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We directly measure the low energy excitation modes of the quantum Ising magnet LiHoF$_4$ using microwave spectroscopy. Instead of a single electronic mode, we find a set of collective electronuclear modes, in which the spin-$1/2$ Ising electronic spins hybridize with the bath of spin-$7/2$ Ho nuclear spins. The lowest-lying electronuclear mode softens at the approach to the quantum critical point, even in the presence of disorder. This softening is rapidly quenched by a longitudinal magnetic field. Similar electronuclear structures should exist in other spin-based quantum Ising systems., 12 pages, 5 figures. Accepted for publication in Phys. Rev. Lett

Soft factorization has been shown to hold to sub-leading order in QED and to sub-sub-leading order in perturbative quantum gravity, with various loop and non-universal corrections that can be found. Here we show that all terms factorizing at tree level can be uniquely identified as boundary terms that exist already in the classical expressions for the electric current and stress tensor of a point particle. Further, we show that one cannot uniquely identify such boundary terms beyond the sub-leading or sub-sub-leading orders respectively, providing evidence that the "universality" of the tree level soft factor only holds to these orders. Finally, we show that these boundary terms factor out of all tree level amplitudes as expected, in a theory where gravitons couple to a scalar field., v2: Incorporated additional references and discussions suggested by referee

Underwater noise pollution from impulsive sources (e.g. explosions, seismic airguns, percussive pile driving) can affect marine fauna through mortality, physical injury, auditory damage, physiological stress, acoustic masking, and behavioural responses. Given the potential for large-scale impact on marine ecosystems, some countries are now monitoring impulsive noise activity, coordinated internationally through Regional Seas Conventions. Here, we assess impulsive noise activity in the Northeast Atlantic reported during 2015–2017 to the first international impulsive noise register (INR), established in 2016 under the OSPAR Convention. Seismic airgun surveys were the dominant noise source (38%–56% of annual activity) and declined by 23% during 2015–2017. Reported pile driving activity increased 72%. Explosions and sonar/acoustic deterrent devices both had year-on-year increases in reported activity. Some increases were attributable to more comprehensive reporting in later years. We discuss utilising the INR for risk assessment, target setting, and forward planning, and the implementation of similar systems in other regions.

We give a formal treatment of the "Correlated Worldline" theory of quantum gravity. The generating functional is written as a product over multiple copies of the coupled matter and gravitational fields; paths for fields are correlated via gravity itself. In the limit where the gravitational coupling $G \rightarrow 0$, conventional quantum field theory is recovered; in the classical limit $\hbar \rightarrow 0$, General Relativity is recovered. A formal loop expansion is derived, with all terms up to one-loop order $\sim O(l_P^2)$ given explicitly, where $l_P$ is the Planck length. We then derive the form of a perturbation expansion in $l_P^2$ around a background field, with the correlation functions given explicitly up to $\sim O(l_P^2)$. Finally, we explicitly demonstrate the on-shell gauge independence of the theory, to order $l_P^2$ in gravitational coupling and to all orders in matter loops, and derive the relevant Ward identities., Comment: 20 pages, 6 figures

We consider the interaction between a matter system and soft gravitons. We use a functional eikonal expansion to deal with the infrared divergences, and introduce a "composite generating functional" which allows us to calculate a decoherence functional for the time evolution of the system. These techniques allow us to formulate scattering problems in a way which deals consistently with infrared effects, as well as being manifestly diffeomorphism invariant. We show how the asymptotic form of the decoherence functional can be written in terms of the infinitely many conserved charges associated with asymptotic BMS symmetries, and allow us to address the question of how much information is lost during the scattering., 20 pages, 4 figures

We study the effect of coupling a spin-bath environment to a system which, at low energies, can be modeled as a quantum Ising system. A field theoretic formalism incorporating both thermal and quantum fluctuations is developed to derive results for the thermodynamic properties and response functions, both for a toy model and for the ${\text{LiHoF}}_{4}$ system, in which spin-8 electronic spins couple to a spin-$7/2$ nuclear spin bath: The phase transition then occurs in a system of electronuclear degrees of freedom, coupled by long-range dipolar interactions. The quantum Ising phase transition still exists, and one hybridized mode of the Ising and bath spins always goes soft at the transition.

Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics., Comment: 32 pages, 7 figures, 1 summary table, 145 (!!) references. Invited submission to "Gravity in the Lab" issue of Class. Quant. Grav. v2: less longwinded title, various presentational tweaks, references added; thanks to many people for comments. Version submitted to CQG

We consider the general form of "Correlated Worldline" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple copies of the coupled matter and gravitational fields. In both versions, the paths in a functional formulation are correlated via gravity itself, causing a breakdown of the superposition principle; however, the product form survives consistency tests not satisfied by the summed form. To better understand the structure of these two theories, we show how to perform diagrammatic expansions in the gravitational coupling for each version of CWL theory, using particle propagation and scalar fields as examples. We explicitly calculate contributions to 2-point and 4-point functions, again for each version of the theory, up to 2nd-order in the gravitational coupling., Comment: 20 pages, 6 figures

Nondiagonal couplings to a bosonic bath completely change polaronic dynamics, from the usual diagonally coupled paradigm of smoothly varying properties. We study, using analytic and numerical methods, a model having both diagonal Holstein and nondiagonal Su-Schrieffer-Heeger (SSH) couplings. The critical coupling found previously in the pure SSH model, at which the $k=0$ effective mass diverges, now becomes a transition line in the coupling constant plane---the form of the line depends on the adiabaticity parameter. Detailed results are given for the quasiparticle and ground-state properties, over a wide range of couplings and adiabaticity ratios. The new paradigm involves a destabilization, at the transition line, of the simple Holstein polaron to one with a finite ground-state momentum, but with everywhere a continuously evolving band shape. No ``self-trapping transition'' exists in any of these models. The physics may be understood entirely in terms of competition between different hopping terms in a simple renormalized effective band theory. The possibility of further transitions is suggested by the results.

Decoherence in Nature has become one of the most pressing problems in physics. Many applications, including quantum information processing, depend on understanding it; and fundamental theories going beyond quantum mechanics have been suggested [1-3], where the breakdown of quantum theory appears as an 'intrinsic decoherence', mimicking environmental decoherence [4]. Such theories cannot be tested until we have a handle on ordinary environmental decoherence processes. Here we show that the theory for insulating electronic spin systems can make accurate predictions for environmental decoherence in molecular-based quantum magnets [5]. Experimental understanding of decoherence in molecular magnets has been limited by short decoherence times, which make coherent spin manipulation extremely difficult [6-9]. Here we reduce the decoherence by applying a strong magnetic field. The theory predicts the contributions to the decoherence from phonons, nuclear spins, and intermolecular dipolar interactions, for a single crystal of the Fe8 molecular magnet. In experiments we find that the decoherence time varies strongly as a function of temperature and magnetic field. The theoretical predictions are fully verified experimentally - there are no other visible decoherence sources. Our investigation suggests that the decoherence time is ultimately limited by nuclear spins, and can be extended up to about 500 microseconds, by optimizing the temperature, magnetic field, and nuclear isotopic concentrations., Submitted version including 11 pages, 3 figures and online supporting materials. Appeared on Nature Advance Online Publication (AOP) on July 20th, 2011. (http://www.nature.com/nature/journal/vaop/ncurrent/full/nature10314.html)

Decoherence is the major stumbling block in the realization of a large-scale quantum computer. Ingenious methods have been devised to overcome decoherence, but their success has been proven only for over-simplified models of system-environment interaction. Whether such methods will be reliable in the face of more realistic models is a fundamental open question. In this partly pedagogical article, we study two toy models of quantum information processing, using the language of \emph{quantum walks}. Decoherence is incorporated in 3 ways - by coupling to a noisy `projective measurement' system, and by coupling to oscillator and spin baths., Comment: 8 pages, 3 figures; to appear in Theory Canada 3 special issue if the Canadian Journal of Physics

We derive an effective time independent Hamiltonian for the transverse Ising model coupled to a spin bath, in the presence of a high frequency AC magnetic field. We show that the spin blocking mechanism that removes the quantum phase transition can be suppressed by the AC field, allowing high tunability of the quantum critical point. Finally, we calculate the phase diagram within the RPA approximation for the case of spin $7/2$ nuclei, appropriate to the $LiHo_{x}Y_{1-x}F_{4}$ system., Comment: 11 pages, 2 figures and Appendix

We revisit the exact solution of the two space-time dimensional quantum field theory of a free massless boson with a periodic boundary interaction and self-dual period. We analyze the model by using a mapping to free fermions with a boundary mass term originally suggested in ref.[22]. We find that the entire SL(2,C) family of boundary states of a single boson are boundary sine-Gordon states and we derive a simple explicit expression for the boundary state in fermion variables and as a function of sine-Gordon coupling constants. We use this expression to compute the partition function. We observe that the solution of the model has a strong-weak coupling generalization of T-duality. We then examine a class of recently discovered conformal boundary states for compact bosons with radii which are rational numbers times the self-dual radius. These have simple expression in fermion variables. We postulate sine-Gordon-like field theories with discrete gauge symmmetries for which they are the appropriate boundary states., Comment: 33 pages, 1 figure, references added, typos corrected

The understanding of decoherence is critical to philosophical debates on several different topics, including measurements, the ‘emergence’ of classical mechanics from quantum mechanics, and the arrows of time. This paper first reviews the basic mechanisms of decoherence in Nature, stressing recent discoveries and the crucial importance of ‘low-energy’ physics. The way in which the interpretation of some recent experiments relates to the problem is also delineated. Finally, some of the more common questions posed by philosophers about decoherence are reformulated, and partial answers are given to these. Throughout the article, the incomplete nature of our understanding is stressed, and the way it depends on several different unresolved questions in both low- and high-energy physics.

We investigate the motion of a domain wall in the presence of a dynamical hyperfine field. At temperature T high compared to the hyperfine coupling, the nuclear spins create a spatially random potential landscape, with dynamics dictated by the nuclear relaxation time T2. The distribution of the domain wall relaxation times (both in the thermal and quantum regimes) can show a long tail, characteristic of stochastic processes where rare events are important. Here, these are due to occasional strong fluctuations in the nuclear spin polarisation.

We calculate the magnetization relaxation in the short-time regime for an ensemble of nanornagnets in the presence of a low frequency external AC biasing field at temperatures lower than the magnetic anisotropy energy of the individual nanornagnets. It is found that the relaxation is strongly affected by AC fields with amplitude larger than that of the T2fluctuations in the nuclear field. This will allow experimental probing of the nuclear spin relaxation mechanism.

Recent theory and experiment in crystals of molecular magnets suggest that fundamental tests of the decoherence mechanisms of macroscopic quantum phenomena may be feasible in these systems (which are also almost ideal quantum spin glasses). We review these, and suggest new experiments.

We consider the quantum dynamics of a magnetic domain wall at low temperatures, where dissipative couplings to magnons and electrons are very small. The wall motion is then determined by its coupling to phonons and nuclear spins, and any pinning potentials. In the absence of nuclear spins there is a dominant superOhmic l-phonon coupling to the wall velocity, plus a strongly T-dependent Ohmic coupling to pairs of phonons. There is also a T-independent Ohmic coupling between single phonons and the wall chirality, which suppresses "chirality tunneling". We calculate the effect of these couplings on the T-dependent tunneling rate of a wall out of a pinning potential. Nuclear spins have a very strong and hitherto unsuspected influence on domain wall dynamics, coming from a hyperfine-mediated coupling to the domain wall position. For kBT»co0 this coupling yields a spatially random potential, fluctuating at a rate governed by the nuclear T2. When kBT « w0, the hyperfine potential fluctuates around a linear binding potential. The wall dynamics is influenced by the fluctuations of this potential, ie., by the nuclear spin dynamics. Wall tunneling can occur when fluctuations open an occasional "tunneling window". This changes the crossover to tunneling and also causes a slow "wandering", in time, of the energy levels associated with domain wall motion inside the pinning potential. This effect is fairly weak in Ni- and Fe-based magnets, and we give an approximate treatment of its effect on the tunneling dynamics, as well as a discussion of the relationship to recent domain wall tunneling experiments.

The low-energy behaviour of 2 coupled nanomagnets or 2 coupled SQUIDs, interacting with their environment, can be described by the model of a “Pair or Interacting Spins Coupled to an Environmental Sea” (PISCES). These physical systems can then be used for a measurement operation in which system, apparatus and environment are all treated quantum mechanically. We design a “Bell/Coleman-Hepp” measuring system, and show that in principle one may design a situation in which quantum interference between system and apparatus can upset the usual measurement operation.

We consider the self-energy and quasiparticle spectrum, for both electrons interacting with phonons, and composite fermions interacting with gauge fluctuations. In both cases we incorporate the singular structure arising from Landau level quantization in a finite field. This is then used to determine the renormalised gap between the Fermi energy and the first excited states. The electron-phonon problem is treated for both Debye and Einstein phonons. In the case of composite fermions, it is found that the singular Landau level structure strongly affects the renormalised gap in the intermediate coupling regime, which is relevant to experiments on the fractional quantum Hall effect. We compare our findings with measurements of the gap in fractional Hall states with filling fraction nu near nu=1/2., 13 pages including 11 figures, revtex

The low-temperature universal properties in disordered and amorphous solids are considered. We introduce a model that includes two types of two-level systems (TLSs), which, based on their local symmetry, interact weakly or strongly with the phonon field. This accounts well for the experimental results and addresses some long-standing questions: the nature of the TLSs, the smallness and universality of the phonon attenuation, and the energy scale of 3 K below which universality is observed. Our model describes disordered lattices; we also discuss its application to amorphous solids.

We calculate the first vertex correction $\delta\Lambda_{\bf k}$ to the bare vertex $\Lambda_\circ$ in the nearly antiferromagnetic spin fluctuation Fermi liquid theory of the cuprate superconductor ${\rm YBa_2Cu_3O_7}$. It is calculated for $\bf k$ on the Fermi surface, and ${\bf Q}=(\pm {\pi\over a}, \pm {\pi\over a})$. We find that the dimensionless ratio $|\delta\Lambda_{\bf k}|/\Lambda_\circ$, which parametrizes the vertex correction, is not small. It is a maximum for ${\bf k=k_h}$, where ${\bf k_h}$ is a ``hot spot'' on the Fermi surface. This makes large quantitative corrections to the theory., Comment: 13 pages, RevTeX, 2 figures, Minor changes including tabular values have been made. The main conclusions have not been changed.The revised version is to appear in Phys. Rev. Lett. 77, 3017 (1996)

We study the motion of a vortex under the influence of a harmonic force in an approximately two dimensional trapped Bose-condensed gas. The Hall-Vinen-Iordanskii equations, modified to include a fluctuational force and an inertial mass term, are solved for the vortex motion. The mass of the vortex has a strong influence on the time it takes the vortex to escape the trap. Since the vortex mass also depends on the trap size we have an additional dependence on the trap size in the escape time which we compare to the massless case., Submitted to J. Low. Temp. Phys

For many years the classical Hall-Vinen-Iordanski (HVI) equation has been used to analyse vortex dynamics in superfluids. Here we discuss the extension of the theory of vortex dynamics to the quantum regime, in which the characteristic vortex frequency is higher than the temperature. At the same time we justify, in the low-frequency classical regime, the use of the HVI equation, provided an inertial mass term and a noise fluctuation term are added to it. The crossover to the quantum regime is discussed, and an intuitive picture is given of the vortex dynamics, which in general is described by 2 equations (one for the vortex coordinate, and one for its quantum fluctuations); we also discuss the simple equation of motion found in the extreme quantum regime., Comment: QFS2012: International Conference on Quantum Fluids and Solids

We study the behavior of response functions of two-dimensional (2D) fermions interacting via a long-range transverse gauge field in the eikonal approximation. We observe that an exponentially vanishing wave-function renormalization prevents divergences in the density-density correlation function and the pairing susceptibility. The wave-function renormalization also shows up in a suppression of the dHvA effect. Elaborating on an observation recently made by Ioffe, Lidsky, and Altschuler, we also infer an effective bosonic description which makes it possible to reproduce our eikonal results in terms of free 2D bosons.

We derive a fully quantum-mechanical equation of motion for a vortex in a 2-dimensional Bose superfluid, in the temperature regime where the normal fluid density $\rho_n(T)$ is small. The coupling between the vortex "zero mode" and the quasiparticles has no term linear in the quasiparticle variables -- the lowest-order coupling is quadratic. We find that as a function of the dimensionless frequency $\tilde \Omega = \hbar \Omega/k_BT$, the standard Hall-Vinen/Iordanskii equations are valid when $\tilde \Omega \ll 1$ (the "classical regime"), but elsewhere, the equations of motion become highly retarded, with significant experimental implications when $\tilde \Omega \gtrsim 1$., Comment: 12 pages (4 pages + supp info), 2 figures, accepted to PRL

We study the topological decoherence, arising from environmental spins, which acts to suppress the quantum coherent behaviour of grain magnetization. It is found that this decoherence mechanism is so effective that even under the most favourable conditions, it will be very difficult to see quantum coherent behaviour of grains having a quantum number S greater than approximately O(10). This conclusion does not affect the possibility of seeing tunnelling behaviour for larger grains.

This article gives a fairly detailed survey of some of the problems raised when the interaction energy If() between 2 fermionic quasiparticles (in 2 dimensions) is singular when (k k'( - 0. Before dealing with singular interactions, it is shown how a ~ f(() leads to a 2-dimensional Fermi liquid theory, which is internally consistent, at least as far ailts infrared properties are concerned. The quasiparticle properties are calculated in detail. The question of whether singular interactions arise for the dilute Fermi gas, with short~range repulsive interactions, is investigated perturbatively. One finds a weak singularity in f(() when the dimensionality D = 2, but it does not destabilize the Fermi liquid. A more sophisticated analysis is then given, to all orders in the interaction, using the Lippman-Schwinger equation as well as a phase shift analysis for a finite box. The conclusion is that any breakdown of Fermi liquid theory must come from non-perturbative effects. An examination is then made of some of the consequences arising if a singular interaction is introduced the form proposed by Anderson is used as an example. A hierarchy of singular terms arise in all quantities this is shown for the selLenergy, and also the 3-point and 4-point scattering functions. These may be summed in a perfectly consistent manner. Most attention is given to the particle~hole channel, since it appears to lead to results different from those of Anderson. Nevertheless it appears that it is possible to derive a sensible theory starting from a singular effective Hamiltonian although Fermi Liquid theory breaks down, all fermionic quantities may be calculated consistently. Finally, the effect of a magnetic field (which cuts off the infrared divergences) is investigated, and the de Haas-van Alphen amplitude calculated, for such a singular Fermionic system.

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).

We present a detailed study of the influence of various interactions on the spin quantum tunneling in a ${\text{Mn}}_{12}$ wheel molecule. The effects of single-ion and exchange (spin-orbit) anisotropy are first considered, followed by an analysis of the roles played by secondary influences, e.g., disorder, dipolar and hyperfine fields, and magnetoelastic interactions. Special attention is paid to the role of the antisymmetric Dzyaloshinski-Moriya (DM) interaction. This is done within the framework of a 12-spin microscopic model, and also using simplified dimer and tetramer approximations in which the electronic spins are grouped in two or four blocks, respectively. If the molecule is inversion symmetric, the DM interaction between the dimer halves must be zero. In an inversion symmetric tetramer, two independent DM vectors are allowed but no new tunneling transitions are generated by the DM interaction. In an effort to explain the experiments, we consider a breaking of the molecular inversion symmetry, and we explore this in detail using both models, focusing on the asymmetric disposition and rounding of Berry phase minima associated with quantum interference between states of opposite parity. A remarkable behavior exists for the ``Berry phase zeroes'' as a function of the directions of the internal DM vectors and the external transverse field. However, in both dimer and tetramer models, a rather drastic breaking of the molecular inversion symmetry is required to explain the experiments using DM interactions. Such a symmetry breaking cannot be attributed to sample disorder, and there is no evidence for it in experiments. In the absence of DM interactions, we suggest a number of other ways to explain the experiments. These results are of general interest for the quantum dynamics of tunneling spins, and lead to some interesting experimental predictions.

Recent de Haas\char21{}van Alphen (dHvA) experiments on high-${T}_{c}$ compounds have been interpreted using Lifshitz-Kosevich (LK) theory, which ignores many-body effects. However in quasi-2d systems, interactions plus Landau-level quantization give strong singularities in the self-energy $\ensuremath{\Sigma}$ and the thermodynamic potential $\ensuremath{\Omega}$. These are rapidly suppressed as one increases the c-axis tunneling amplitude ${t}_{\ensuremath{\perp}}$ and/or impurity scattering. We show that interaction effects should show up in these experiments, and that they can lead to strong deviations from LK behavior. Moreover, dHvA experiments in quasi-2d systems should clearly distinguish between Fermi-liquid and non-Fermi-liquid states, for sufficiently weak impurity scattering.

It is shown how the onset of superconductivity in a metal will allow objects moving in the metal to make the entire transition from incoherent diffusion to quantum coherent motion, in an experimentally controllable way, as the gap suppresses the infrared divergent coupling to electrons. An observable measure of the crossover is the diffusion constant D(T) of the object, which the authors calculate in detail. This will allow a stringent experimental test of the understanding of this transition.

Magnetic solids should, under certain circumstances, show macroscopic quantum behavior, in which coherence exists between completely distinct magnetization states, each involving a very large number of spins (~1012 spins). This article reviews the recent work in this field, concentrating particularly on macroscopic quantum tunneling (MQT) of magnetization. The two main phenomena discussed are (a) the tunneling of magnetization in singledomain particles or grains (in which some 103−104 spins rotate together through an energy barrier), and (b) the tunneling of domain walls in films or in bulk magnets; where walls containing ~ 1010 spins may tunnel off a pinning potential, or from one pinning centre to another. Some attention is also given to the quantum nucleation of magnetization reversal in a bulk magnet, and to the quantum motion of other magnetic solitons (such as vortices). After a thorough analysis of the basic grain and wall tunneling phenomena, we continue on to a discussion of the various dissipative or “decoherence” mechanisms, which destroy the phase correlations involved in tunneling. The coupling of grain magnetization to phonons, photons, and electrons is shown to have little consequence for weaklyconducting or insulating grains. Domain walls couple to these and also to magnons and impurities or defects; the 3rd order coupling to magnons can have serious effects, but if one uses pure insulators at low temperatures, these can also be ignored. As a result, theory indicates that MQT should be visible in both grains and bulk magnets at low temperatures (at least below ~1 K). The present experimental evidence for such behavior is inconclusive, partly because few experiments have been done. We discuss these experiments, and make some suggestions for future work. It is hoped this review will stimulate such work, not only because of the fundamental interest in macroscopic quantum phenomena, but also because of the considerable scope for technological innovation.

Both orientational glasses and dipolar glasses possess an intrinsic random field, coming from the volume difference between impurity and host ions. We show this suppresses the glass transition, causing instead a crossover to the low $T$ phase. Moreover the random field is correlated with the inter-impurity interactions, and has a broad distribution. This leads to a peculiar variant of the Imry-Ma mechanism, with 'domains' of impurities oriented by a few frozen pairs. These domains are small: predictions of domain size are given for specific systems, and their possible experimental verification is outlined. In magnetic glasses in zero field the glass transition survives, because the random fields are disallowed by time-reversal symmetry; applying a magnetic field then generates random fields, and suppresses the spin glass transition., minor modifications, final version

We present low temperature magnetometry measurements on a new Mn3 single-molecule magnet in which the quantum tunneling of magnetization (QTM) displays clear evidence for quantum mechanical selection rules. A QTM resonance appearing only at high temperatures demonstrates tunneling between excited states with spin projections differing by a multiple of three. This is dictated by the C3 molecular symmetry, which forbids pure tunneling from the lowest metastable state. Transverse field resonances are understood by correctly orienting the Jahn-Teller axes of the individual manganese ions and including transverse dipolar fields. These factors are likely to be important for QTM in all single-molecule magnets.

We study the dynamics of pure phase decoherence for a particle hopping around an N-site ring, coupled both to a spin bath and to an Aharonov-Bohm flux which threads the ring. Analytic results are found for the dynamics of the influence functional and of the reduced density matrix of the particle, both for initial single wave-packet states, and for states split initially into 2 separate wave-packets moving at different velocities. We also give results for the dynamics of the current as a function of time., Comment: 17 pages, 6 figures, accepted by Phys. Rev. A

It is shown how large domain walls, containing \ensuremath{\ge}${10}^{10}$ spins, can behave as quantum objects at low temperatures. They move quantum diffusively, and exhibit macroscopic tunneling from defect pinning centers. The dissipation is calculated and shown to be very small; it does not involve the usual Caldeira-Leggett environmental couplings. The theory can also be used to treat smaller single-domain-wall behavior.

It is shown how the dynamic response of lattice fermions in a magnetic field (the Wannier-Azbel-Hofstadter'' system) may be calculated. Details are given for electromagnetic perturbations {delta}{bold A}({bold r},{ital t}){similar to}{delta}{bold A}({bold Q},{omega})exp({ital i}{bold Q}{center dot}{bold r}{minus}{ital i}{omega}{ital t}). Linear-response theory is valid for periodic boundary conditions, and can be justified in general for rational filling. Analytic results are given for the various current-current responses. Applications are briefly discussed.

We have searched for anomalous internal magnetic fields in highTc materials which are predicted to occur in anyon and flux phase models of superconductivity. The magnitude, anisotropy and temperature dependence of the observed fields inc-axis oriented samples of sintered YBa2CuO3O7 and of thick-film Bi2Sr2CaCu2O8 are consistent with a conventional nuclear dipolar origin. An upper limit of ≲0.08 mT is set for any anomalous magnetic fields along thec-axis atμ+ sites in bulk CuO2 superconductors.

The ${\rm LiHo_xY_{1-x}F_4}$ compound is widely considered to be the archetypal dipolar Quantum Ising system, with longitudinal dipolar interactions $V_{ij}^{zz}$ between ${\rm Ho}$ spins $\{i,j \}$ competing with transverse field-induced tunneling, to give a T=0 quantum phase transition. By varying the ${\rm Ho}$ concentration x, the typical strength $V_0$ of $V_{ij}^{zz}$ can be varied over many orders of magnitude; and so can the transverse field $H_{\perp}$. A new effective Hamiltonian is derived, starting from the electronuclear degrees of freedom, and valid at low and intermediate temperatures. For any such dipolar Quantum Ising system, the hyperfine interaction will dominate the physics at low temperatures, even if its strength $A_0 < V_0$: one must therefore go beyond an electronic transverse field Quantum Ising model. We derive the full phase diagram of this system, including all nuclear levels, as a function of transverse field $H_{\perp}$, temperature $T$, and dipole concentration x. For ${\rm LiHo_xY_{1-x}F_4}$ we predict a re-entrant critical field as a function of x. We also predict the phase diagram for x$=0.045$, and the behavior of the system in magnetic resonance and $\mu$SR experiments.

This introductory review discusses the main problems facing the attempt to build quantum information processing systems (like quantum computers) from spin-based qubits. We emphasize 'bottom-up' attempts using methods from chemistry. The essentials of quantum computing are explained, along with a description of the qubits and their interactions in terms of physical spin qubits. The main problem to be overcome is decoherence - how this works is described, along with ways to suppress contributions from spin bath and oscillator bath environments, and from dipolar interactions. Finally we discuss various strategies for making chemistry-based spin qubits, using both magnetic molecules and magnetic ions., 13 pages, 10 figures

It is shown that longitudinal field muon spin relaxation may be used to probe the local charge density correlations in two-dimensional systems and heterostructures. Magnetic quantum oscillations in the local density of extended states show up in the relaxation time T1. This method should reveal the variation of electronic parameters within the sample.

Several recent models of high-${\mathit{T}}_{\mathit{c}}$ superconductivity predict static internal magnetic fields along the c axis due to spontaneously broken parity and time-reversal symmetries. Muon spin relaxation has been used to study the internal fields in c-axis-oriented samples of sintered ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and of thick-film ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$. The magnitude, anisotropy, and temperature dependence of the observed fields favor a nuclear dipolar origin. Any anomalous fields at ${\mathrm{\ensuremath{\mu}}}^{+}$ sites in bulk ${\mathrm{CuO}}_{2}$ superconductors must be \ensuremath{\lesssim}0.08 mT.

We investigate the stability of the recently discovered room-temperature Bose-Einstein condensate (BEC) of magnons in yttrium iron garnet films. We show that magnon-magnon interactions depend strongly on the external field orientation, and that the BEC in current experiments is actually metastable-it only survives because of finite-size effects, and because the BEC density is very low. On the other hand a strong field applied perpendicular to the sample plane leads to a repulsive magnon-magnon interaction; we predict that a high-density room-temperature magnon BEC should then form in this perpendicular field geometry.

The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between quantum walk Hamiltonians and Hamiltonians for qubit systems and quantum circuits; this is done for both a single- and multi-excitation coding, and for more general mappings. Specific examples of spin chains, as well as static and dynamic systems of qubits, are mapped to quantum walks, and walks on hyperlattices and hypercubes are mapped to various gate systems. We also show how to map a quantum circuit performing the quantum Fourier transform, the key element of Shor's algorithm, to a quantum walk system doing the same. The results herein are an essential preliminary to a Hamiltonian formulation of quantum walks in which coupling to a dynamic quantum environment is included., Comment: 17 pages, 10 figures

It is argued that gravity should cause a breakdown of quantum mechanics, at low energies, accessible to table-top experiments. It is then shown that one can formulate a theory of quantum gravity in which gravitational correlations exist between worldline or worldsheet paths, for the particle or field of interest. Using a generalized equivalence principle, one can give a unique form for the correlators, yielding a theory with no adjustable parameters. A key feature of the theory is the ?bunching? of quantum trajectories caused by the gravitational correlations?this is not a decoherence or a ?collapse? mechanism. This bunching causes a breakdown of the superposition principle for large masses, with a very rapid crossover to classical behaviour at an energy scale which depends on the physical structure of the object. Formal details, and applications of the theory, are kept to a minimum in this paper; but we show how physical quantities can be calculated, and give a detailed discussion of the dynamics of a single particle.

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., 6 pages, 2 figures, to appear in J. Phys. Condens. Matter (proceedings of the HFM2006 conference)

Experiments involving phase coherent dynamics of networks of spins, such as echo experiments, will only work if decoherence can be suppressed. We show here, by analyzing the particular example of a crystalline network of Fe8 molecules, that most decoherence typically comes from pairwise interactions (particularly dipolar interactions) between the spins, which cause `correlated errors'. However at very low T these are strongly suppressed. These results have important implications for the design of quantum information processing systems using electronic spins., 4 pages, 4 figures. Final PRL version