arXiv subjects

Juan Hernandez

Publications and source records attributed to Juan Hernandez.

21 records · Page 2Linked to original sources

arXiv2020

The First Law of Complexity

We investigate the variation of holographic complexity for two nearby target states. Based on Nielsen's geometric approach, we find the variation only depends on the end point of the optimal trajectory, a result which we designate the first law of complexity. As an example, we examine the complexity=action conjecture when the AdS vacuum is perturbed by a scalar field excitation, which corresponds to a coherent state. Remarkably, the gravitational contributions completely cancel and the final variation reduces to a boundary term coming entirely from the scalar field action. Hence the null boundary of Wheeler-DeWitt patch appears to act like the "end of the quantum circuit".

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arXiv2018

Circuit Complexity for Coherent States

We examine the circuit complexity of coherent states in a free scalar field theory, applying Nielsen's geometric approach as in [1]. The complexity of the coherent states have the same UV divergences as the vacuum state complexity and so we consider the finite increase of the complexity of these states over the vacuum state. One observation is that generally, the optimal circuits introduce entanglement between the normal modes at intermediate stages even though our reference state and target states are not entangled in this basis. We also compare our results from Nielsen's approach with those found using the Fubini-Study method of [2]. For general coherent states, we find that the complexities, as well as the optimal circuits, derived from these two approaches, are different.

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arXiv2017

Relativistic magnetohydrodynamics

We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfven waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfven-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).

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