Related papers: Adiabatic dynamics of one-dimensional classical Ha…
The theory of adiabatic invariants has a long history and important applications in physics but is rarely rigorous. Here we treat exactly the general time-dependent 1-D harmonic oscillator, $\ddot{q} + \omega^2(t) q=0$ which cannot be…
In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the…
Large amplitude collective motion is investigated for a model pairing Hamiltonian containing an avoided level crossing. A classical theory of collective motion for the adiabatic limit is applied utilising either a time-dependent mean-field…
While it is well-known that every nearly-periodic Hamiltonian system possesses an adiabatic invariant, extant methods for computing terms in the adiabatic invariant series are inefficient. The most popular method involves the heavy…
By using the effective Hamiltonian approach, we present a self-consistent framework for the analysis of geometric phases and dynamically stable decoherence-free subspaces in open systems. Comparisons to the earlier works are made. This…
Non-Hermitian systems are widespread in both classical and quantum physics. The dynamics of such systems has recently become a focal point of research, showcasing surprising behaviors that include apparent violation of the adiabatic theorem…
The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic…
We study a general quantum system interacting with environment modeled by the bosonic heat bath of Caldeira and Leggett type. General interaction Hamiltonians are considered that commute with the system's Hamiltonian so that there is no…
In this paper we proposed a proposition: for any nonconservative classical mechanical system and any initial condition, there exists a conservative one; the two systems share one and only one common phase curve; the Hamiltonian of the…
A new and intuitive perturbative approach to time-dependent quantum mechanics problems is presented, which is useful in situations where the evolution of the Hamiltonian is slow. The state of a system which starts in an instantaneous…
We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to…
By examining both the divergence of the velocity vector in orthogonal Cartesian coordinate space $\mathbf{\Gamma} $ of dimension $\R^{\textrm {2fN}}$ and the structure of the Hamiltonian determining a system trajectory, it is shown that the…
In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden type nonlinear oscillator equation with linear forcing, $\ddot{x}+\alpha x\dot{x}+\beta x^3+\gamma…
High control in the preparation and manipulation of states is an experimental and theoretical important task in many quantum protocols. Shortcuts to adiabaticity methods allow to obtain desirable states of a adiabatic dynamics but in short…
Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. We consider an…
We consider a nonlinear pendulum whose suspension point undergoes stochastic vibrations in its plane of motion. Stochastic vibrations are constructed by stochastic differential equations with random periodic solutions. Averaging over these…
By considering a solvable driven-dissipative quantum model, we demonstrate that continuous second order phase transitions in dissipative systems may occur without an accompanying spontaneous symmetry breaking. As such, the underlying…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
Conditions for the validity of the quantum adiabatic approximation are analyzed. For the case of linear Hamiltonians, a simple and general sufficient condition is derived, which is valid for arbitrary spectra and any kind of time variation.…
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between non-degenerate instantaneous eigen-energy levels in such a…