low Temp. Phy

Internal Magnus effects in superfluid 3A

Orbital angular momentum of the coherently aligned Cooper pairs in superfluid 3A is encountered by an object immersed in the condensate. We evaluate the associated quasiparticle-scattering asymmetry experienced by a negative ion; this leads to a measureable, purely quantum-mechanical reactive force deflecting the ion’s trajectory. Possible hydrodynamic Magnus effects are also discussed.Peer reviewe

Quantum, Stochastic, and Pseudo Stochastic Languages with Few States

Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers. More general computational models over the same field such as generalized finite automata (GFAs) and quantum finite automata (QFAs) define the same class. In 1963, Rabin proved the set of stochastic languages to be uncountable presenting a single 2-state PFA over the binary alphabet recognizing uncountably many languages depending on the cutpoint. In this paper, we show the same result for unary stochastic languages. Namely, we exhibit a 2-state unary GFA, a 2-state unary QFA, and a family of 3-state unary PFAs recognizing uncountably many languages; all these numbers of states are optimal. After this, we completely characterize the class of languages recognized by 1-state GFAs, which is the only nontrivial class of languages recognized by 1-state automata. Finally, we consider the variations of PFAs, QFAs, and GFAs based on the notion of inclusive/exclusive cutpoint, and present some results on their expressive power.Comment: A new version with new results. Previous version: Arseny M. Shur, Abuzer Yakaryilmaz: Quantum, Stochastic, and Pseudo Stochastic Languages with Few States. UCNC 2014: 327-33

Half-Quantum Vortices in Thin Film of Superfluid 3^3He

Stability of a half-quantum vortex (HQV) in superfluid $^3$He has been discussed recently by Kawakami, Tsutsumi and Machida in Phys. Rev. B {\bf 79}, 092506 (2009). We further extend this work here and consider the A$_2$ phase of superfluid $^3$He confined in thin slab geometry and analyze the HQV realized in this setting. Solutions of HQV and singly quantized singular vortex are evaluated numerically by solving the Ginzburg-Landau (GL) equation and respective first critical angular velocities are obtained by employing these solutions. We show that the HQV in the A$_2$ phase is stable near the boundary between the A$_2$ and A$_1$ phases. It is found that temperature and magnetic field must be fixed first in the stable region and subsequently the angular velocity of the system should be increased from zero to a sufficiently large value to create a HQV with sufficiently large probability. A HQV does not form if the system starts with a fixed angular velocity and subsequently the temperature is lowered down to the A$_2$ phase. It is estimated that the external magnetic field with strength on the order of 1 T is required to have a sufficiently large domain in the temperature-magnetic field phase diagram to have a stable HQV.Comment: 5 pages, 5 figure

Unconventional Vortices and Phase Transitions in Rapidly Rotating Superfluid ^{3}He

This paper studies vortex-lattice phases of rapidly rotating superfluid ^3He based on the Ginzburg-Landau free-energy functional. To identify stable phases in the p-Omega plane (p: pressure; Omega: angular velocity), the functional is minimized with the Landau-level expansion method using up to 3000 Landau levels. This system can sustain various exotic vortices by either (i) shifting vortex cores among different components or (ii) filling in cores with components not used in the bulk. In addition, the phase near the upper critical angular velocity Omega_{c2} is neither the A nor B phases, but the polar state with the smallest superfluid density as already shown by Schopohl. Thus, multiple phases are anticipated to exist in the p-Omega plane. Six different phases are found in the present calculation performed over 0.0001 Omega_{c2} <= Omega <= Omega_{c2}, where Omega_{c2} is of order (1- T/T_c) times 10^{7} rad/s. It is shown that the double-core vortex experimentally found in the B phase originates from the conventional hexagonal lattice of the polar state near Omega_{c2} via (i) a phase composed of interpenetrating polar and Scharnberg-Klemm sublattices; (ii) the A-phase mixed-twist lattice with polar cores; (iii) the normal-core lattice found in the isolated-vortex calculation by Ohmi, Tsuneto, and Fujita; and (iv) the A-phase-core vortex discovered in another isolated-vortex calculation by Salomaa and Volovik. It is predicted that the double-core vortex will disappear completely in the experimental p-T phase diagram to be replaced by the A-phase-core vortex for Omega >~ 10^{3} ~ 10^{4} rad/s. C programs to minimize a single-component Ginzburg-Landau functional are available at {http://phys.sci.hokudai.ac.jp/~kita/index-e.html}.Comment: 13 pages, 9 figure

Fermion zero modes at the boundary of superfluid 3He-B

Superfluid 3He-B belongs to the important special class of time-reversal invariant topological superfluids. It has Majorana fermions as edge states on the surface of bulk 3He-B. On the rough wall these fermion zero modes have finite density of states at E=0. It is possible that Lancaster experiments with a wire vibrating in 3He-B have already probed Majorana fermions living on the surface of the wire.Comment: 4 pages, no Figures, JETP Letters style, version to be published in JETP Letter

Quantum circuits with uniformly controlled one-qubit gates

Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single diagonal n-qubit gate. The circuit is based on the so-called quantum multiplexor, for which we provide a modified construction. We illustrate the versatility of these gates by applying them to the decomposition of a general n-qubit gate and a local state preparation procedure. Moreover, we study their implementation using only nearest-neighbor gates. We give upper bounds for the one-qubit and controlled-NOT gate counts for all the aforementioned applications. In all four cases, the proposed circuit topologies either improve on or achieve the previously reported upper bounds for the gate counts. Thus, they provide the most efficient method for general gate decompositions currently known.Comment: 8 pages, 10 figures. v2 has simpler notation and sharpens some result

Stability of multi-electron bubbles in liquid helium

The stability of multi-electron bubbles in liquid helium is investigated theoretically. We find that multi-electron bubbles are unstable against fission whenever the pressure is positive. It is shown that for moving bubbles the Bernoulli effect can result in a range of pressures over which the bubbles are stable.Comment: 7 pages, 5 figure

Resonant Tunneling through Multi-Level and Double Quantum Dots

We study resonant tunneling through quantum-dot systems in the presence of strong Coulomb repulsion and coupling to the metallic leads. Motivated by recent experiments we concentrate on (i) a single dot with two energy levels and (ii) a double dot with one level in each dot. Each level is twofold spin-degenerate. Depending on the level spacing these systems are physical realizations of different Kondo-type models. Using a real-time diagrammatic formulation we evaluate the spectral density and the non-linear conductance. The latter shows a novel triple-peak resonant structure.Comment: 4 pages, ReVTeX, 4 Postscript figure