Related papers: Notes on quantum evolution across singularities
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
After stating the measurement problem, physicists usually assume the problem to be coming from the measurement part. Since classical probabilities also collapse when updating information, there is nothing special about quantum state…
The treatment of time in relativity does not conform to that in quantum theory. In the context of quantum gravity this is called "the problem of time". A crucial difference is that time $t$ may be seen as an observable in relativity theory,…
The Hamiltonian constraint system is the canonical formulation of a physical system with a Hamiltonian constrained to vanish. In terms of the canonical variables, we define what we call reference observable, with respect to which other…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic…
The level of current understanding of the physics of time-dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
Open systems acquire time-dependent coupling constants through interaction with an external field or environment. We generalize the Lewis-Riesenfeld invariant theorem to open system of quantum fields after second quantization. The…
We consider $d$-dimensional quantum systems which for positive times evolve with a time-independent Hamiltonian in a nonequilibrium state that we keep generic in order to account for arbitrary evolution at negative times. We show how the…
Rovelli's `` quantum mechanics without time'' motivates an intrinsically time-slicing independent picture of reduced phase space quantum gravity, which may be described as ``quantization after evolution''. Sufficient criteria for carrying…
Models of effective stellar collapse inspired by loop quantum gravity predict a bounce when the stellar energy density reaches the Planck scale, typically followed by the formation of shell-crossing singularities. This work aims to extend…
The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological…
A definition of quantum singularity for the case of static spacetimes has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed, and then applied…
Certain time dependent configurations in the c=1 matrix model correspond to string theory backgrounds which have spacelike boundaries and appear geodesically incomplete. We investigate quantum mechanical properties of a class of such…
A compact analysis of development and prospects in the study of the tunnelling evolution is given. A new systematization of various approaches to defining tunnelling times in the light of time as a quantum mechanical observable is proposed.…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Using the improved quantization technique to the mini-superspace approximation of loop quantum gravity, we study the evolution of black holes supported by a cosmological constant. The addition of a cosmological constant allows for classical…
This is a review of recent progress concerning generic spacelike singularities in general relativity. For brevity the main focus is on singularities in vacuum spacetimes, although the connection with, and the role of, matter for generic…