Related papers: The First Law of Complexity
It is believed that a primary principle of the theory of quantum gravity is the Holographic Principle according to which a physical system can be described only by degrees of freedom living on its boundary. The generalized covariant…
The entanglement "first law" in conformal field theories relates the entanglement entropy for a ball-shaped region to an integral over the same region involving the expectation value of the CFT stress-energy tensor, for infinitesimal…
In a recent note I argued that the holographic origin of gravitational attraction is the quantum mechanical tendency for operators to grow under time evolution. In a followup the claim was tested in the context of the SYK theory and its…
Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of…
We study the dynamical complexity of an open quantum driven double-well oscillator, mapping its dependence on effective Planck's constant $\hbar_{eff}\equiv\beta$ and coupling to the environment, $\Gamma$. We study this using stochastic…
Contrary to popular belief, asymptotically anti-de Sitter solutions of gravitational theories cannot be obtained by taking initial data (satisfying the constraints) on a spacelike surface, and choosing an arbitrary conformal metric on the…
The Weiss variational principle in mechanics and classical field theory is a variational principle which allows displacements of the boundary. We review the Weiss variation in mechanics and classical field theory, and present a novel…
We discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum…
Consider Ginibre's ensemble of $N \times N$ non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance $\frac{1}{N}$. As $N \uparrow \infty$ the normalized counting measure of the…
In the last decade, the first law of binary black hole mechanics played an important unifying role in the gravitational two-body problem. More recently, binary black hole scattering and the application of high-energy physics methods have…
We compute the quantum circuit complexity of the evolution of scalar curvature perturbations on expanding backgrounds, using the language of squeezed vacuum states. In particular, we construct a simple cosmological model consisting of an…
In physical theories, boundary or initial conditions play the role of selecting special situations which can be described by a theory with its general laws. Cosmology has long been suspected to be different in that its fundamental theory…
We consider a quantum scalar field in a classical (Euclidean) De Sitter background, whose radius is fixed dynamically by Einstein's equations. In the case of a free scalar, it has been shown by Becker and Reuter that if one regulates the…
We employ holography to calculate the quantum complexity of $T\bar{T}$-deformation, utilizing the complexity equals volume (CV) and the complexity equals action (CA) proposals within the bulk spacetime with a finite radius cutoff. We find…
We initiate quantitative studies of complexity in (1+1)-dimensional conformal field theories with a view that they provide the simplest setting to find a gravity dual to complexity. Our work pursues a geometric understanding of complexity…
The Einstein-Cartan theory of gravity can arise from a mechanism of spontaneous symmetry breaking within the context of pre-geometric gauge theories. In this work, we develop the Hamiltonian analysis of such theories. By making contact with…
We discuss the coupled Einstein-Klein-Gordon equations for a complex scalar field with and without a quartic self-interaction in a zero curvature Friedman-Lema\^{\i}tre Universe. The complex scalar field, as well as the metric, is…
Spontaneous Lorentz violation is a viable mechanism to look for Planck scale physics. In this work, we study spontaneous Lorentz violation models, in flat spacetime, where a vector field produces such a violation and matter is modeled by a…
When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential…
We employ the "complexity equals action" conjecture to investigate the action growth rate for the charged and neutral AdS black branes of a holographic toy model consisting of Einstein-Maxwell theory in $d + 1$-dimensional bulk spacetime…