Related papers: Quantum & Classical Eigenfunctions in Calogero & S…
We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the…
We study entanglement in two coupled quartic oscillators. It is shown that the entanglement, as measured by the von Neumann entropy, increases with the classical chaos parameter for generic chaotic eigenstates. We consider certain isolated…
We prove that the Calogero-Sutherland Model with reflections (the BC_N model) possesses a property of duality relating the eigenfunctions of two Hamiltonians with different coupling constants. We obtain a generating function for their…
Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum…
We study quantum coarse-grained entropy and demonstrate that the gap in entropy between local and global coarse-grainings is a natural generalization of entanglement entropy to mixed states and multipartite systems. This "quantum…
As examples of quantum-"classical" coupling systems, multi-component systems are studied by semiclassical evaluations of the Feynman kernels in the coherent-state representation. From the observation of the phase space caustics due to the…
While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of…
We study quantum caustics in $d$-dimensional systems with quadratic Lagrangians. Based on Schulman's procedure in the path-integral we derive the transition amplitude on caustics in a closed form for generic multiplicity $f$, and thereby…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
The semi-classical Lifshitz-Kosevich (LK) description of quantum oscillations is extended to a multiband two-dimensional Fermi liquid with a constant number of electrons. The amplitudes of novel oscillations with combination frequencies,…
A new form of quasiclassical space-time dynamics for constrained systems reveals how quantum effects can be derived systematically from canonical quantization of gravitational systems. These quasiclassical methods lead to additional fields,…
In this paper we demonstrate that there exists a close relationship between quasi-exactly solvable quantum models and two special classes of classical dynamical systems. One of these systems can be considered a natural generalization of the…
We explore the quantum scattering of systems classically described by binary and other low order Smale horseshoes, in a stage of development where the stable island associated with the inner periodic orbit is large, but chaos around this…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a…
By applying methods already discussed in a previous series of papers by the same authors, we construct here classes of integrable quantum systems which correspond to n fully resonant oscillators with nonlinear couplings. The same methods…
Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and…
We study many-body properties of quantum harmonic oscillator lattices with disorder. A sufficient condition for dynamical localization, expressed as a zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the…