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Classical clocks measure proper time along their worldline, and Riemannian geometry provides tools for predicting the time shown by clocks in both flat and curved spacetimes. Common approaches to time in quantum systems, based for instance…
We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…
We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. We show that a mixed phase space comprising both regular and chaotic motion is required and derive a classical sum…
While the impact of locality restrictions on quantum dynamics and algorithmic complexity has been well studied in the general case of time-dependent Hamiltonians, the capabilities of time-independent protocols are less well understood.…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
We investigate how the quantum dynamics of gravitational models depends on the internal clock employed in quantisation. Our previous result on the quantum Friedmann-Lemaitre model demonstrates that almost all physical predictions from the…
We present two applications of emergent local Hamiltonians to speed up quantum adiabatic protocols for isolated noninteracting and weakly interacting fermionic systems in one-dimensional lattices. We demonstrate how to extract maximal work…
We construct a periodically time-dependent Hamiltonian with a phase transition in the quantum Hall universality class. One spatial dimension can be eliminated by introducing a second incommensurate driving frequency, so that we can study…
Rydberg-atom quantum simulators are of keen interest because of their possibilities towards high-dimensional qubit architectures. Here we report three-dimensional conformation spectra of quantum-Ising Hamiltonian systems with programmed…
To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its…
We present a unitary control pulse design method for a scalable quantum computer architecture based on electron spins in lateral quantum dots. We employ simultaneous control of spin interactions and derive the functional forms of spin…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
We develop a mathematical framework for quantum time transfer based on commuting families of Hamiltonians and synchronization observables. The synchronization subspace is defined as the kernel of a difference operator between local clocks,…
Quaternionic quantum Hamiltonians describing nonrelativistic spin particles require the ambient physical space to have five dimensions. The quantum dynamics of a spin-1/2 particle system characterised by a generic such Hamiltonian is worked…
A quantum unitary gate is realized in this paper by perturbing a free charged particle in a one-dimensional box with a time- and position-varying electric field. The perturbed Hamiltonian is composed of a free particle Hamiltonian plus a…
We characterize the set of generalized quantum measurements that can be decomposed into a continuous measurement process using a stream of probe qubits and a tunable interaction Hamilto- nian. Each probe in the stream interacts weakly with…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
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…