Related papers: A magnetic clock for a harmonic oscillator
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…
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…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…
Recently, some attention has been given to the so-called Page-Wootters mechanism of quantum clocks. Among the various proposals to explore the mechanism using more modern techniques, some have chosen to use a quantum information…
Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…
In this paper, we further develop a recently proposed theory of time based on wavefunction collapse in general relativity. It is based on the postulations that quantum states, which violate the momentum and Hamiltonian constraints,…
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…
We outline formal and physical similarities between the quantum dynamics of open systems, and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, that,…
The nonequilibrium dynamics of a small quantum system coupled to a dissipative environment is studied. We show that (1) the oscillatory dynamics close to a coherent-to-incoherent transition is surprisingly different from the one of the…
It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with…
Uncertainty relations play a crucial role in quantum mechanics. Well-defined methods exist for the derivation of such uncertainties for pairs of observables. Other approaches also allow the formulation of time-energy uncertainty relations,…
The canonical proper time formulation of relativistic dynamics provides a framework from which one can describe the dynamics of classical and quantum systems using the clock of those very systems. The framework utilizes a canonical…
Time crystals, a unique non-equilibrium quantum phenomenon with promising applications in current quantum technologies, mark a significant advance in quantum mechanics. Although traditionally studied in atom-cavity and optical lattice…
In previous works, we showed that both time and space can emerge from entanglement within a globally constrained quantum Universe, with no background coordinates. By extending the Page and Wootters quantum time formalism to include both…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external…
The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine…
We provide a synopsis of an effective approach to the problem of time in the semiclassical regime. The essential features of this new approach to evaluating relational quantum dynamics in constrained systems are illustrated by means of a…
The apparent difficulty in recovering classical nonlinear dynamics and chaos from standard quantum mechanics has been the subject of a great deal of interest over the last twenty years. For open quantum systems - those coupled to a…
A harmonic oscillator with time-dependent mass $m(t)$ and a time-dependent (squared) frequency $\omega^2(t)$ occurs in the modelling of several physical systems. It is generally believed that systems, with $m(t)>0$ and $\omega^2(t)>0$…