Related papers: Symmetry-Resolved Spread Complexity
The study of quantum reference frames has received renewed interest over the last years, leading to the parallel development of non-equivalent frameworks by different communities. We clarify the differences between these frameworks. At the…
We study a collection of discrete Markov chains related to the causal set approach to modeling discrete theories of quantum gravity. The transition probabilities of these chains satisfy a general covariance principle, a causality principle,…
Two desireable properties of a quantum dynamics for Loop Quantum Gravity (LQG) are that its generators provide an anomaly free representation of the classical constraint algebra and that physical states which lie in the kernel of these…
The classical variational approach to brittle fracture propagation does not distinguish between strain energy accumulation in tension versus compression and consequently results in physically unrealistic cracking under compression. A…
We construct a class of systems for which quantum dynamics can be expanded around a mean field approximation with essentially classical content. The modulus of the quantum overlap of mean field states naturally introduces a classical…
This Thesis explores the notion of Krylov complexity as a probe of quantum chaos and as a candidate for holographic complexity. The first Part is devoted to presenting the fundamental notions required to conduct research in this area.…
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived,…
This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules,…
The Bertaut approach associated with charge spreading so as to enhance the rate of convergence of Coulomb series in crystals is extended to the case of an arbitrary multiple spreading with a given initial spreading function. It is shown…
The recently-developed techniques of Noether analysis of the quantum-group spacetime symmetries of some noncommutative field theories rely on the {\it ad hoc} introduction of some peculiar auxiliary transformation parameters, which appear…
We investigate operator growth in quantum systems with two-dimensional Schr\"odinger group symmetry by studying the Krylov complexity. While feasible for semisimple Lie algebras, cases such as the Schr\"odinger algebra which is…
We investigate one-dimensional systems with both energy conservation and a continuous symmetry, focusing on the impact of a boundary perturbation that breaks the continuous symmetry. Our study reveals two distinct dynamical phases: one in…
Recent proposals suggest that a notion of generalized complexity, analogous to generalized entropy, may be necessary for understanding the dynamics of holographic complexity in settings where quantum effects are non-negligible, such as…
We identify the mechanism of slow heterogeneous relaxation in quantum kinetically constrained models (KCMs) in which the potential energy strength is controlled by a coupling parameter. The regime of slow relaxation includes the…
In an isolated system, the time evolution of a given observable in the Heisenberg picture can be efficiently represented in Krylov space. In this representation, an initial operator becomes increasingly complex as time goes by, a feature…
The expected indefinite causal structure in quantum gravity poses a challenge to the notion of entanglement: If two parties are in an indefinite causal relation of being spacelike and timelike, can they still be entangled? If so, how does…
In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…
In this work, the generalization of Friedel formula and Krein's theorem in complex potential scattering theory is presented. The consequence of various symmetry constraints on dynamical system are discussed. In addition,…
We develop a general theory for quantum key distribution (QKD) in both the forward error correction and the reverse error correction cases when the QKD system is equipped with phase-randomized coherent light with arbitrary number of decoy…
In this article and a companion paper we address the question of how one might obtain the semiclassical limit of ordinary matter quantum fields (QFT) propagating on curved spacetimes (CST) from full fledged Quantum General Relativity (QGR),…