Related papers: A Discrete Time Presentation of Quantum Dynamics
For quantum effects $a$ and $b$ we define the $a$-evolution of $b$ at time $t$ denoted by $b(t\mid a)$. We interpret $b(t\mid a)$ as the influence that $a$ has on $b$ at time $t$ when $a$ occurs, but is not measured at time $t=0$. Using…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded…
This colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. We particularly focus on quantum quenches: the temporal evolution following a sudden or…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
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…
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…
In loop quantum cosmology, a difference equation for the wave function describes the evolution of a universe model. This is different from the differential equations that arise in Wheeler-DeWitt quantizations, and some aspects of general…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
We study the time it takes for all states of a finite quantum system to return simultaneously to their original configuration. In particular, we define the recurrence time for a quantum system to be the time at which all time-evolved states…
We describe the application of methods from the study of discrete dynanmical systems to the problem of the continuum limit of evolving spin networks. These have been found to describe the small scale structure of quantum general relativity…
An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The…
Understanding the evolution of entropy in the universe is a fundamental aspect of cosmology. This paper investigates the evolution of entropy in a spatially flat $K=0$ universe, focusing on the contributions of matter, radiation, and dark…
Three postulates are discussed: first that well-defined properties cannot be assigned to an isolated system, secondly that quantum unitary evolution is atemporal, and thirdly that some physical processes are never reversed. It is argued…
We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…
This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational…
A model quantum cosmology is used to illustrate how arrows of time emerge in a universe governed by a time-neutral dynamical theory constrained by time asymmetric initial and final boundary conditions represented by initial and final…
The existence of a scaling evolution for cosmic string loops in an expanding universe is demonstrated for the first time by means of numerical simulations. In contrast with what is usually assumed, this result does not rely on any…