Related papers: Path Integral Complexity and Kasner singularities
We show that strongly coupled holographic matter at finite charge density can exhibit charge density wave phases which spontaneously break translation invariance while preserving time-reversal and parity invariance. We show that such phases…
Following a methodology similar to \cite{Alishahiha:2015rta}, we derive a holographic complexity for two dimensional holographic superconductors (gauge/string superconductors) with backreactions. Applying a perturbation method proposed by…
We study the UV divergences in the action of the "Wheeler-de Witt patch" in asymptotically AdS spacetimes, which has been conjectured to be dual to the computational complexity of the state of the dual field theory on a spatial slice of the…
This work investigates the quantum transport in a narrow constriction acted upon by a finite-range transversely polarized time-dependent electric field. A generalized scattering-matrix method is developed that has incorporated a…
In this paper we propose a space-time random tensor network approach for understanding holographic duality. Using tensor networks with random link projections, we define boundary theories with interesting holographic properties, such as the…
Properties of the space $\Ab$ of generalized connections in the Ashtekar framework are investigated. First a construction method for new connections is given. The new parallel transports differ from the original ones only along paths that…
Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro-Kac-Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS$_3$…
We suggest that the principle of holographic duality can be extended beyond conformal invariance and AdS isometry. Such an extension is based on a special relation between functional determinants of the operators acting in the bulk and on…
Within the framework of generalized combinatorial approach, the complexity is determined for infinite set of self-similar hierarchical ensembles. This complexity is shown to increase with strengthening of the hierarchy coupling to the…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
We study the interior dynamics of a top-down holographic superconductor from M-theory. The condense of the charged scalar hair necessarily removes the inner Cauchy horizon and the spacetime ends at a spacelike singularity. Although there is…
Considering a doubly holographic model, we study the evolution of holographic subregion complexity corresponding to deformations of bath state by a relevant scalar operator, which corresponds to a renormalization group flow from the…
We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The results are obtained by constructing and studying the…
For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated…
The time dependent entropy (or Leipnik's entropy) of harmonic and damped harmonic oscillators is extensively investigated by using time dependent wave function obtained by the Feynman path integral method. Our results for simple harmonic…
Three simple examples illustrate properties of path integral amplitudes in fixed background spacetimes with closed timelike curves: non-relativistic potential scattering in the Born approximation is non-unitary, but both an example with…
We consider the dependence of the recently proposed action/complexity duality conjecture on time and on the underlying topology of the bulk spacetime. For the former, we compute the dependence of the CFT complexity on a boundary temporal…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…
We discuss relevant scalar deformations of a holographic theory with a compact boundary. An example of such a theory would be the global AdS$_4$ with its spatially compact boundary $S^2$. To introduce a relevant deformation, we choose to…
The existence of local bases in which the components of derivations of tensor algebras over a differentiable manifold vanish along paths is proved. The holonomicity of these bases is investigated. The obtained results are applied to the…