Related papers: Path Integral Complexity and Kasner singularities
We study holographic volume complexity for various families of holographic cosmologies with Kasner-like singularities, in particular with $AdS$, hyperscaling violating and Lifshitz asymptotics. We find through extensive numerical studies…
We perform a comparative study of the time dependence of the holographic quantum complexity of some space like singular bulk gravitational backgrounds. This is done by considering the two available notions of complexity, one that relates it…
We propose a gravity dual description of the path-integral optimization in conformal field theories arXiv:1703.00456, using Hartle-Hawking wave functions in anti-de Sitter spacetimes. We show that the maximization of the Hartle-Hawking wave…
The effects of a boundary on the circuit complexity are studied in two dimensional theories. The analysis is performed in the holographic realization of a conformal field theory with a boundary by employing different proposals for the dual…
Exact solutions to Einstein's equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz)…
In the presence of a scalar hair perturbation, the Cauchy horizon of a Reissner-Nordstr\"om black hole disappears and is replaced by the rapid collapse of the Einstein-Rosen bridge, which leads to a Kasner singularity [1,2]. We study the…
For autonomous systems it is well known how to extract tunneling probabilities from wavepacket calculations. Here we present a corresponding approach for periodically time-dependent Hamiltonians, valid at all frequencies, field strengths,…
This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By…
In this paper, we will analyse the holographic complexity for time-dependent asymptotically $AdS$ geometries. We will first use a covariant zero mean curvature slicing of the time-dependent bulk geometries, and then use this co-dimension…
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…
We discuss the interpretation of path integral optimization as a uniformization problem in even dimensions. This perspective allows for a systematical construction of the higher-dimensional path integral complexity in holographic conformal…
The holographic complexity has been studied in a background which includes a critical point in the dual field theory. We have examined how the complexity rate and the saturation time of dynamical variables in the theory behave as one moves…
Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and…
It is well known that Kasner geometry with space-like singularity can be extended to bulk AdS-like geometry, furthermore one can study field theory on this Kasner space via its gravity dual. In this paper, we show that there exists a…
The propagator for a certain class of two time-dependent coupled and driven harmonic oscillators with time-varying angular frequencies and masses is evaluated by path integration. This is simply done through suitably chosen generalized…
We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is…
We propose that holographic spacetimes can be regarded as collections of quantum circuits based on path-integrals. We relate a codimension one surface in a gravity dual to a quantum circuit given by a path-integration on that surface with…
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time…
It has been shown that the "complexity=anything" observables allow more possibilities to probe the geometry behind the horizon of AdS black holes compared to the volume complexity. For uncharged black holes, these observables access the…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…