Related papers: An ode to instantons
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
We survey the equations of continuous-time quantum walks on simple one-dimensional lattices, which include the finite and infinite lines and the finite cycle, and compare them with the classical continuous-time Markov chains. The focus of…
The article explores a new formalism for describing motion in quantum mechanics. The construction is based on generalized coherent states with evolving fiducial vector. Weyl-Heisenberg coherent states are utilised to split quantum systems…
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…
We propose to use the effect of measurements instead of their number to study the time evolution of quantum systems under monitoring. This time redefinition acts like a microscope which blows up the inner details of seemingly instantaneous…
Fluctuation terms and higher moments of a quantum state imply corrections to the classical equations of motion that may have implications in early-universe cosmology, for instance in the state-dependent form of effective potentials. In…
We present a detailed discussion of some features of quantum mechanical metastability. We analyze the nature of decaying (quasistationary) states and the regime of validity of the exponencial law, as well as decays at finite temperature. We…
Reversible lattice dynamics embody basic features of physics that govern the time evolution of classical information. They have finite resolution in space and time, don't allow information to be erased, and easily accommodate other…
We investigate quantum mechanical Hamiltonians with explicit time dependence. We find a class of models in which an analogue of the time independent \S equation exists. Among the models in this class is a new exactly soluble model, the…
The semiclassical gravity describes gravitational back-reactions of the classical spacetime interacting with quantum matter fields but the quantum effects on the background is formally defined as higher derivative curvatures. These induce…
We show how to do semiclassical nonperturbative computations within the worldline approach to quantum field theory using ``worldline instantons''. These worldline instantons are classical solutions to the Euclidean worldline loop equations…
Starting from trace formulae for the tunnelling splittings (or decay rates) analytically continued in the complex time domain, we obtain explicit semiclassical expansions in terms of complex trajectories that are selected with appropriate…
Invariance under translation is exploited to efficiently simulate one-dimensional quantum lattice systems in the limit of an infinite lattice. Both the computation of the ground state and the simulation of time evolution are considered.
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially…
Analyses of phenomena exhibiting finite-time decay of quantum entanglement have recently attracted considerable attention. Such decay is often referred to as sudden vanishing (or sudden death) of entanglement, which can be followed by its…
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…
The origin and nature of time in complex systems is explored using quantum (or 'Feynman') clocks and the signals produced by them. Networks of these clocks provide the basis for the evolution of complex systems. The general concept of…
Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive…
Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over space-time geometries in nonperturbative quantum gravity. We show that the macroscopic four-dimensional world which emerges in…