8,943 research outputs found
A model for conservative chaos constructed from multi-component Bose-Einstein condensates with a trap in 2 dimensions
To show a mechanism leading to the breakdown of a particle picture for the
multi-component Bose-Einstein condensates(BECs) with a harmonic trap in high
dimensions, we investigate the corresponding 2- nonlinear Schr{\"o}dinger
equation (Gross-Pitaevskii equation) with use of a modified variational
principle. A molecule of two identical Gaussian wavepackets has two degrees of
freedom(DFs), the separation of center-of-masses and the wavepacket width.
Without the inter-component interaction(ICI) these DFs show independent regular
oscillations with the degenerate eigen-frequencies. The inclusion of ICI
strongly mixes these DFs, generating a fat mode that breaks a particle picture,
which however can be recovered by introducing a time-periodic ICI with zero
average. In case of the molecule of three wavepackets for a three-component
BEC, the increase of amplitude of ICI yields a transition from regular to
chaotic oscillations in the wavepacket breathing.Comment: 5 pages, 4 figure
Instanton classical solutions of SU(3) fixed point actions on open lattices
We construct instanton-like classical solutions of the fixed point action of
a suitable renormalization group transformation for the SU(3) lattice gauge
theory. The problem of the non-existence of one-instantons on a lattice with
periodic boundary conditions is circumvented by working on open lattices. We
consider instanton solutions for values of the size (0.6-1.9 in lattice units)
which are relevant when studying the SU(3) topology on coarse lattices using
fixed point actions. We show how these instanton configurations on open
lattices can be taken into account when determining a few-couplings
parametrization of the fixed point action.Comment: 23 pages, LaTeX, 4 eps figures, epsfig.sty; some comments adde
Structural instability of vortices in Bose-Einstein condensates
In this paper we study a gaseous Bose-Einstein condensate (BEC) and show
that: (i) A minimum value of the interaction is needed for the existence of
stable persistent currents. (ii) Vorticity is not a fundamental invariant of
the system, as there exists a conservative mechanism which can destroy a vortex
and change its sign. (iii) This mechanism is suppressed by strong interactions.Comment: 4 pages with 3 figures. Submitted to Phys. Rev. Let
Exact renormalization in quantum spin chains
We introduce a real-space exact renormalization group method to find exactly
solvable quantum spin chains and their ground states. This method allows us to
provide a complete list for exact solutions within SU(2) symmetric quantum spin
chains with and nearest-neighbor interactions, as well as examples
with S=5. We obtain two classes of solutions: One of them converges to the
fixed points of renormalization group and the ground states are matrix product
states. Another one does not have renormalization fixed points and the ground
states are partially ferromagnetic states.Comment: 8 pages, 5 figures, references added, published versio
Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex
The locality conditions for the vanishing of local anomalies in field theory
are shown to admit a geometrical interpretation in terms of local equivariant
cohomology, thus providing a method to deal with the problem of locality in the
geometrical approaches to the study of local anomalies based on the
Atiyah-Singer index theorem. The local cohomology is shown to be related to the
cohomology of jet bundles by means of the variational bicomplex theory. Using
these results and the techniques for the computation of the cohomology of
invariant variational bicomplexes in terms of relative Gel'fand-Fuks cohomology
introduced in [6], we obtain necessary and sufficient conditions for the
cancellation of local gravitational and mixed anomalies.Comment: 36 pages. The paper is divided in two part
Random Unitaries Give Quantum Expanders
We show that randomly choosing the matrices in a completely positive map from
the unitary group gives a quantum expander. We consider Hermitian and
non-Hermitian cases, and we provide asymptotically tight bounds in the
Hermitian case on the typical value of the second largest eigenvalue. The key
idea is the use of Schwinger-Dyson equations from lattice gauge theory to
efficiently compute averages over the unitary group.Comment: 14 pages, 1 figur
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