results for au:Magan_J in:hep-th

- We study aspects of black holes and quantum chaos through the behavior of computational costs, which are distance notions in the manifold of unitaries of the theory. To this end, we enlarge Nielsen geometric approach to quantum computation and provide metrics for finite temperature/energy scenarios and CFT's. From the framework, it is clear that costs can grow in two different ways: operator vs `simple' growths. The first type mixes operators associated to different penalties, while the second does not. Important examples of simple growths are those related to symmetry transformations, and we describe the costs of rotations, translations, and boosts. For black holes, this analysis shows how infalling particle costs are controlled by the maximal Lyapunov exponent, and motivates a further bound on the growth of chaos. The analysis also suggests a correspondence between proper energies in the bulk and average `local' scaling dimensions in the boundary. Finally, we describe these complexity features from a dual perspective. Using recent results on SYK we compute a lower bound to the computational cost growth in SYK at infinite temperature. At intermediate times it is controlled by the Lyapunov exponent, while at long times it saturates to a linear growth, as expected from the gravity description.
- The de Finetti theorem and its extensions concern the structure of multipartite probability distributions with certain symmetry properties, the paradigmatic original example being permutation symmetry. These theorems assert that such symmetric distributions are well approximated by convex combinations of uncorrelated ones. In this article, we apply de Finetti theorems to quantum gravity theories, such as the Sachdev-Ye-Kitaev (SYK) model or large-N vector and gauge theories. For SYK we put recent studies of information/entanglement dynamics in a general and rigorous basis. For vector and gauge theories, we find a gauge invariant operator whose expectation value provides the leading term in the entanglement entropy in all states close enough to a given classical state. These results can be unified through a generic statement about the nature of Schmidt decompositions and decoherence in large-N theories. In the reverse direction, we extend de Finetti theorems in various ways and provide an independent approach to the theorems only based on the large-N properties of the gauge invariant coherence group.
- We discuss and compute entanglement entropy (EE) in (1+1)-dimensional free Lifshitz scalar field theories with arbitrary dynamical exponents. We consider both the subinterval and periodic sublattices in the discretized theory as subsystems. In both cases, we are able to analytically demonstrate that the EE grows linearly as a function of the dynamical exponent. Furthermore, for the subinterval case, we determine that as the dynamical exponent increases, there is a crossover from an area law to a volume law. Lastly, we deform Lifshitz field theories with certain relevant operators and show that the EE decreases from the ultraviolet to the infrared fixed point, giving evidence for a possible c-theorem for deformed Lifshitz theories.
- Sachdev-Ye-Kitaev (SYK) or embedded random ensembles are models of $N$ fermions with random k-body interactions. They play an important role in understanding black hole dynamics, quantum chaos, and thermalization. We study out of equilibrium scenarios in these systems and show they display perfect decoherence at all times. This peculiar feature makes them very attractive in the context of the quantum-to-classical transition and the emergence of classical general relativity. Based on this feature and unitarity, we propose a rate/continuity equation for the dynamics of the $\mathcal{O}(e^N)$ microstates probabilities. The effective permutation symmetry of the models drastically reduces the number of variables, allowing for compact expressions of n-point correlation functions and entropy of the microscopic distribution. Further assuming a generalized Fermi golden rule allows finding analytic formulas for the kernel spectrum at finite $N$, providing a series of short and long time scales controlling the out of equilibrium dynamics of this model. This approach to chaos, long time scales, and $1/N$ corrections might be tested in future experiments.
- We study the entanglement entropy (EE) of Gaussian systems on a lattice with periodic boundary conditions, both in the vacuum and at nonzero temperatures. By restricting the reduced subsystem to periodic sublattices, we can compute the entanglement spectrum and EE exactly. We illustrate this for a free (1+1)-dimensional massive scalar field at a fixed temperature. Consistent with previous literature, we demonstrate that for a sufficiently large periodic sublattice the EE grows extensively, even in the vacuum. Furthermore, the analytic expression for the EE allows us probe its behavior both in the massless limit and in the continuum limit at any temperature.
- Apr 14 2016 hep-th arXiv:1604.03772v1We study the evolution of black hole entropy and temperature in collapse scenarios, finding three generic lessons. First, entropy evolution is extensive. Second, at large times, entropy and temperature ring with twice the frequency of the lowest quasinormal mode. Third, the entropy oscillations saturate black hole area theorems in general relativity. The first two features are characteristic of entanglement dynamics in `democratic' models. Solely based on general relativity and Bekenstein-Hawking entropy formula, our results point to democratic models as microscopic theories of black holes. The third feature can be taken as a prediction for democratic models coming from black hole physics.
- We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector physics of large-$\mathcal{N}$ matrix models. Considering out of equilibrium initial states, we analytically compute the time evolution of every correlator of the theory and of the entanglement entropies, allowing a proper discussion of global thermalization/scrambling of information through the entire system. Microscopic non-locality causes factorization of reduced density matrices, and entanglement just depends on the time evolution of occupation densities. In the second part of the article, we show how the gained intuition extends to large-$\mathcal{N}$ matrix models, where we provide a gauge invariant entanglement entropy for `generalized free fields', again depending solely on the quasinormal frequencies. The results challenge the fast scrambling conjecture and point to a natural scenario for the emergence of the so-called brick wall or stretched horizon. Finally, peculiarities of these models in regards to the thermodynamic limit and the information paradox are highlighted.
- Having analytical instances of the Eigenstate Thermalization Hypothesis (ETH) is of obvious interest, both for fundamental and applied reasons. This is generically a hard task, due to the belief that non-linear interactions are basic ingredients of the thermalization mechanism. In this article we proof that random gaussian free fermions satisfy ETH in the multiparticle sector, by analytically computing the correlations and entanglement entropies of the theory. With the explicit construction at hand, we finally comment on the differences between fully random Hamiltonians and random Gaussian systems, and on the connection between chaotic energy spectra and ETH.
- We study a family of weighted random walks on complete graphs. These `democratic walks' turn out to be explicitly solvable, and we find the hierarchy window for which the characteristic time scale saturates the so-called fast scrambling conjecture. We show that these democratic walks describe well the properties of information spreading in systems in which every degree of freedom interacts with every other degree of freedom, such as Matrix or infinite range models. The argument is based on the analysis of suitably defined `Information fields' ($\mathcal{I}$), which are shown to evolve stochastically towards stationarity due to unitarity of the microscopic model. The model implies that in democratic systems, stabilization of one subsystem is equivalent to global scrambling. We use these results to study scrambling of infalling perturbations in black hole backgrounds, and argue that the near horizon running coupling constants are connected to entanglement evolution of single particle perturbations in democratic systems.
- Entanglement in random states has turned into a useful approach to quantum thermalization and black hole physics. In this article, we refine and extend the `random unitaries framework' to quantum field theories (QFT), and to include conserved charges. We show that in QFT, the connection between typical states, reduced subsystems and thermal dynamics is more transparent within the Fock basis. We provide generic formulae for the typical reduced density matrices and entanglement entropies of any given subset of particles. To illustrate our methods, we apply the generic framework to the simplest but non trivial cases, a massless scalar field in two dimensions and its generalization to the case of N scalar fields, including the large N limit. We find the effective temperature, by matching the reduced dynamics to a Gibbs ensemble, and derive the equation of state of the QFT. The deviations from perfect thermality are shown to be of order 1/S instead of exp(-S), a result which might be relevant for black hole physics. Finally we describe the analogue of the so-called `Page curve' in the QFT scenario as a function of the energy scale which divides high from low energy degrees of freedom.
- Aug 13 2014 hep-th arXiv:1408.2580v1A proposal to describe gravity duals of conformal theories with boundaries (AdS/BCFT correspondence) was put forward by Takayanagi few years ago. However interesting solutions describing field theories at finite temperature and charge density are still lacking. In this paper we describe a class of theories with boundary, which admit black hole type gravity solutions. The theories are specified by stress-energy tensors that reside on the extensions of the boundary to the bulk. From this perspective AdS/BCFT appears analogous to the fluid/gravity correspondence. Among the class of the boundary extensions there is a special (integrable) one, for which the stress-energy tensor is fluid-like. We discuss features of that special solution as well as its thermodynamic properties.
- Given a many-body system, we define a quantity, the Codification Volume of an operator algebra, which measures the size of the subspace with whom a given algebra is correlated. We explicitly calculate it for some limit cases, including vacuum states of local Hamiltonians and random states taken from the Haar ensemble. We argue that this volume should grow irreversibly in a thermalization process, and illustrate it numerically on a non-integrable quantum spin chain.
- We propose that fast scrambling on finite-entropy stretched horizons can be modeled by a diffusion process on an effective ultrametric geometry. A scrambling time scaling logarithmically with the entropy is obtained when the elementary transition rates saturate causality bounds on the stretched horizon. The so-defined ultrametric diffusion becomes unstable in the infinite-entropy limit. A formally regularized version can be shown to follow a particular case of the Kohlrausch law.
- We propose that local quantum systems defined on expander graphs provide a simple microscopic model for thermalization on quantum horizons. Such systems are automatically fast scramblers and are motivated from the membrane paradigm by a conformal transformation to the so-called optical metric.
- We investigate various geometrical aspects of the notion of `optical depth' in the thermal atmosphere of black hole horizons. Optical depth has been proposed as a measure of fast-crambling times in such black hole systems, and the associated optical metric suggests that classical chaos plays a leading role in the actual scrambling mechanism. We study the behavior of the optical depth with the size of the system and find that AdS/CFT phase transitions with topology change occur naturally as the scrambler becomes smaller than its thermal length. In the context of detailed AdS/CFT models based on D-branes, T-duality implies that small scramblers are described in terms of matrix quantum mechanics.
- Fast scramblers process information in characteristic times scaling logarithmically with the entropy, a behavior which has been conjectured for black hole horizons. In this note we use the AdS/CFT fold to argue that causality bounds on information flow only depend on the properties of a single thermal cell, and admit a geometrical interpretation in terms of the optical depth, i.e. the thickness of the Rindler region in the so-called optical metric. The spatial sections of the optical metric are well approximated by constant-curvature hyperboloids. We use this fact to propose an effective kinetic model of scrambling which can be assimilated to a compact hyperbolic billiard, furnishing a classic example of hard chaos. It is suggested that classical chaos at large N is a crucial ingredient in reconciling the notion of fast scrambling with the required saturation of causality.