Related papers: Anharmonic quantum mechanical systems do not featu…
Quantum mechanics is able to predict challenging behaviors even in the simplest physical scenarios. These behaviors are possible because of the important dynamical role that phase plays in the evolution of quantum systems, and are very…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the…
The basic elements of the mathematical theory of states of thermal equilibrium of infinite systems of quantum anharmonic oscillators (quantum crystals) are outlined. The main concept of this theory is to describe the states of finite…
Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards generating quantum states beyond this equilibrium…
Instabilities of equilibrium quantum mechanics are common and well-understood. They are manifested for example in phase transitions, where a quantum system becomes so sensitive to perturbations that a symmetry can be spontaneously broken.…
We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems.…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions…
In recent years, analysis and control of quantum chaos are increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. This research aims to connect…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…
It has been recently argued that near-integrable nonautonomous one-degree-of-freedom Hamiltonian systems are constrained by KAM theory even when the time-dependent (nonintegrable) part of the Hamiltonian is given in the form of a…