Scrambling and thermalization in a diffusive quantum many-body system

Out-of-time ordered (OTO) correlation functions describe scrambling of information in correlated quantum matter. They are of particular interest in incoherent quantum systems lacking well defined quasi-particles. Thus far, it is largely elusive how OTO correlators spread in incoherent systems with diffusive transport governed by a few globally conserved quantities. Here, we study the dynamical response of such a system using high-performance matrix-product-operator techniques. Specifically, we consider the non-integrable, one-dimensional Bose-Hubbard model in the incoherent high-temperature regime. Our system exhibits diffusive dynamics in time-ordered correlators of globally conserved quantities, whereas OTO correlators display a ballistic, light-cone spreading of quantum information. The slowest process in the global thermalization of the system is thus diffusive, yet information spreading is not inhibited by such slow dynamics. We furthermore develop an experimentally feasible protocol to overcome some challenges faced by existing proposals and to probe time-ordered and OTO correlation functions. Our study opens new avenues for both the theoretical and experimental exploration of thermalization and information scrambling dynamics.Comment: 7+4 pages, 8+3 figures; streamlined versio

Density functional theory for strongly-correlated bosonic and fermionic ultracold dipolar and ionic gases

We introduce a density functional formalism to study the ground-state properties of strongly-correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Due to its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-field theories fail.Comment: 5 pages, 2 figure

Correlations in Disordered Solvable Tensor Network States

Solvable matrix product and projected entangled pair states evolved by dual and ternary-unitary quantum circuits have analytically accessible correlation functions. Here, we investigate the influence of disorder. Specifically, we compute the average behavior of a physically motivated two-point equal-time correlation function with respect to random disordered solvable tensor network states arising from the Haar measure on the unitary group. By employing the Weingarten calculus, we provide an exact analytical expression for the average of the $k$th moment of the correlation function. The complexity of the expression scales with $k!$ and is independent of the complexity of the underlying tensor network state. Our result implies that the correlation function vanishes on average, while its covariance is nonzero.Comment: 28 pages, 2 figures, comments welcom

Bridging the gap:human emotions and animal emotions

Our experiences of the conscious mental states that we call emotions drive our interest in whether such states also exist in other animals. Because linguistic report can be used as a gold standard (albeit indirect) indicator of subjective emotional feelings in humans but not other species, how can we investigate animal emotions and what exactly do we mean when we use this term? Linguistic reports of human emotion give rise to emotion concepts (discrete emotions; dimensional models), associated objectively measurable behavioral and bodily emotion indicators, and understanding of the emotion contexts that generate specific states. We argue that many animal studies implicitly translate human emotion concepts, indicators and contexts, but that explicit consideration of the underlying pathways of inference, their theoretical basis, assumptions, and pitfalls, and how they relate to conscious emotional feelings, is needed to provide greater clarity and less confusion in the conceptualization and scientific study of animal emotion

Evaluating pharmacological models of high and low anxiety in sheep

New tests of animal affect and welfare require validation in subjects experiencing putatively different states. Pharmacological manipulations of affective state are advantageous because they can be administered in a standardised fashion, and the duration of their action can be established and tailored to suit the length of a particular test. To this end, the current study aimed to evaluate a pharmacological model of high and low anxiety in an important agricultural and laboratory species, the sheep. Thirty-five 8-month-old female sheep received either an intramuscular injection of the putatively anxiogenic drug 1-(m-chlorophenyl)piperazine (mCPP; 1 mg/kg; n = 12), an intravenous injection of the putatively anxiolytic drug diazepam (0.1 mg/kg; n = 12), or acted as a control (saline intramuscular injection n = 11). Thirty minutes after the treatments, sheep were individually exposed to a variety of tests assessing their general movement, performance in a ‘runway task’ (moving down a raceway for a food reward), response to startle, and behaviour in isolation. A test to assess feeding motivation was performed 2 days later following administration of the drugs to the same animals in the same manner. The mCPP sheep had poorer performance in the two runway tasks (6.8 and 7.7 × slower respectively than control group; p < 0.001), a greater startle response (1.4 vs. 0.6; p = 0.02), a higher level of movement during isolation (9.1 steps vs. 5.4; p < 0.001), and a lower feeding motivation (1.8 × slower; p < 0.001) than the control group, all of which act as indicators of anxiety. These results show that mCPP is an effective pharmacological model of high anxiety in sheep. Comparatively, the sheep treated with diazepam did not display any differences compared to the control sheep. Thus we suggest that mCPP is an effective treatment to validate future tests aimed at assessing anxiety in sheep, and that future studies should include other subtle indicators of positive affective states, as well as dosage studies, so conclusions on the efficacy of diazepam as a model of low anxiety can be drawn

Geometrization of the Gauge Connection within a Kaluza-Klein Theory

Within the framework of a Kaluza-Klein theory, we provide the geometrization of a generic (Abelian and non-Abelian) gauge coupling, which comes out by choosing a suitable matter fields dependence on the extra-coordinates. We start by the extension of the Nother theorem to a multidimensional spacetime being the direct sum of a 4-dimensional Minkowski space and of a compact homogeneous manifold (whose isometries reflect the gauge symmetry); we show, how on such a ``vacuum'' configuration, the extra-dimensional components of the field momentum correspond to the gauge charges. Then we analyze the structure of a Dirac algebra as referred to a spacetime with the Kaluza-Klein restrictions and, by splitting the corresponding free-field Lagrangian, we show how the gauge coupling terms outcome.Comment: 10 pages, no figure, to appear on Int. Journ. Theor. Phy

Efficient Algorithm for Asymptotics-Based Configuration-Interaction Methods and Electronic Structure of Transition Metal Atoms

Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schr\"odinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement, and apply to 3d transition metal atoms an efficient and accurate algorithm for asymptotics-based CI. Efficiency gains come from exact (symbolic) decomposition of the CI space into irreducible symmetry subspaces at essentially linear computational cost in the number of radial subshells with fixed angular momentum, use of reduced density matrices in order to avoid having to store wavefunctions, and use of Slater-type orbitals (STO's). The required Coulomb integrals for STO's are evaluated in closed form, with the help of Hankel matrices, Fourier analysis, and residue calculus. Applications to 3d transition metal atoms are in good agreement with experimental data. In particular we reproduce the anomalous magnetic moment and orbital filling of Chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.Comment: 14 pages, 1 figur

A novel task to assess mood congruent memory bias in non-human animals

Background: Assessing the affective state of animals is important for a range of research areas, including neuroscience. The use of cognitive judgement and attention biases to determine affective state has been demonstrated in animals, but approaches to assess mood-congruent biases in memory have yet to become established. New Method: We describe a novel methodology to investigate memory bias in animals, presenting initial data using the influence of social status to manipulate affective state. The method required laboratory rats to achieve criterion at a working-memory task in an eight-arm radial maze before probing their memory of putative negative, positive or neutral events that occurred in specific arms of the maze. They were tested 2hrs and 24hrs after experiencing each event to determine how the affective valence of the event influenced task performance. Results: Regardless of social status, rats avoided arms where they had experienced negative events and preferred arms where they had experienced positive events. However, subordinate rats made errors sooner than dominant rats in tests following exposure to the negative event. Furthermore, whilst subordinate individuals made errors earlier in tests following the negative event relative to the neutral or positive event, dominant rats made errors earlier in tests that followed the positive event. Comparison with existing method(s): Changes in performance thus appeared to reflect social status and associated affective state, confirming a new method for assessing animal affect. Conclusions: This new memory bias task could potentially be used to determine affective state in a range of non-human animal species

Stereotyping starlings are more 'pessimistic'.

Negative affect in humans and animals is known to cause individuals to interpret ambiguous stimuli pessimistically, a phenomenon termed 'cognitive bias'. Here, we used captive European starlings (Sturnus vulgaris) to test the hypothesis that a reduction in environmental conditions, from enriched to non-enriched cages, would engender negative affect, and hence 'pessimistic' biases. We also explored whether individual differences in stereotypic behaviour (repetitive somersaulting) predicted 'pessimism'. Eight birds were trained on a novel conditional discrimination task with differential rewards, in which background shade (light or dark) determined which of two covered dishes contained a food reward. The reward was small when the background was light, but large when the background was dark. We then presented background shades intermediate between those trained to assess the birds' bias to choose the dish associated with the smaller food reward (a 'pessimistic' judgement) when the discriminative stimulus was ambiguous. Contrary to predictions, changes in the level of cage enrichment had no effect on 'pessimism'. However, changes in the latency to choose and probability of expressing a choice suggested that birds learnt rapidly that trials with ambiguous stimuli were unreinforced. Individual differences in performance of stereotypies did predict 'pessimism'. Specifically, birds that somersaulted were more likely to choose the dish associated with the smaller food reward in the presence of the most ambiguous discriminative stimulus. We propose that somersaulting is part of a wider suite of behavioural traits indicative of a stress response to captive conditions that is symptomatic of a negative affective state