Reply to the Comment on the 'Hole-digging' in ensembles of tunneling molecular magnets

Reply to the Comment of J.J. Alonso and J.F. Fernandez on the paper "'Hole-digging' in ensembles of tunneling molecular magnets" of I.S. Tupitsyn, P.C.E. Stamp and N.V. Prokof'ev (Phys. Rev. B 69, 132406, (2004)).Comment: 1 LaTeX page, 1 PS figure; submitted to PR

Effective Hamiltonian in the Problem of a "Central Spin" Coupled to a Spin Environment

We consider here the problem of a "giant spin", with spin quantum number S>>1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes the low-energy properties of magnetic grains or magnetic macromolecules interacting with a surrounding spin environment, such as nuclear spins. We describe a general method for truncating the model to another one, valid at low energies, in which a two-level system interacts with the environmental spins, and higher energy terms are absorbed into a new set of couplings. This is done using an instanton technique. We then verify the accuracy of this technique, by comparing the results for the low energy effective Hamiltonian, with results derived for the original giant spin, coupled to a microscopic spin, using exact diagonalisation techniques.Comment: 15 pages, Latex, with 9 ps figure

Quantum spin glass in anisotropic dipolar systems

The spin-glass phase in the \LHx compound is considered. At zero transverse field this system is well described by the classical Ising model. At finite transverse field deviations from the transverse field quantum Ising model are significant, and one must take properly into account the hyperfine interactions, the off-diagonal terms in the dipolar interactions, and details of the full J=8 spin Hamiltonian to obtain the correct physical picture. In particular, the system is not a spin glass at finite transverse fields and does not show quantum criticality.Comment: 6 pages, 2 figures, to appear in J. Phys. Condens. Matter (proceedings of the HFM2006 conference

Development of food photographs for use with children aged 18 months to 16 years:comparison against weighed food diaries – The Young Person’s Food Atlas (UK)

Traditional dietary assessment methods, used in the UK, such as weighed food diaries impose a large participant burden, often resulting in difficulty recruiting representative samples and underreporting of energy intakes. One approach to reducing the burden placed on the participant is to use portion size assessment tools to obtain an estimate of the amount of food consumed, removing the need to weigh all foods. An age range specific food atlas was developed for use in assessing children’s dietary intakes. The foods selected and portion sizes depicted were derived from intakes recorded during the UK National Diet and Nutrition Surveys of children aged 1.5 to 16 years. Estimates of food portion sizes using the food atlas were compared against 4-day weighed intakes along with in-school / nursery observations, by the research team. Interviews were conducted with parents the day after completion of the diary, and for children aged 4 to 16 years, also with the child. Mean estimates of portion size consumed were within 7% of the weight of food recorded in the weighed food diary. The limits of agreement were wide indicating high variability of estimates at the individual level but the precision increased with increasing age. For children 11 years and over, agreement with weighed food diaries, was as good as that of their parents in terms of total weight of food consumed and of intake of energy and key nutrients. The age appropriate food photographs offer an alternative to weighed intakes for dietary assessment with children

Decoherence and Quantum Walks: anomalous diffusion and ballistic tails

The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasi-classical (in fact, diffusive) in the long time limit. We present here a counter-example, in which a particle makes quantum transitions between the sites of a d-dimensional hypercubic lattice whilst strongly coupled to a bath of two-level systems which 'record' the transitions. The long-time evolution of an initial wave packet is found to be most unusual: the mean square displacement of the particle density matrix shows long-range ballitic behaviour, but simultaneously a kind of weakly-localised behaviour near the origin. This result may have important implications for the design of quantum computing algorithms, since it describes a class of quantum walks.Comment: 4 pages, 1 figur

Sharp transition for single polarons in the one-dimensional Su-Schrieffer-Heeger model

We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength $\lambda$, in all models where this coupling depends only on phonon momentum $q$. In the SSH model the coupling also depends on the electron momentum $k$; we find it has a sharp transition, at a critical coupling strength $\lambda_c$, between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at $\lambda = \lambda_c$, except the average number of phonons in the polaronic cloud. This result is representative of all polarons with coupling depending on $k$ and $q$, and will have important experimental consequences (eg., in ARPES and conductivity experiments)

What are the interactions in quantum glasses?

The form of the low-temperature interactions between defects in neutral glasses is reconsidered. We analyse the case where the defects can be modelled either as simple 2-level tunneling systems, or tunneling rotational impurities. The coupling to strain fields is determined up to 2nd order in the displacement field. It is shown that the linear coupling generates not only the usual $1/r^3$ Ising-like interaction between the rotational tunneling defect modes, which cause them to freeze around a temperature $T_G$, but also a random field term. At lower temperatures the inversion symmetric tunneling modes are still active - however the coupling of these to the frozen rotational modes, now via the 2nd-order coupling to phonons, generates another random field term acting on the inversion symmetric modes (as well as shorter-range $1/r^5$ interactions between them). Detailed expressions for all these couplings are given.Comment: 12 pages, 2 figures. Minor modifications, published versio