Related papers: General solution of the time evolution of two inte…

We construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time-independent, local, one-dimensional, and translation invariant. As a…

The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time…

We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…

A method of exactly solving the master equation is presented in this letter. The explicit form of the solution is determined by the time evolution of a composite system including an auxiliary system and the open system in question. The…

In this work we study the validity of the rotating wave approximation of an ideal system composed of two harmonic oscillators evolving with a quadratic Hamiltonian and arbitrarily strong interaction. We prove its validity for arbitrary…

A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the…

All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…

In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of classical hamiltonian systems that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure plays a…

We examine the time evolution of an asymmetric Hubbard dimer, which has a different on-site interaction on the two sites. The Hamiltonian has a time-dependent hopping term, which can be employed to describe an electric field (which creates…

In this paper, we consider a class of highly oscillatory Hamiltonian systems which involve a scaling parameter $\varepsilon\in(0,1]$. The problem arises from many physical models in some limit parameter regime or from some time-compressed…

We study the time evolution of bosonic systems where multiple driven bosonic modes of light interact with multiple mechanical resonators through arbitrary, time-dependent, optomechanical-like interactions. We find the analytical expression…

We study the dynamics of the entanglement between two oscillators that are initially prepared in a general two-mode Gaussian state and evolve while coupled to the same environment. In a previous paper we showed that there are three…

We study the process by which quantum correlations are created when an interaction Hamiltonian is repeatedly applied to a system of two harmonic oscillators for some characteristic time interval. We show that, for the case where the…

Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is…

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 study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest neighbour interactions. For a one-dimensional chain we provide compact…

We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…

We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly time-dependent. We determine various new equivalence pairs for Hermitian and non-Hermitian…

A system of a quantum harmonic oscillator bi-linearly coupled with a Glauber amplifier is analysed considering a time-dependent Hamiltonian model. The Hilbert space of this system may be exactly subdivided into invariant finite dimensional…

We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach…