Related papers: Classical Trajectories for Complex Hamiltonians
A trajectory of a harmonic oscillator obeying the Schreodinger wave equation is exactly derived and illustrated. The trajectory resembles well the classical orbit between the turning points, and also runs through the tunneling region. The…
We offer a new Hamiltonian formulation of the classical Pais-Uhlenbeck Oscillator and consider its canonical quantization. We show that for the non-degenerate case where the frequencies differ, the quantum Hamiltonian operator is a…
Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum…
In this work, we investigate generic classical two-dimensional (2D) superintegrable Hamiltonian systems H, characterized by the existence of three functionally independent integrals of motion (I_0=H,I_1,I_2). Our main result, formulated and…
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…
Assuming that the Hamiltonian of a canonical field theory can be written in the form N H + N^i H_i, and using as the only input the actual choice of the canonical variables, we derive: (i) The algebra satisfied by H and H_i, (ii) any…
The classical and quantum dynamics of the noncanonically coupled oscillators is considered. It is shown that though the classical dynamics is well--defined for both harmonic and anharmonic oscillators, the quantum one is well--defined in…
We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics…
We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we…
Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigated. In order to study semiclassical dynamics of trapped ions, coherent state orbits are introduced as sub-manifolds of the quantum state space,…
We classify the Hamiltonians $H=p_x^2+p_y^2+V(x,y)$ of all classical superintegrable systems in two dimensional complex Euclidean space with second-order constants of the motion. We similarly classify the superintegrable Hamiltonians…
The quantum theories of boson and fermion fields with quadratic nonstationary Hamiltoanians are rigorously constructed. The representation of the algebra of observables is given by the Hamiltonian diagonalization procedure. The sufficient…
According to some generalized correspondence principle the classical limit of a non-Hermitian Quantum theory describing quantum degrees of freedom is expected to be well known classical mechanics of classical degrees of freedom in the…
We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is…
We prove quantitative decay estimates of macroscopic quantities generated by the solutions to linear transport equations driven by a general family of Hamiltonians. The associated particle trajectories are all trapped in a compact region of…
We study the Hamiltonian motion of an ensemble of unconfined classical particles driven by an external field F through a translationally-invariant, thermal array of monochromatic Einstein oscillators. The system does not sustain a…
We consider a class of simple quasi one-dimensional classically non-integrable systems which capture the essence of the periodic orbit structure of general hyperbolic nonintegrable dynamical systems. Their behavior is simple enough to allow…
Motivated by the generalization of quantum theory for the case of non-Hermitian Hamiltonians with PT symmetry, we show how a classical cosmological model describes a smooth transition from ordinary dark energy to the phantom one. The model…
We develop a Bohmian analysis of a two-dimensional ghost Hamiltonian and its mapping to the degenerate Pais-Uhlenbeck model. Using Gaussian wavepackets, we derive the corresponding guidance equations, the centre and width evolution, and the…
We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a…