Asymptotic Inverse Problem for Almost-Periodically Perturbed Quantum Harmonic Oscillator

Consider quantum harmonic oscillator, perturbed by an even almost-periodic complex-valued potential with bounded derivative and primitive. Suppose that we know the first correction to the spectral asymptotics $\{\Delta\mu_n\}_{n=0}^\infty$ ($\Delta\mu_n=\mu_n-\mu_n^0+o(n^{-1/4})$, where $\mu_n^0$ and $\mu_n$ is the spectrum of the unperturbed and the perturbed operators, respectively). We obtain the formula that recovers the frequencies and the Fourier coefficients of the perturbation.Comment: 6 page

Topological Quantum Computing with p-Wave Superfluid Vortices

It is shown that Majorana fermions trapped in three vortices in a p-wave superfluid form a qubit in a topological quantum computing (TQC). Several similar ideas have already been proposed: Ivanov [Phys. Rev. Lett. {\bf 86}, 268 (2001)] and Zhang {\it et al.} [Phys. Rev. Lett. {\bf 99}, 220502 (2007)] have proposed schemes in which a qubit is implemented with two and four Majorana fermions, respectively, where a qubit operation is performed by exchanging the positions of Majorana fermions. The set of gates thus obtained is a discrete subset of the relevant unitary group. We propose, in this paper, a new scheme, where three Majorana fermions form a qubit. We show that continuous 1-qubit gate operations are possible by exchanging the positions of Majorana fermions complemented with dynamical phase change. 2-qubit gates are realized through the use of the coupling between Majorana fermions of different qubits.Comment: 5 pages, 2 figures. Two-qubit gate implementation is added

Vortex arrays for sinh-Poisson equation of two-dimensional fluids: Equilibria and stability

The sinh-Poisson equation describes a stream function configuration of a stationary two-dimensional (2D) Euler flow. We study two classes of its exact solutions for doubly periodic domains (or doubly periodic vortex arrays in the plane). Both types contain vortex dipoles of different configurations, an elongated "cat-eye" pattern, and a "diagonal" (symmetric) configuration. We derive two new solutions, one for each class. The first one is a generalization of the Mallier-Maslowe vortices, while the second one consists of two corotating vortices in a square cell. Next, we examine the dynamic stability of such vortex dipoles to initial perturbations, by numerical simulations of the 2D Euler flows on periodic domains. One typical member from each class is chosen for analysis. The diagonally symmetric equilibrium maintains stability for all (even strong) perturbations, whereas the cat-eye pattern relaxes to a more stable dipole of the diagonal type. © 2004 American Institute of Physics.published_or_final_versio

One Dimensional Gas of Bosons with Feshbach Resonant Interactions

We present a study of a gas of bosons confined in one dimension with Feshbach resonant interactions, at zero temperature. Unlike the gas of one dimensional bosons with non-resonant interactions, which is known to be equivalent to a system of interacting spinless fermions and can be described using the Luttinger liquid formalism, the resonant gas possesses novel features. Depending on its parameters, the gas can be in one of three possible regimes. In the simplest of those, it can still be described by the Luttinger liquid theory, but its Fermi momentum cannot be larger than a certain cutoff momentum dependent on the details of the interactions. In the other two regimes, it is equivalent to a Luttinger liquid at low density only. At higher densities its excitation spectrum develops a minimum, similar to the roton minimum in helium, at momenta where the excitations are in resonance with the Fermi sea. As the density of the gas is increased further, the minimum dips below the Fermi energy, thus making the ground state unstable. At this point the standard ground state gets replaced by a more complicated one, where not only the states with momentum below the Fermi points, but also the ones with momentum close to that minimum, get filled, and the excitation spectrum develops several branches. We are unable so far to study this new regime in detail due to the lack of the appropriate formalism.Comment: 20 pages, 18 figure

Magnon Localization in Mattis Glass

We study the spectral and transport properties of magnons in a model of a disordered magnet called Mattis glass, at vanishing average magnetization. We find that in two dimensional space, the magnons are localized with the localization length which diverges as a power of frequency at small frequencies. In three dimensional space, the long wavelength magnons are delocalized. In the delocalized regime in 3d (and also in 2d in a box whose size is smaller than the relevant localization length scale) the magnons move diffusively. The diffusion constant diverges at small frequencies. However, the divergence is slow enough so that the thermal conductivity of a Mattis glass is finite, and we evaluate it in this paper. This situation can be contrasted with that of phonons in structural glasses whose contribution to thermal conductivity is known to diverge (when inelastic scattering is neglected).Comment: 11 page

Feshbach molecule production in fermionic atomic gases

This paper examines the problem of molecule production in an atomic fermionic gas close to an s-wave Feshbach resonance by means of a magnetic field sweep through the resonance. The density of molecules at the end of the process is derived for narrow resonance and slow sweep.Comment: 4 page

Non-adiabacity and large flucutations in a many particle Landau Zener problem

We consider the behavior of an interacting many particle system under slow external driving -- a many body generalization of the Landau-Zener paradigm. We find that a conspiracy of interactions and driving leads to physics profoundly different from that of the single particle limit: for practically all values of the driving rate the particle distributions in Hilbert space are very broad, a phenomenon caused by a strong amplification of quantum fluctuations in the driving process. These fluctuations are 'non-adiabatic' in that even at very slow driving it is exceedingly difficult to push the center of the distribution towards the limit of full ground state occupancy. We obtain these results by a number of complementary theoretical approaches, including diagrammatic perturbation theory, semiclassical analysis, and exact diagonalization.Comment: 25 pages, 16 figure

Non-unitary Conformal Field Theory and Logarithmic Operators for Disordered Systems

We consider the supersymmetric approach to gaussian disordered systems like the random bond Ising model and Dirac model with random mass and random potential. These models appeared in particular in the study of the integer quantum Hall transition. The supersymmetric approach reveals an osp(2/2)_1 affine symmetry at the pure critical point. A similar symmetry should hold at other fixed points. We apply methods of conformal field theory to determine the conformal weights at all levels. These weights can generically be negative because of non-unitarity. Constraints such as locality allow us to quantize the level k and the conformal dimensions. This provides a class of (possibly disordered) critical points in two spatial dimensions. Solving the Knizhnik-Zamolodchikov equations we obtain a set of four-point functions which exhibit a logarithmic dependence. These functions are related to logarithmic operators. We show how all such features have a natural setting in the superalgebra approach as long as gaussian disorder is concerned.Comment: Latex, 20 pages, one figure. Version accepted for publication in Nuclear Physics B, minor correction

Single particle Green's functions and interacting topological insulators

We study topological insulators characterized by the integer topological invariant Z, in even and odd spacial dimensions. These are well understood in case when there are no interactions. We extend the earlier work on this subject to construct their topological invariants in terms of their Green's functions. In this form, they can be used even if there are interactions. Specializing to one and two spacial dimensions, we further show that if two topologically distinct topological insulators border each other, the difference of their topological invariants is equal to the difference between the number of zero energy boundary excitations and the number of zeroes of the Green's function at the boundary. In the absence of interactions Green's functions have no zeroes thus there are always edge states at the boundary, as is well known. In the presence of interactions, in principle Green's functions could have zeroes. In that case, there could be no edge states at the boundary of two topological insulators with different topological invariants. This may provide an alternative explanation to the recent results on one dimensional interacting topological insulators.Comment: 16 pages, 2 figure

Scaling fields in the two-dimensional abelian sandpile model

We consider the isotropic two-dimensional abelian sandpile model from a perspective based on two-dimensional (conformal) field theory. We compute lattice correlation functions for various cluster variables (at and off criticality), from which we infer the field-theoretic description in the scaling limit. We find a perfect agreement with the predictions of a c=-2 conformal field theory and its massive perturbation, thereby providing direct evidence for conformal invariance and more generally for a description in terms of a local field theory. The question of the height 2 variable is also addressed, with however no definite conclusion yet.Comment: 22 pages, 1 figure (eps), uses revte