17,954 research outputs found
Gluino zero-modes for non-trivial holonomy calorons
We couple fermion fields in the adjoint representation (gluinos) to the SU(2)
gauge field of unit charge calorons defined on R^3 x S_1. We compute
corresponding zero-modes of the Dirac equation. These are relevant in
semiclassical studies of N=1 Super-symmetric Yang-Mills theory. Our formulas,
show that, up to a term proportional to the vector potential, the modes can be
constructed by different linear combinations of two contributions adding up to
the total caloron field strength.Comment: 17 pages, 3 Postscript figures, late
Undecidability of the Spectral Gap
We construct families of translationally-invariant, nearest-neighbour
Hamiltonians on a 2D square lattice of d-level quantum systems (d constant), for which determining whether the system is gapped or gapless is an
undecidable problem. This is true even with the promise that each Hamiltonian is either gapped or gapless in the strongest sense: it is promised to either
have continuous spectrum above the ground state in the thermodynamic limit,
or its spectral gap is lower-bounded by a constant. Moreover, this constant
can be taken equal to the operator norm of the local operator that generates
the Hamiltonian (the local interaction strength). The result still holds true if
one restricts to arbitrarily small quantum perturbations of classical Hamiltonians. The proof combines a robustness analysis of Robinson’s aperiodic
tiling, together with tools from quantum information theory: the quantum
phase estimation algorithm and the history state technique mapping Quantum
Turing Machines to Hamiltonians
Improved superposition schemes for approximate multi-caloron configurations
Two improved superposition schemes for the construction of approximate
multi-caloron-anticaloron configurations, using exact single (anti)caloron
gauge fields as underlying building blocks, are introduced in this paper. The
first improvement deals with possible monopole-Dirac string interactions
between different calorons with non-trivial holonomy. The second one, based on
the ADHM formalism, improves the (anti-)selfduality in the case of small
caloron separations. It conforms with Shuryak's well-known ratio-ansatz when
applied to instantons. Both superposition techniques provide a higher degree of
(anti-)selfduality than the widely used sum-ansatz, which simply adds the
(anti)caloron vector potentials in an appropriate gauge. Furthermore, the
improved configurations (when discretized onto a lattice) are characterized by
a higher stability when they are exposed to lattice cooling techniques.Comment: New version accepted for publication in Nucl. Phys. B. Text partly
shortened, changes in the introduction, new results added on the comparison
with exact solution
Numerical study of Yang-Mills classical solutions on the twisted torus
We use the lattice cooling method to investigate the structure of some gauge
fixed SU(2) Yang-Mills classical solutions of the euclidean equations of motion
which are defined in the 3-torus with symmetric twisted boundary conditions.Comment: 20pp (fig.included
Fundamental limitations in the purifications of tensor networks
We show a fundamental limitation in the description of quantum many-body
mixed states with tensor networks in purification form. Namely, we show that
there exist mixed states which can be represented as a translationally
invariant (TI) matrix product density operator (MPDO) valid for all system
sizes, but for which there does not exist a TI purification valid for all
system sizes. The proof is based on an undecidable problem and on the
uniqueness of canonical forms of matrix product states. The result also holds
for classical states.Comment: v1: 11 pages, 1 figure. v2: very minor changes. About to appear in
Journal of Mathematical Physic
Assessing non-Markovian dynamics
We investigate what a snapshot of a quantum evolution - a quantum channel
reflecting open system dynamics - reveals about the underlying continuous time
evolution. Remarkably, from such a snapshot, and without imposing additional
assumptions, it can be decided whether or not a channel is consistent with a
time (in)dependent Markovian evolution, for which we provide computable
necessary and sufficient criteria. Based on these, a computable measure of
`Markovianity' is introduced. We discuss how the consistency with Markovian
dynamics can be checked in quantum process tomography. The results also clarify
the geometry of the set of quantum channels with respect to being solutions of
time (in)dependent master equations.Comment: 5 pages, RevTex, 2 figures. (Except from typesetting) version to be
published in the Physical Review Letter
An Elemental Assay of Very, Extremely, and Ultra Metal-Poor Stars
We present a high-resolution elemental-abundance analysis for a sample of 23
very metal-poor (VMP; [Fe/H] < -2.0) stars, 12 of which are extremely
metal-poor (EMP; [Fe/H] < -3.0), and 4 of which are ultra metal-poor (UMP;
[Fe/H] < -4.0). These stars were targeted to explore differences in the
abundance ratios for elements that constrain the possible astrophysical sites
of element production, including Li, C, N, O, the alpha-elements, the iron-peak
elements, and a number of neutron-capture elements. This sample substantially
increases the number of known carbon-enhanced metal-poor (CEMP) and
nitrogen-enhanced metal-poor (NEMP) stars -- our program stars include eight
that are considered "normal" metal-poor stars, six CEMP-no stars, five CEMP-s
stars, two CEMP-r stars, and two CEMP-r/s stars. One of the CEMP- stars and
one of the CEMP-r/s stars are possible NEMP stars. We detect lithium for three
of the six CEMP-no stars, all of which are Li-depleted with respect to the
Spite plateau. The majority of the CEMP stars have [C/N] > 0. The stars with
[C/N] < 0 suggest a larger degree of mixing; the few CEMP-no stars that exhibit
this signature are only found at [Fe/H] < -3.4, a metallicity below which we
also find the CEMP-no stars with large enhancements in Na, Mg, and Al. We
confirm the existence of two plateaus in the absolute carbon abundances of CEMP
stars, as suggested by Spite et al. We also present evidence for a "floor" in
the absolute Ba abundances of CEMP-no stars at A(Ba)~ -2.0.Comment: 20 pages, 16 figures, Accepted for publication in Ap
Complete Characterization of the Ground Space Structure of Two-Body Frustration-Free Hamiltonians for Qubits
The problem of finding the ground state of a frustration-free Hamiltonian
carrying only two-body interactions between qubits is known to be solvable in
polynomial time. It is also shown recently that, for any such Hamiltonian,
there is always a ground state that is a product of single- or two-qubit
states. However, it remains unclear whether the whole ground space is of any
succinct structure. Here, we give a complete characterization of the ground
space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a
span of tree tensor network states of the same tree structure. This
characterization allows us to show that the problem of determining the ground
state degeneracy is as hard as, but no harder than, its classical analog.Comment: 5pages, 3 figure
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