Time dependence of entanglement entropy on the fuzzy sphere

We numerically study the behaviour of entanglement entropy for a free scalar field on the noncommutative ("fuzzy") sphere after a mass quench. It is known that the entanglement entropy before a quench violates the usual area law due to the non-local nature of the theory. By comparing our results to the ordinary sphere, we find results that, despite this non-locality, are compatible with entanglement being spread by ballistic propagation of entangled quasi-particles at a speed no greater than the speed of light. However, we also find that, when the pre-quench mass is much larger than the inverse of the short-distance cutoff of the fuzzy sphere (a regime with no commutative analogue), the entanglement entropy spreads faster than allowed by a local model.Comment: 1+14 pages, 8 figures v2: References added, matches published versio

Mutual information on the fuzzy sphere

We numerically calculate entanglement entropy and mutual information for a massive free scalar field on commutative (ordinary) and noncommutative (fuzzy) spheres. We regularize the theory on the commutative geometry by discretizing the polar coordinate, whereas the theory on the noncommutative geometry naturally posseses a finite and adjustable number of degrees of freedom. Our results show that the UV-divergent part of the entanglement entropy on a fuzzy sphere does not follow an area law, while the entanglement entropy on a commutative sphere does. Nonetheless, we find that mutual information (which is UV-finite) is the same in both theories. This suggests that nonlocality at short distances does not affect quantum correlations over large distances in a free field theory.Comment: 16 pages, 10 figures. Fixed minor typos, references updated, discussion slightly expande

Entanglement entropy on the fuzzy sphere

We obtain entanglement entropy on the noncommutative (fuzzy) two-sphere. To define a subregion with a well defined boundary in this geometry, we use the symbol map between elements of the noncommutative algebra and functions on the sphere. We find that entanglement entropy is not proportional to the length of the region's boundary. Rather, in agreement with holographic predictions, it is extensive for regions whose area is a small (but fixed) fraction of the total area of the sphere. This is true even in the limit of small noncommutativity. We also find that entanglement entropy grows linearly with N, where N is the size of the irreducible representation of SU(2) used to define the fuzzy sphere.Comment: 18 pages, 7 figures. v3 to appear in JHEP. Clarified statements about UV/IR mixing and interpretation in terms of degrees of freedom on the fuzzy sphere vs. matrix degrees of freedom, fixed some typos and added reference

A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled

In the AdS/CFT correspondence eternal black holes can be viewed as a specific entanglement between two copies of the CFT: the thermofield double. The statistical CFT Wightman function can be computed from a geodesic between the two boundaries of the Kruskal extended black hole and therefore probes the geometry behind the horizon. We construct a kernel for the AdS3/CFT2 Wightman function that is independent of the entanglement. This kernel equals the average off-diagonal matrix element squared of a primary operator. This allows us to compute the Wightman function for an arbitrary entanglement between the double copies and probe the emergent geometry between a left- and right-CFT that are not thermally entangled.Comment: 18 pages, 8 figures v2: Added appendix on spatial dependence, minor changes, matches published versio

Sunspots, cycles and adjustment costs in the two-sectors model

Do adjustment costs able to modify the dynamic of the two sectors model? We examine the impact of adjustment costs in capital on the properties of long-run equilibrium. We propose to analyse how the positive and negative degrees of adjustment costs could interplay with the local indeterminacy mechanism coming from the presence of sector specific externalities. When the adjustments costs function is convex there exists a Höpf bifurcation and the trajectory describes a cycle around the steady state. We give an heuristic economic explanation of the role of the adjustment costs leading to economic cycles.

Endogenous fluctutations: a financial transmission Mechanism

We propose to study the dynamic impact of adjustment costs in capital on the two sectors model with positive sector specific externalities. We proove that such costs are able to lead to endogenous fluctuations by financial transmission mechanism. Indeed, since adjustments costs are linked to the marginal Q of Tobin, the firm's investment decision depends on the gap between the true value of the assets of this firm and their market value. The marginal Q of Tobin is an indicator of this market value and when adjustment costs are sufficiently high they can interplay with sector-specific externalities to provide endogenous fluctuations. We can prove fluctuations and cycle arise for new configurations of capital intensity across sectors. Classically, in this model, these fluctuations take place with sufficiently high level of sector-specific externalities but only with capital intensity reversal across sector. When adjustment costs are considered, reversal is no longer necessary condition to endogenous fluctuations to arise. Moreover, we show that there exists a link between financial volatility, mesured by variations of the marginal Q of Tobin, and fluctuations

Keeping-up with the Joneses, a new source of endogenous fluctuations

Our main objective is to study the impact of consumption externality like keeping of with the Joneses on the properties of long-run equilibrium in the two-sector optimal growth model. Does this consumption externality lead to a new mechanism of local indeterminacy and endogenous fluctuations? We will see that, in two-sector growth models with exogenous labor and without technological externalities, if the representative agent is able to give more value to his social status than his own consumption, this is the keys of a new mechanism for endogenous fluctuations. Moreover, by opposition with the other endogenous fluctuation mechanisms, we will see that this one doesn't need to have restriction on the factor intensity configuration of the consumption sector

Keeping-up with the Joneses, a new source of fluctuations in the two-sector continuous-time models

Our main objective is to study the impact of consumption externality like keeping of with the Joneses on the properties of long-run equilibrium in the two-sector optimal growth model. Does this consumption externality lead to a new mechanism of local indeterminacy and endogenous fluctuations? We will see that, in two-sector growth models with exogenous labor and without technological externalities, if the representative agent is able to give more value to his social status than his own consumption, this is the keys of a new mechanism for endogenous fluctuations. Moreover, by opposition with the other endogenous fluctuation mechanisms, we will see that this one doesn't need to have restriction on the factor intensity configuration of the consumption sector

Theory for planetary exospheres: III. Radiation pressure effect on the Circular Restricted Three Body Problem and its implication on planetary atmospheres

The planetary exospheres are poorly known in their outer parts, since the neutral densities are low compared with the instruments detection capabilities. The exospheric models are thus often the main source of information at such high altitudes. We present a new way to take into account analytically the additional effect of the stellar radiation pressure on planetary exospheres. In a series of papers, we present with an Hamiltonian approach the effect of the radiation pressure on dynamical trajectories, density profiles and escaping thermal flux. Our work is a generalization of the study by Bishop and Chamberlain (1989). In this third paper, we investigate the effect of the stellar radiation pressure on the Circular Restricted Three Body Problem (CR3BP), called also the photogravitational CR3BP, and its implication on the escape and the stability of planetary exospheres, especially for Hot Jupiters. In particular, we describe the transformation of the equipotentials and the location of the Lagrange points, and we provide a modified equation for the Hill sphere radius that includes the influence of the radiation pressure. Finally, an application to the hot Jupiter HD 209458b reveals the existence of a blow-off escape regime induced by the stellar radiation pressure

Inviolable energy conditions from entanglement inequalities

Via the AdS/CFT correspondence, fundamental constraints on the entanglement structure of quantum systems translate to constraints on spacetime geometries that must be satisfied in any consistent theory of quantum gravity. In this paper, we investigate such constraints arising from strong subadditivity and from the positivity and monotonicity of relative entropy in examples with highly-symmetric spacetimes. Our results may be interpreted as a set of energy conditions restricting the possible form of the stress-energy tensor in consistent theories of Einstein gravity coupled to matter.Comment: 25 pages, 3 figures, v2: refs added, expanded discussion of strong subadditivity constraints in sections 2.1 and 4.