Related papers: Temporal evolution of a driven optomechanical syst…
The time-ordered exponential representation of a complex time evolution operator in the interaction picture is studied. Using the complex time evolution, we prove the Gell-Mann -- Low formula under certain abstract conditions, in…
An important aspect in understanding the dynamics in the context of deparametrized models of LQG is to obtain a sufficient control on the quantum evolution generated by a given Hamiltonian operator. More specifically, we need to be able to…
Time-driven quantum systems are important in many different fields of physics like cold atoms, solid state, optics, etc. Many of their properties are encoded in the time evolution operator which is calculated by using a time-ordered product…
We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We…
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
A novel perturbative treatment of the time evolution operator of a quantum system is applied to the model describing a Raman-driven trapped ion in order to obtain a suitable 'effective model'. It is shown that the associated effective…
Given a Hamiltonian $H$ on a Hilbert space $\mathcal H$ it is shown that, under the assumption that $\sigma(H)=\sigma_{ac}(H)=R^+$, there exist unique positive operators $T_F$ and $T_B$ registering the Schr\"odinger time evolution generated…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
Typical optomechanical systems involving optical cavities and mechanical oscillators rely on a coupling that varies linearly with the oscillator displacement. However, recently a coupling varying instead as the square of the mechanical…
We investigate the classical-quantum correspondence in the inverted harmonic oscillator (IHO) system. It is shown that the out-of-time-order correlators (OTOCs) which the initial states are located at any position in the IHO system possess…
Few-photon optomechanical effects are not only important physical evidences for understanding the radiation-pressure interaction between photons and mechanical oscillation, but also have wide potential applications in modern quantum…
The evolution operator U(t) for a time-independent parity-time-symmetric systems is well studied in the literature. However, for the non-Hermitian time-dependent systems, a closed form expression for the evolution operator is not available.…
We find explicit solutions of the Heisenberg equations of motion for a quadratic Hamiltonian, describing a generic model of variable media, in the case of multi-parameter squeezed input photon configuration. The corresponding probability…
Some mechanical systems with dissipation can be described within the framework of the so-called contact mechanics: a modified form of the Euler-Lagrange equations stemming from Herglotz's variational principle, which admits a geometric…
There is a widespread belief in the quantum physical community, and in textbooks used to teach Quantum Mechanics, that it is a difficult task to apply the time evolution operator Exp{-itH/h} on an initial wave function. That is to say,…
In this paper we study the time evolution of an observable in the interacting fermion systems driven out of equilibrium. We present a method for solving the Heisenberg equations of motion by constructing excitation operators which are…
We derive an equation for the time evolution of the natural occupation numbers for fermionic systems with more than two electrons. The evolution of such numbers is connected with the symmetry-adapted generalized Pauli exclusion principle,…
For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as…
Quantum optomechanical system serves as an interface for coupling between photons and phonons due to mechanical oscillations. We used the Heisenberg-Langevin approach under Markovian white noise approximation to study a quadratically…