Related papers: Notes on quantum evolution across singularities
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial…
We analize the relational quantum evolution of generally covariant systems in terms of Rovelli's evolving constants of motion and the generalized Heisenberg picture. In order to have a well defined evolution, and a consistent quantum…
We continue our analysis of a quantum cosmology model describing a flat Friedmann--Lema\^itre--Robertson--Walker universe filled with a (free) massless scalar field and an arbitrary perfect fluid. For positive energy density in the scalar…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…
The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static…
We describe a novel class of quantum mechanical particle oscillations in both relativistic and non-relativistic systems based on $PT$ symmetry and $T^2=-1$ (relevant for fermions), where $P$ is parity and $T$ is time reversal. The…
The study of the physical properties of open quantum systems is at the heart of many present investigations which aim to describe their dynamical evolution, on theoretical ground and through physical realizations. Here we develop a…
We present a relational framework in which temporal structure is not fundamental but emerges from correlations within a globally stationary quantum state. Each subsystem includes an internal clock, and conditional states evolve effectively…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
The temporal evolution of the entanglement between two qubits evolving by random interactions is studied analytically and numerically. Two different types of randomness are investigated. Firstly we analyze an ensemble of systems with…
We investigate the cosmological behavior in a universe governed by time asymmetric extensions of general relativity, which is a novel modified gravity based on the addition of new, time-asymmetric, terms on the Hamiltonian framework, in a…
We examine the properties of open quantum systems with respect to their time evolution in different regimes, Markovian and non-Markovian. We analyze their behaviour with respect to their coherent or decoherent time evolution by means of…
Time-dependent quantum evolution is described by an algebraic connection on a $C^\infty(R)$-module of sections of a $C^*$-algebra (or Hilbert) fibre bundle.
The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global…
This is a summary of how the definition of quantum singularity is extended from static space-times to conformally static space-times. Examples are given.
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…