Related papers: Quantum Complexity as Hydrodynamics
The curved geometry of a spacetime manifold arises as a solution of Einstein's gravitational field equation. We show that the metric of a spherically symmetric gravitational field configuration can be viewed as an optical metric created by…
We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
We formulate Nielsen's geometric approach to complexity in the context of two dimensional conformal field theories, where series of conformal transformations are interpreted as unitary circuits. We show that the complexity functional can be…
Inspired by the close relationship between Kolmogorov complexity and unsupervised machine learning, we explore quantum circuit complexity, an important concept in quantum computation and quantum information science, as a pivot to understand…
We apply one of the formalisms of noncommutative geometry to $R^N_q$, the quantum space covariant under the quantum group $SO_q(N)$. Over $R^N_q$ there are two $SO_q(N)$-covariant differential calculi. For each we find a frame, a metric and…
Identifying universal properties of non-equilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics emerges universally in the evolution of any interacting quantum system.…
We outline a general formalism of hydrodynamics for quantum systems with multiple particle species which undergo completely elastic scattering. In the thermodynamic limit, the complete kinematic data of the problem consists of the particle…
A thermodynamic analysis of weakly nonlocal non-relativistic fluids is presented under the assumption that an additional scalar field also contributes to the dynamics. The most general evolution of this field and the constitutive relations…
We extend existing results for the Nielsen complexity of scalar primaries and spinning primaries in four dimensions by including supersymmetry. Specifically, we study the Nielsen complexity of circuits that transform a superconformal…
Motivated by the geometrical structures of quantum mechanics, we introduce an almost-complex structure $J$ on the product $M\times M$ of any parallelizable statistical manifold $M$. Then, we use $J$ to extract a pre-symplectic form and a…
We provide a comprehensive picture for the formulation of the perfect fluid in the modern effective field theory formalism at both the classical and quantum level. Due to the necessity of decomposing the hydrodynamical variables $(\rho, p,…
We investigate aspects of non-equilibrium dynamics of strongly coupled field theories within holography. We establish a hydrodynamic description for anomalous quantum field theories subject to a strong external field for the first time in…
We investigate a one dimensional flow described with the non-compressible coupled Euler and non-compressible Navier-Stokes equations in Cartesian coordinate systems. We couple the two fluids through the continuity equation where different…
We numerically analyze the complexity of unitary time-evolution and precursor operators in one- and two-qubit systems using the framework of Nielsen complexity geometry. We find that, as expected, the complexities of unitary time evolution…
We apply the recently developed notion of complexity for field theory to a quantum quench through a critical point in 1+1 dimensions. We begin with a toy model consisting of a quantum harmonic oscillator, and show that complexity exhibits…
In this paper the quantum hydrodynamic approach for the KGE owning a perturbative self-interaction term is developed. The generalized model to non-Euclidean space-time allows to determine the quantum energy impulse tensor density of mesons…
Circuit complexity for two-dimensional topological quantum field theories (2D TQFT) was defined by Couch, Fan, and Shashi in [12]. In this paper, we study complexity for the 2D TQFT given by quantum cohomology of compact symplectic…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
Several papers from the mid to late 1990s suggest that Einstein's equations should be thought of as the hydrodynamic equations of a special class of quantum systems. A classical solution defines subsystems by dividing space-time up into…
We consider five-dimensional gravity coupled to a negative cosmological constant and a single U(1) gauge field, including a general set of four-derivative interactions. In this framework, we construct charged planar AdS black hole solutions…