5,493 research outputs found
Perturbation Theory for Singular Potentials in Quantum Mechanics
We study perturbation theory in certain quantum mechanics problems in which
the perturbing potential diverges at some points, even though the energy
eigenvalues are smooth functions of the coefficient of the potential. We
discuss some of the unusual techniques which are required to obtain
perturbative expansions of the energies in such cases. These include a
point-splitting prescription for expansions around the Dirichlet (fermionic)
limit of the -function potential, and performing a similarity
transformation to a non-Hermitian potential in the Calogero-Sutherland model.
As an application of the first technique, we study the ground state of the
-function Bose gas near the fermionic limit.Comment: LaTeX, 19 pages, no figure
Quark mass and condensate in HQCD
We extend the Sakai-Sugimoto holographic model of QCD (HQCD) by including the
scalar bi-fundamental "tachyon" field in the 8-brane-anti-8-brane probe theory.
We show that this field is responsible both for the spontaneous breaking of the
chiral symmetry, and for the generation of (current algebra) quark masses, from
the point of view of the bulk theory. As a by-product we show how this leads to
the Gell-Mann- Oakes-Renner relation for the pion mass.Comment: 23 pages, 7 figures; v2: corrected typos in eqs. (4.3), (4.4), (4.5),
(4.9) and (4.11), and corrected figures 3, 4, 5 and 6; v3: section 5.3 on the
pion mass rewritten in a clearer way, version published in JHE
Momentum modes of M5-branes in a 2d space
We study M5 branes by considering the selfdual strings parallel to a plane.
With the internal oscillation frozen, each selfdual string gives a 5d SYM
field. All selfdual strings together give a 6d field with 5 scalars, 3 gauge
degrees of freedom and 8 fermionic degrees of freedom in adjoint representation
of U(N). Selfdual strings with the same orientation have the SYM-type
interaction. For selfdual strings with the different orientations, which could
also be taken as the unparallel momentum modes of the 6d field on that plane or
the (p,q) (r,s) strings on D3 with (p,q)\neq (r,s), the [i,j]+[j,k]\rightarrow
[i,k] relation is not valid, so the coupling cannot be written in terms of the
standard N \times N matrix multiplication. 3-string junction, which is the
bound state of the unparallel [i,j] [j,k] selfdual strings, may play a role
here.Comment: 37 pages, 5 figures, to appear in JHEP; v2: reference adde
Local dynamics of topological magnetic defects in the itinerant helimagnet FeGe
Chiral magnetic interactions induce complex spin textures including helical
and conical spin waves, as well as particle-like objects such as magnetic
skyrmions and merons. These spin textures are the basis for innovative device
paradigms and give rise to exotic topological phenomena, thus being of interest
for both applied and fundamental sciences. Present key questions address the
dynamics of the spin system and emergent topological defects. Here we analyze
the micromagnetic dynamics in the helimagnetic phase of FeGe. By combining
magnetic force microscopy, single-spin magnetometry, and
Landau-Lifschitz-Gilbert simulations we show that the nanoscale dynamics are
governed by the depinning and subsequent motion of magnetic edge dislocations.
The motion of these topologically stable objects triggers perturbations that
can propagate over mesoscopic length scales. The observation of stochastic
instabilities in the micromagnetic structure provides new insight to the
spatio-temporal dynamics of itinerant helimagnets and topological defects, and
discloses novel challenges regarding their technological usage
Quantum 1/4 BPS Dyons
Classical properties of 1/4 BPS dyons were previously well understood both in
field theory context and in string theory context. Its quantum properties,
however, have been more difficult to probe, although the elementary information
of the supermultiplet structures is known from a perturbative construction.
Recently, a low energy effective theory of monopoles was constructed and argued
to contain these dyons as quantum bound states. In this paper, we find these
dyonic bound states explicitly in the N=4 supersymmetric low energy effective
theory. After identifying the correct angular momentum operators, we motivate
an anti-self-dual ansatz for all BPS bound states. The wavefunctions are found
explicitly, whose spin contents and degeneracies match exactly the expected
results.Comment: 20 pages, no figure
Exactly stable non-BPS spinors in heterotic string theory on tori
Considering SO(32) heterotic string theory compactified on a torus of
dimension 4 and less, stability of non-supersymmetric states is studied. A
non-supersymmetric state with robust stability is constructed, and its exact
stability is proven in a large region of moduli space against all the possible
decay mechanisms allowed by charge conservation. Using various T-duality
transform matrices, we translate various selection rules about conserved
charges into simpler problems resembling partition and parity of integers. For
heterotic string on T^4, we give a complete list of BPS atoms with elementary
excitations, and we study BPS and non-BPS molecules with various binding
energies. Using string-string duality, the results are interpreted in terms of
Dirichlet-branes in type IIA string theory compactified on an orbifold limit of
a K3 surface.Comment: 47 pages, 14 figures, LaTe
The nonperturbative closed string tachyon vacuum to high level
We compute the action of closed bosonic string field theory at quartic order
with fields up to level ten. After level four, the value of the potential at
the minimum starts oscillating around a nonzero negative value, in contrast
with the proposition made in [5]. We try a different truncation scheme in which
the value of the potential converges faster with the level. By extrapolating
these values, we are able to give a rather precise value for the depth of the
potential.Comment: 24 pages. v2: typos corrected, clarified extrapolation in scheme B,
and added extrapolated tachyon and dilaton vev's at the end of Section
Holographic DC conductivities from the open string metric
We study the DC conductivities of various holographic models using the open
string metric (OSM), which is an effective metric geometrizing density and
electromagnetic field effect. We propose a new way to compute the nonlinear
conductivity using OSM. As far as the final conductivity formula is concerned,
it is equivalent to the Karch-O'Bannon's real-action method. However, it yields
a geometrical insight and technical simplifications. Especially, a real-action
condition is interpreted as a regular geometry condition of OSM. As
applications of the OSM method, we study several holographic models on the
quantum Hall effect and strange metal. By comparing a Lifshitz background and
the Light-Cone AdS, we show how an extra parameter can change the temperature
scaling behavior of conductivity. Finally we discuss how OSM can be used to
study other transport coefficients, such as diffusion constant, and effective
temperature induced by the effective world volume horizon.Comment: 33 page
D-brane interactions in type IIB plane-wave background
The cylinder diagrams that determine the static interactions between pairs of
Dp-branes in the type IIB plane wave background are evaluated. The resulting
expressions are elegant generalizations of the flat-space formulae that depend
on the value of the Ramond-Ramond flux of the background in a non-trivial
manner. The closed-string and open-string descriptions consistently transform
into each other under a modular transformation only when each of the
interacting D-branes separately preserves half the supersymmetries. These
results are derived for configurations of euclidean signature
D(p+1)-instantons but also generalize to lorentzian signature Dp-branes.Comment: 24 pages, Normalisation of boundary states correcte
Clear-cuts are temporary habitats, not matrix, for endangered grassland burnet moths (Zygaena spp.)
Burnet moths (Zygaena spp.) are day-flying Lepidoptera considered indicative of species-rich grasslands. In the present study, our aim was to clarify whether clear-cuts are habitat, supporting habitat or matrix for three species of Zygaena. We did so by sampling these species with sex pheromones on 48 clear-cuts, varying in amount of host and nectar plants, in southern Sweden. To compare the efficiency of such sampling, we also conducted transect walks on these clearcuts. Overall, host-plants on clear-cuts best explained the abundance of Zygaena spp. recorded, better than nectar-plants or connectivity with nearby grasslands. These results indicate that clear-cuts with an abundance of host plants are used as a fully functional habitat, and not a supporting habitat in the sense of only providing nectar. There is no support in these results for considering clear-cuts as an inert matrix. With about half the work-effort, pheromone traps recorded 100 times more Zygaena spp. as transect walks. The poor correspondence between observations during transects walks and pheromone trap catches suggest Zygaena spp. being difficult to monitor by transect walks. In contrast to grasslands, clear-cuts are short-term in nature requiring repeated recolonization, indicating the importance of permanent grasslands. However, clear-cuts are important temporary insect habitats due to their great acreage, and suitable management can increase the time they remain a habitat
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