Related papers: Spectral Oscillations, Periodic Orbits, and Scalin…
The surprisingly long-lasting oscillations observed in the dynamics of highly excited states of chains of Rydberg atoms defy the expectation that interacting systems should thermalize fast. The phenomenon is reminiscent of wavepackets in…
In the present note, we uncover a remarkable connection between the length of periodic orbit of a classical particle enclosed in a class of 2-dimensional planar billiards and the energy of a quantum particle confined to move in an identical…
[This is the unpublished supplemental information from 1989 to the paper: J.M. Deutsch, "Quantum statistical mechanics in a closed system." Phys. Rev. A, 43(4), 2046 (1991).] A closed quantum mechanical system does not necessarily give time…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
By means of periodic orbit theory and deformed cavity model, we have investigated semiclassical origin of superdeformed shell structure and also of reflection-asymmetric deformed shapes. Systematic analysis of quantum-classical…
This review summarizes and amplifies on recent investigations of coupled quantum dynamical systems in the short wavelength limit. We formulate and attempt to answer three fundamental questions: (i) What drives a dynamical quantum system to…
Quantum magnetic oscillations in crystals are typically understood in terms of Bohr-Sommerfeld quantisation, the frequency of oscillation is given by the area of a closed electron trajectory. However, since the 1970s, oscillations have been…
The mixed density operator for coarsegrained eigenlevels of a static Hamiltonian is represented in phase space by the spectral Wigner function, which has its peak on the corresponding classical energy shell. The action of trajectory…
We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum…
We consider dissipative one-dimensional systems subject to a periodic force and study numerically how a time-varying friction affects the dynamics. As a model system, particularly suited for numerical analysis, we investigate the driven…
Classical and quantum theories of time-symmetric smoothing, which can be used to optimally estimate waveforms in classical and quantum systems, are derived using a discrete-time approach, and the similarities between the two theories are…
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…
We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
A single wave component of a quantum particle can in principle be detected by the way that it interferes with itself, that is, through the local wave function correlation. The interpretation as the expectation of a local translation…
Semiclassical periodic orbit theory is used in many branches of physics. However, most applications of the theory have been to systems which involve only single particle dynamics. In this work, we develop a semiclassical formalism to…
We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all…
Simple theorems relating a quantum mechanical system to the corresponding classical one at equilibrium and connecting the quantum eigenvalues to the frequencies of normal modes oscillations are presented. Corresponding to each quantum…
We introduce the one-dimensional PT-symmetric Schrodinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatory-like…