344 research outputs found
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
(, where
and 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
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
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
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
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