137 research outputs found
Persistence of Anderson localization in Schr\"odinger operators with decaying random potentials
We show persistence of both Anderson and dynamical localization in
Schr\"odinger operators with non-positive (attractive) random decaying
potential. We consider an Anderson-type Schr\"odinger operator with a
non-positive ergodic random potential, and multiply the random potential by a
decaying envelope function. If the envelope function decays slower than
at infinity, we prove that the operator has infinitely many
eigenvalues below zero. For envelopes decaying as at infinity,
we determine the number of bound states below a given energy ,
asymptotically as . To show that bound states located at
the bottom of the spectrum are related to the phenomenon of Anderson
localization in the corresponding ergodic model, we prove: (a) these states are
exponentially localized with a localization length that is uniform in the decay
exponent ; (b)~ dynamical localization holds uniformly in
Effect of housing enrichment and type of flooring on the performance and behaviour of female rabbits
[EN] This study investigated the effect of housing enrichments (scratching card, gnawing material and a platform), of a change in height and in the type of flooring on the live weight, reproductive performance and behaviour of female rabbits, as well as on the feed intake and spatial distribution of females and their kits. A total of 40 multiparous female rabbits were monitored in three consecutive reproductive cycles (48-d intervals). Four days before parturition in each reproductive cycle, the females were randomly assigned to one of the five types of housing: Control (CNT: 102Ă47Ă30 cm, LĂWĂ H); Scratching card (SCT: containing a scratching card); Gnawing materials (GNW: CNT dimensions plus a compressed lucerne hay block and a wooden stick); Platform (PLT: 102Ă47Ă60 cm, including a platform with a plastic floor) and Combination (CBN: PLT dimensions with the scratching card, the gnawing materials and a platform). Data were only recorded during the first and third reproductive cycles. The living conditions did not significantly alter the femalesâ live weight (4889 g at housing; 4890 g at mid-lactation; 4867 g at weaning), reproductive performance (9.0 kits born alive), survival of the kits (90%), nor the feed intake of females and their litters (542 g/day). Providing animals with a gnawing block stimulated Gnawing behaviour (median frequency per group: CTL=0.00, SCT=0.00, GNW=4.69, PLT=0.00, and CBN=2.34; PRearing up behaviour (median frequencies per group: CTL=0.00, SCT=0.00, GNW=0.00, PLT=2.08, and CBN=3.12; P=0.06), and when a platform was present, the rabbits used it (mean values per group: CTL=0.00, SCT=0.00, GNW=0.00, PLT=1.79, and CBN=4.91; P=0.003). Regarding the type of floor, females appeared to prefer the plastic mesh flooring (31.2%) to the wire mesh flooring (18.8%). To sum up, providing female rabbits with simple enrichments appears to stimulate specific behaviours like Gnawing and Rearing up and may contribute to their wellbeing.Huang, Y.; BrĂ©da, J.; Savietto, D.; Debrusse, A.; BonnemĂšre, J.; Gidenne, T.; Combes, S.... (2021). Effect of housing enrichment and type of flooring on the performance and behaviour of female rabbits. World Rabbit Science. 29(4):275-285. https://doi.org/10.4995/wrs.2021.15848OJS275285294Altmann J. 1974. Observational study of behavior: sampling methods. Behaviour, 49: 227-266. https://doi.org/10.1163/156853974X00534Animal Welfare Committee. 2009. Five Freedoms. Available at https://webarchive.nationalarchives.gov.uk/20110909181150/http://www.fawc.org.uk/freedoms.htm. Accessed February 2021.ANSES. 2018. ANSES proposes a definition of animal welfare and sets the foundation for its research and expert appraisal work. 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Acta Agriculturae Slovenica, 98: 51-61.Jordan D., Gorjanc G., Ć tuhec I. 2008. Wooden sticks as environmental enrichment: effect on fattening and carcass traits of individually housed growing rabbits. World Rabbit Sci., 16: 237-243. https://doi.org/10.4995/wrs.2008.619Lang C., Hoy S. 2011. Investigations on the use of an elevated platform in group cages by growing rabbits. World Rabbit Sci., 19: 95-101. https://doi.org/10.4995/wrs.2011.800Leach M.C., Allweiler S., Richardson C., Roughan J.V., Narbe R., Flecknell P.A. 2009. Behavioural effects of ovariohysterectomy and oral administration of meloxicam in laboratory housed rabbits. Res. Vet. Sci., 87: 336-347. https://doi.org/10.1016/j.rvsc.2009.02.001Luzi F., Ferrante V., Heinzl E. Verga M. 2003. Effect of environmental enrichment on productive performance and welfare aspects in fattening rabbits. Ital. J. Anim. Sci., 2: 438-440.Matics Z., Farkas T. 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World Rabbit Sci., 15: 29-36. https://doi.org/10.4995/wrs.2007.607Rommers J.M., Bracke M., Reuvekamp B., Gunnink H., de Jong I.C. 2014. Cage-enrichment: rabbit does prefer straw or a compressed wooden block. World Rabbit Sci., 22: 301-309. https://doi.org/10.4995/wrs.2014.1353Rommers J., de Greef K. H. 2018. Are combi parks just as useful as regular parks for fatteners for part-time group housing of rabbit does? World Rabbit Sci., 26: 299-305. https://doi.org/10.4995/wrs.2018.9587Rosell J.M., De la Fuente L.F. 2009. Effect of footrests on the incidence of ulcerative pododermatitis in domestic rabbit does. Animal Welfare, 18: 199-204.Rosell J.M., De la Fuente L. 2013. Assessing ulcerative pododermatitis of breeding rabbits. Animals, 3: 318-326. https://doi.org/10.3390/ani3020318SzendrĆ Z., Matics Z., Odermatt M., GerencsĂ©r Z., Nagy I., SzendrĆ K., Dalle Zotte A. 2012. Use of different areas of pen by growing rabbits depending on the elevated platforms' floor-type. 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Asymptotic behaviour of the spectrum of a waveguide with distant perturbations
We consider the waveguide modelled by a -dimensional infinite tube. The
operator we study is the Dirichlet Laplacian perturbed by two distant
perturbations. The perturbations are described by arbitrary abstract operators
''localized'' in a certain sense, and the distance between their ''supports''
tends to infinity. We study the asymptotic behaviour of the discrete spectrum
of such system. The main results are a convergence theorem and the asymptotics
expansions for the eigenvalues. The asymptotic behaviour of the associated
eigenfunctions is described as well. We also provide some particular examples
of the distant perturbations. The examples are the potential, second order
differential operator, magnetic Schroedinger operator, curved and deformed
waveguide, delta interaction, and integral operator
Generalized eigenvalue-counting estimates for the Anderson model
We generalize Minami's estimate for the Anderson model and its extensions to
eigenvalues, allowing for arbitrary intervals and arbitrary single-site
probability measures with no atoms. As an application, we derive new results
about the multiplicity of eigenvalues and Mott's formula for the
ac-conductivity when the single site probability distribution is H\"older
continuous.Comment: Minor revisio
Widths of the Hall Conductance Plateaus
We study the charge transport of the noninteracting electron gas in a
two-dimensional quantum Hall system with Anderson-type impurities at zero
temperature. We prove that there exist localized states of the bulk order in
the disordered-broadened Landau bands whose energies are smaller than a certain
value determined by the strength of the uniform magnetic field. We also prove
that, when the Fermi level lies in the localization regime, the Hall
conductance is quantized to the desired integer and shows the plateau of the
bulk order for varying the filling factor of the electrons rather than the
Fermi level.Comment: 94 pages, v2: a revision of Sec. 5; v3: an error in Sec. 7 is
corrected, major revisions of Sec. 7 and Appendix E, Sec. 7 is enlarged to
Secs. 7-12, minor corrections; v4: major revisions, accepted for publication
in Journal of Statistical Physics; v5: minor corrections, accepted versio
Eta-Helium Quasi-Bound States
The cross section and tensor analysing power t_20 of the d\vec{d}->eta 4He
reaction have been measured at six c.m. momenta, 10 < p(eta) < 90 MeV/c. The
threshold value of t_20 is consistent with 1/\sqrt{2}, which follows from
parity conservation and Bose symmetry. The much slower momentum variation
observed for the reaction amplitude, as compared to that for the analogous
pd->eta 3He case, suggests strongly the existence of a quasi-bound state in the
eta-4He system and optical model fits indicate that this probably also the case
for eta-3He.Comment: LaTeX, uses elsart.sty, 10 pages, 3 Postscript figures, Submitted to
Physics Letters
Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method
A technically convenient signature of Anderson localization is exponential
decay of the fractional moments of the Green function within appropriate energy
ranges. We consider a random Hamiltonian on a lattice whose randomness is
generated by the sign-indefinite single-site potential, which is however
sign-definite at the boundary of its support. For this class of Anderson
operators we establish a finite-volume criterion which implies that above
mentioned the fractional moment decay property holds. This constructive
criterion is satisfied at typical perturbative regimes, e. g. at spectral
boundaries which satisfy 'Lifshitz tail estimates' on the density of states and
for sufficiently strong disorder. We also show how the fractional moment method
facilitates the proof of exponential (spectral) localization for such random
potentials.Comment: 29 pages, 1 figure, to appear in AH
On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum
We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum
of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha,
with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay
as n^{\alpha-1}. V(t) is supposed to be periodic, bounded, continuously
differentiable in the strong sense and such that the matrix entries with
respect to the spectral decomposition of H obey the estimate
|V(t)_{m,n}|0,
p>=1 and \gamma=(1-\alpha)/2. We show that the energy diffusion exponent can be
arbitrarily small provided p is sufficiently large and \epsilon is small
enough. More precisely, for any initial condition \Psi\in Dom(H^{1/2}), the
diffusion of energy is bounded from above as _\Psi(t)=O(t^\sigma) where
\sigma=\alpha/(2\ceil{p-1}\gamma-1/2). As an application we consider the
Hamiltonian H(t)=|p|^\alpha+\epsilon*v(\theta,t) on L^2(S^1,d\theta) which was
discussed earlier in the literature by Howland
Reconciling MOND and dark matter?
Observations of galaxies suggest a one-to-one analytic relation between the
inferred gravity of dark matter at any radius and the enclosed baryonic mass, a
relation summarized by Milgrom's law of modified Newtonian dynamics (MOND).
However, present-day covariant versions of MOND usually require some additional
fields contributing to the geometry, as well as an additional hot dark matter
component to explain cluster dynamics and cosmology. Here, we envisage a
slightly more mundane explanation, suggesting that dark matter does exist but
is the source of MOND-like phenomenology in galaxies. We assume a canonical
action for dark matter, but also add an interaction term between baryonic
matter, gravity, and dark matter, such that standard matter effectively obeys
the MOND field equation in galaxies. We show that even the simplest realization
of the framework leads to a model which reproduces some phenomenological
predictions of cold dark matter (CDM) and MOND at those scales where these are
most successful. We also devise a more general form of the interaction term,
introducing the medium density as a new order parameter. This allows for new
physical effects which should be amenable to observational tests in the near
future. Hence, this very general framework, which can be furthermore related to
a generalized scalar-tensor theory, opens the way to a possible unification of
the successes of CDM and MOND at different scales.Comment: 9 page
Adiabatic non-equilibrium steady states in the partition free approach
Consider a small sample coupled to a finite number of leads, and assume that
the total (continuous) system is at thermal equilibrium in the remote past. We
construct a non-equilibrium steady state (NESS) by adiabatically turning on an
electrical bias between the leads. The main mathematical challenge is to show
that certain adiabatic wave operators exist, and to identify their strong limit
when the adiabatic parameter tends to zero. Our NESS is different from, though
closely related with the NESS provided by the Jak{\v s}i{\'c}-Pillet-Ruelle
approach. Thus we partly settle a question asked by Caroli {\it et al} in 1971
regarding the (non)equivalence between the partitioned and partition-free
approaches
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