Related papers: Time Dependent Quantum Mechanics
The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
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…
Quantum dynamics simulations (QDSs) are one of the most highly anticipated applications of quantum computing. Quantum circuit depth for implementing Hamiltonian simulation algorithms is commonly time dependent so that long time dynamics…
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
The self adjoint operator of time in non-relativistic quantum mechanics is found within the approach where the ordinary Hamiltonian is not taken to be conjugate to time. The operator version of the reexpressed Liouville equation with the…
A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…
In recent works we have used quantum tools in the analysis of the time evolution of several macroscopic systems. The main ingredient in our approach is the self-adjoint Hamiltonian $H$ of the system $\Sc$. This Hamiltonian quite often, and…
The phenomenon of quantum tunneling is reviewed and an overview of applying approximate methods for studying this effect is given. An approach to a time-dependent formalism is proposed in one dimension and generalized to higher dimensions.…
While quantum simulation is one of the most promising applications of modern quantum devices, accessible simulation times are fundamentally limited by finite coherence times due to omnipresent noise. Based on the ideas of relational…
It is shown that linear time-dependent invariants for arbitrary multi\-dimensional quadratic systems can be obtained from the Lagrangian and Hamiltonian formulation procedures by considering a variation of coordinates and momenta that…
A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in…
We consider quantum dynamics for which the strict adiabatic approximation fails but which do not escape too far from the adiabatic limit. To treat these systems we introduce a generalisation of the time dependent wave operator theory which…
Parameterized quantum circuits are a promising technology for achieving a quantum advantage. An important application is the variational simulation of time evolution of quantum systems. To make the most of quantum hardware, variational…
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…
Existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to quantum simulations of time-independent quantum systems. We overcome this restriction to perturbative treatments with…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
This study explores the time-dependent Dunkl-Pauli oscillator in two dimensions. We constructed the Dunkl-Pauli Hamiltonian, which incorporates a time-varying magnetic field and a harmonic oscillator characterized by time-dependent mass and…
Changing some of its parameters over time is a paradigmatic way of driving an otherwise isolated many-body quantum system out of equilibrium, and a vital ingredient for building quantum computers and simulators. Here, we further develop a…