Related papers: Time evolution of two harmonic oscillators with cr…
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…
In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterpart are important for the comprehension of posed problems in quantum optics and quantum…
We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions…
We study the time evolution of entangled states of a pair of identical atoms, considered in the harmonic approximation, coupled to an environment represented by an infinite set of free oscillators, with the whole system confined within a…
We consider an ensemble of coupled oscillators whose individual states, in addition to the phase, are characterized by an internal variable with autonomous evolution. The time scale of this evolution is different for each oscillator, so…
We study the quantum-mechanical evolution of the nonrelativistic oscillator, rapidly moving in the media with the random vector fields. We calculate the evolution of the level probability distribution as a function of time, and obtain rapid…
We describe a novel class of quantum mechanical particle oscillations in both relativistic and non-relativistic systems based on $PT$ symmetry and $T^2=-1$ (relevant for fermions), where $P$ is parity and $T$ is time reversal. The…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
In this paper we develop an analogue of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the time-evolution operator, and also…
Time-decaying harmonic oscillators yield dispersive estimates with weak decay, and change the threshold power of the nonlinearity between the short and the long range. In the non-critical case for the time-decaying harmonic oscillator, this…
Kerr oscillators are model systems which have practical applications in nonlinear optics. Optical Kerr effect i.e. interaction of optical waves with nonlinear medium with polarizability $\chi^{(3)}$ is the basic phenomenon needed to explain…
Among the many proposals to approach the concept of time in quantum theory, the Page-Wootters mechanism has attracted much attention in the last few years. Originally, such a mechanism explored a stationary bipartite non-interacting global…
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…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
The existence of a hermitian time operator is proposed in the framework of non-relativistic quantum mechanics.The Heisenberg equation of motion is shown to yield constant rate of flow of time.It is shown to yield results consistent with…
We introduce a novel approach for estimating the spectrum of quantum many-body Hamiltonians, and more generally, of Hermitian operators, using quantum time evolution. In our approach we are evolving a maximally mixed state under the…
We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed…