Related papers: Pentahedral volume, chaos, and quantum gravity
In hybrid classical-quantum theories, the dynamics of the classical system induce the classicality of the quantum system, meaning that such models do not necessarily require a measurement postulate to describe probabilistic measurement…
The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given…
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
QCD at the classical level possesses scale invariance which is broken by quantum effects. This ``dimensional transmutation'' phenomenon can be mathematically described by formulating classical gluodynamics in a curved, conformally flat,…
This article examines the relationship between classical and quantum propagation of chaos. (In this context, "chaos" refers to the Boltzmann's Ansatz of molecular disorder, not to chaotic dynamics.) Classical propagation of chaos is shown…
We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied…
Based on periodic orbit theory we address the individual-system versus ensemble interpretation of quantum gravity from a quantum chaos perspective. To this end we show that the spectrum of geodesic motion on high-dimensional hyperbolic…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
We have identified ultra-cold atoms in magneto-optical double-well potentials as a very clean setting in which to study the quantum and classical dynamics of a nonlinear system with multiple degrees of freedom. In this system, entanglement…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
We investigate the geometry of a quantum universe with the topology of the four-torus. The study of non-contractible geodesic loops reveals that a typical quantum geometry consists of a small semi-classical toroidal bulk part, dressed with…
Recent studies have shown that there is a strong interplay between quantum complexity and quantum chaos. In this work, we consider a new method to study geometric complexity for interacting non-Gaussian quantum mechanical systems to…
We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation, via a regularization procedure; it is finite,…
This article is the written version of a talk delivered at the Workshop on Nonlinear Dynamics and Fundamental Interactions in Tashkent and starts with an introduction into quantum chaos and its relationship to classical chaos. The…
The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schr\"odinger Hamiltonians on metric graphs, with a focus on results related to…
A central aspect of the cosmological constant problem is to understand why vacuum energy does not gravitate. In order to account for this observation, while allowing for nontrivial dynamics of the quantum vacuum, we motivate a novel…
We consider a mixed chaotic Hamiltonian system and compare classical with quantum chaos. As alternative to the methods of enegy level spacing statistics and trace formulas, we construct a quantum action and a quantum analogue phase space to…
We discuss the classical and quantum chaos of closed strings on a recently constructed charged confining holographic background. The confining background corresponds to the charged soliton, which is a solution of minimal $d=5$ gauged…