Spectrum of bound fermion states on vortices in 3^3He-B

We study subgap spectra of fermions localized within vortex cores in $^3$He-B. We develop an analytical treatment of the low-energy states and consider the characteristic properties of fermion spectra for different types of vortices. Due to the removed spin degeneracy the spectra of all singly quantized vortices consist of two different anomalous branches crossing the Fermi level. For singular $o$ and $u$ vortices the anomalous branches are similar to the standard Caroli-de Gennes -Matricon ones and intersect the Fermi level at zero angular momentum yet with different slopes corresponding to different spin states. On the contrary the spectral branches of nonsingular vortices intersect the Fermi level at finite angular momenta which leads to the appearance of a large number of zero modes, i.e. energy states at the Fermi level. Considering the $v$, $w$ and $uvw$ vortices with superfluid cores we show that the number of zero modes is proportional to the size of the vortex core.Comment: 6 pages, 1 figur

Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation

Directed graphs (DG), interpreted as state transition diagrams, are traditionally used to represent finite-state automata (FSA). In the context of formal languages, both FSA and regular expressions (RE) are equivalent in that they accept and generate, respectively, type-3 (regular) languages. Based on our previous work, this paper analyzes effects of graph manipulations on corresponding RE. In this present, starting stage we assume that the DG under consideration contains no cycles. Graph manipulation is performed by deleting or inserting of nodes or arcs. Combined and/or multiple application of these basic operators enable a great variety of transformations of DG (and corresponding RE) that can be seen as mutants of the original DG (and corresponding RE). DG are popular for modeling complex systems; however they easily become intractable if the system under consideration is complex and/or large. In such situations, we propose to switch to corresponding RE in order to benefit from their compact format for modeling and algebraic operations for analysis. The results of the study are of great potential interest to mutation testing

On the effect of variable identification on the essential arity of functions

We show that every function of several variables on a finite set of k elements with n>k essential variables has a variable identification minor with at least n-k essential variables. This is a generalization of a theorem of Salomaa on the essential variables of Boolean functions. We also strengthen Salomaa's theorem by characterizing all the Boolean functions f having a variable identification minor that has just one essential variable less than f.Comment: 10 page

Fermions on half-quantum vortex

The spectrum of the fermion zero modes in the vicinity of the vortex with fractional winding number is discussed. This is inspired by the observation of the 1/2 vortex in high-temperature superconductors (Kirtley, et al, Phys. Rev. Lett. 76 (1996) 1336). The fractional value of the winding number leads to the fractional value of the invariant, which describes the topology of the energy spectrum of fermions. This results in the phenomenon of the "half-crossing": the spectrum approaches zero but does not cross it, being captured at the zero energy level. The similarity with the phenomenon of the fermion condensation is discussed.Comment: In revised version the discussion is extended and 4 references are added. The paper is accepted for publication in JETP Letters. 10 pages, LaTeX file, 3 figures are available at ftp://boojum.hut.fi/pub/publications/lowtemp/LTL-96004.p

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

How to create Alice string (half-quantum vortex) in a vector Bose-Einstein condensate

We suggest a procedure how to prepare the vortex with N=1/2 winding number -- the counterpart of the Alice string -- in a Bose--Einstein condensate with hyperfine spin F=1. Other possible vortices in Bose-condensates are also discussed.Comment: RevTex file, 3 pages, no figures, extended version submitted to JETP Letter

Comment on Vortex Mass and Quantum Tunneling of Vortices

Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov qiasiparticles localized in the core. These bound states form the normal component which is nonzero even in the low temperature limit. In the collisionless regime $\omega_0\tau \gg 1$, the normal component trapped by the vortex is unbound from the normal component in the bulk superfluid/superconductors and adds to the inertial mass of the moving vortex. In the d-wave superconductors, the vortex mass has an additional factor $(B_{c2}/B)^{1/2}$ due to the gap nodes.Comment: 10 pages, no figures, version accepted in JETP Letter

Singular Vortex in Narrow Cylinders of Superfluid 3He-A Phase

Motivated by the on-going rotating cryostat experiments in ISSP, Univ. of Tokyo, we explore the textures and vortices in superfluid 3He-A phase confined in narrow cylinders, whose radii are R=50mum and 115mum. The calculations are based on the Ginzburg-Landau (GL) framework, which fully takes into account the orbital (l-vector) and spin (d-vector) degrees of freedom for chiral p-wave pairing superfluid. The GL free energy functional is solved numerically by using best known GL parameters appropriate for the actual experimental situations at P=3.2MPa and H=21.6mT. We identify the ground state l-vector configuration as radial disgyration (RD) texture with the polar core both at rest and low rotations and associated d-vector textures for both narrow cylinder systems under high magnetic fields. The RD which has a singularity at center, changes into Mermin-Ho texture above the critical rotation speed which is determined precisely, providing an experimental check for own proposal.Comment: 22 pages, 12 figure

Topological superfluid 3^3He-B: fermion zero modes on interfaces and in the vortex core

Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, topology allows us to determine generic features of their fermionic spectrum, which are robust to perturbation and interaction. We discuss the nodeless 3D system, such as superfluid $^3$He-B, vacuum of Dirac fermions, and relativistic singlet and triplet supercondutors which may arise in quark matter. The systems, which have nonzero value of topological invariant, have gapless fermions on the boundary and in the core of quantized vortices. We discuss the index theorem which relates fermion zero modes on vortices with the topological invariants in combined momentum and coordinate space.Comment: paper is prepared for Proceedings of the Workshop on Vortices, Superfluid Dynamics, and Quantum Turbulence held on 11-16 April 2010, Lammi, Finlan

Generation of ultra-short light pulses by a rapidly ionizing thin foil

A thin and dense plasma layer is created when a sufficiently strong laser pulse impinges on a solid target. The nonlinearity introduced by the time-dependent electron density leads to the generation of harmonics. The pulse duration of the harmonic radiation is related to the risetime of the electron density and thus can be affected by the shape of the incident pulse and its peak field strength. Results are presented from numerical particle-in-cell-simulations of an intense laser pulse interacting with a thin foil target. An analytical model which shows how the harmonics are created is introduced. The proposed scheme might be a promising way towards the generation of attosecond pulses. PACS number(s): 52.40.Nk, 52.50.Jm, 52.65.RrComment: Second Revised Version, 13 pages (REVTeX), 3 figures in ps-format, submitted for publication to Physical Review E, WWW: http://www.physik.tu-darmstadt.de/tqe