Codification Volume of an operator algebra and its irreversible growth through thermal processes

Magan, Javier M.; Paganelli, Simone

doi:10.48550/arxiv.1404.2208

Cited by 3 publications

(23 citation statements)

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“…To construct the information field we will use the framework and ideas developed in [22]. In the first part of this section we review that construction.…”

Section: Scrambling As Stochastic Evolution Of Information Fieldsmentioning

confidence: 99%

“…In this section we review the novel approach to study quantum thermalization developed in [22], which serves as the basis for the construction of the information field. In this approach, the task is not to study the relaxation properties of a given subsystem, but to ask for the 'location' in the global pure state of the information lost by the subsystem.…”

Section: Codification Volumesmentioning

confidence: 99%

“…In this article we construct examples of such densities 4 , which we term information fields I n A (ρ), associated to some subsystem A and microscopic state ρ, where n = 1, • • • , N runs over the different degrees of freedom of the system. The construction is based on previous developments in the context of quantum thermalization [22]. We show that these information fields are defined unambigously from the quantum state, and therefore the unitary evolution of ρ, given by ρ(t) = U (t) ρ U † (t), induces a well defined time evolution for I n A (ρ), given by I n A (ρ(t)).…”

Section: Introductionmentioning

confidence: 99%

“…In a classical setting, in [3] it was characterized as the spreading of induced charges at the so-called brick wall [8] or streched horizon [9], in [5] it was characterized as a Lyapunov time of a strongly chaotic system, and in [10,11] diffusion processes, or random walks over the set of degrees of freedom were used in this regard. In more rigorous quantum setups, commutators between different operators in the system at different times were used to characterize signal propagation [12,10,13,14,15,16], while the relaxation of reduced subsystems and entanglement entropies were studied in [17,12,10,18,19,20,21,22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

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Fast Scramblers, Democratic Walks and Information Fields

Magan

2015

Preprint

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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' (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.

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“…To construct the information field we will use the framework and ideas developed in [22]. In the first part of this section we review that construction.…”

Section: Scrambling As Stochastic Evolution Of Information Fieldsmentioning

confidence: 99%

Section: Codification Volumesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fast Scramblers, Democratic Walks and Information Fields

Magan

2015

Preprint

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“…The reason is that entropy is always generated by some type of coarse graining, defined as a practical inability of measuring a certain type of information (correlators). In out of equilibrium scenarios, deterministic evolution distributes information evenly over all types of correlators [5,6], increasing the entropy of the coarse-grained description of the system. Entropy growth is then directly related to the ability of the system to create correlations between the coarse-grained variables and the rest, and these correlations are controlled by the microscopic structure of interactions.…”

Section: Introductionmentioning

confidence: 99%

Black hole collapse and democratic models

Jansen

Magán

2016

Phys. Rev. D

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We 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 BekensteinHawking 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.

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Black holes as random particles: entanglement dynamics in infinite range and matrix models

Magán

2016

J. High Energ. Phys.

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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-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-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.

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Codification Volume of an operator algebra and its irreversible growth through thermal processes

Cited by 3 publications

References 0 publications

Fast Scramblers, Democratic Walks and Information Fields

Fast Scramblers, Democratic Walks and Information Fields

Black hole collapse and democratic models

Black holes as random particles: entanglement dynamics in infinite range and matrix models

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