Related papers: Complexity and Shock Wave Geometries
We construct a time-dependent expression of the computational complexity of a quantum system which consists of two conformal complex scalar field theories in d dimensions coupled to constant electric potentials and defined on the boundaries…
By extending Einstein's separation of wave and particle parts of the second order thermal fluctuation to encompass "generalized fluctuations" in any Bose field, P. E. Gordon has proposed alternative definitions for nth order coherence and…
In this paper we tackle the problem of constructing explicit examples of topological cocycles of Roberts' net cohomology, as defined abstractly by Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum field theory on…
We propose a method to compute complex volume of 2-bridge link complements. Our construction sheds light on a relationship between cluster variables with coefficients and canonical decompositions of link complements.
The Einstein-Cartan-Saa theory of torsion modifies the spacetime volume element so that it is compatible with the connection. The condition of connection compatibility gives constraints on torsion, which are also necessary for the…
After a brief review of current scenarios for the resolution and/or avoidance of the Big Bang, an alternative hypothesis is put forward implying an infinite increase in complexity towards the initial singularity. This may result in an…
Entanglement of light and matter is an essential resource for effective quantum engineering. In particular, collective states of atomic ensembles are robust against decoherence while preserving the possibility of strong interaction with…
We consider a brane-world of co-dimension one without the reflection symmetry that is commonly imposed between the two sides of the brane. Using the coordinate-free formalism of the Gauss-Codacci equations, we derive the effective Einstein…
We consider branes in refined topological strings. We argue that their wave-functions satisfy a Schr\"odinger equation depending on multiple times and prove this in the case where the topological string has a dual matrix model description.…
We explore the complexity equals volume proposal for planar black holes in anti-de Sitter (AdS) spacetime in 2+1 dimensions, with an end of the world (ETW) brane behind the horizon. We allow for the possibility of intrinsic gravitational…
We discuss the semiclassical instability of the Randall-Sundrum brane-world model against a creation of a kind of Kaluza-Klein bubble. An example describing such a bubble space-time is constructed from the five-dimensional AdS-Schwarzschild…
The Multiplicity Conjecture is a deep problem relating the multiplicity (or degree) of a Cohen-Macaulay standard graded algebra with certain extremal graded Betti numbers in its minimal free resolution. In the case of level algebras of…
In this paper, we provide an $O(n \mathrm{polylog} n)$ bound on the expected complexity of the randomly weighted Voronoi diagram of a set of $n$ sites in the plane, where the sites can be either points, interior-disjoint convex sets, or…
Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one…
In this paper, we investigate the fluid/gravity correspondence in the framework of massive Einstein gravity. Treating the gravitational mass terms as an effective energy-momentum tensor and utilizing the Petrov-like boundary condition on a…
The volume inside a Ryu-Takayanagi surface has been conjectured to be related to the complexity of subregions of the boundary field theory. Here, we study the behaviour of this volume analytically, when the entangling surface has a strip…
Einstein Equivalence Principle (EEP) requires all matter components to universally couple to gravity via a single common geometry: that of spacetime. This relates quantum theory with geometry as soon as interactions with gravity are…
Complexity theory embodies some of the hardest, most fundamental and most challenging open problems in modern science. The very term complexity is very elusive, so that the main goal of this theory is to find meaningful quantifiers for it.…
While the exact separability probability of 8/33 for two-qubit states under the Hilbert-Schmidt measure has been reported by Huong and Khoi [\href{https://doi.org/10.1088/1751-8121/ad8493}{J.Phys.A:Math.Theor.{\bf57}, 445304(2024)}],…
The maximum size of a cosmic structure is given by the maximum turnaround radius -- the scale where the attraction due to its mass is balanced by the repulsion due to dark energy. We derive generic formulae for the estimation of the maximum…