相关论文: Isoperiodic classical systems and their quantum co…

In this paper, the quantum spectrum of isochronous potentials is investigated. Given that the frequency of the classical motion in such potentials is energy-independent, it is natural to expect their quantum spectra to be equispaced.…

Revisiting and extending an old idea of Michel H\'enon, we geometrically and algebraically characterize the whole set of isochrone potentials. Such potentials are fundamental in potential theory. They appear in spherically symmetrical…

We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $\cal PT$ symmetry may…

Correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. Periodic orbit theory…

The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability…

A system of chromodynamic fields, which can be treated as classical, is generated at the earliest stage of relativistic heavy-ion collisions. Numerical simulations show that the system is unstable but the nature of the instability is not…

We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of…

The mathematical rules used to handle systems of identical quantum particles bring into question whether the elementary constituents of matter, such as electrons, have the fundamental characteristics of persistence and reidentifiability…

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…

This paper investigates the dynamics of quantum analogs of classical impact oscillators to explore how complex nonlinear behaviors manifest in quantum systems. While classical impact oscillators exhibit chaos and bifurcations, quantum…

We consider several aspects of non-periodic Ising models in one and two dimensions. Here we are not interested in random systems, but rather in models with intrinsic long-range aperiodic order. The most prominent examples in one dimension…

Can classical systems be described analytically at all orders in their interaction strength? For periodic and approximately periodic systems, the answer is yes, as we show in this work. Our analytical approach, which we call the…

The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…

In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…

By analyzing a paradigmatic example of the theory of dissipative systems -- the classical and quantum dissipative standard map -- we are able to explain the main features of the decay to the quantum equilibrium state. The classical…

We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…

We construct the set of theories which share the property that the tree-level amplitudes nullify even if both initial and final states contain the same type of particles. The origin of this phenomenon lies in the fact that the reduced…

Nonlinear classical dissipative systems present a rich phenomenology in their "route to chaos", including period-doubling, i.e. the system evolves with a period which is twice that of the driving. However, typically the attractor of a…

We study deformations of a genus one Riemann surface and of a second order Abelian differential on the surface which preserve the periods of the differential with respect to a chosen canonical homology basis of the surface. We call these…

Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, this leading to the appearance of different classical resonances. In this paper, we study the quantum manifestations of these classical…