Related papers: Quantum-classical correspondence in integrable sys…
The correspondence principle states that classical mechanics emerges from quantum mechanics in the appropriate limits. However, beyond this heuristic rule, an information-theoretic perspective reveals that classical mechanics is a…
Recurrence time quantifies the duration required for a physical system to return to its initial state, playing a pivotal role in understanding the predictability of complex systems. In quantum systems with subspace measurements, recurrence…
(abridged)If the space-time is presupposed, the coordinate representation of the solutions $\psi(\vec x, t)$ of the Schroedinger equation of a quantum system containing one massive scalar particle has a {\it preferred status}. It is then…
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…
We present a method based on the Path Integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose…
Quantum integrable systems and their classical counterparts are considered. We show that the symplectic structure and invariant tori of the classical system can be deformed by a quantization parameter $\hbar$ to produce a new (classical)…
Classical integrable Hamiltonian systems generated by elements of the Poisson commuting ring of spectral invariants on rational coadjoint orbits of the loop algebra $\wt{\gr{gl}}^{+*}(2,{\bf R})$ are integrated by separation of variables in…
An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…
Quantum channels describe subsystem or open system evolution. Using the classical Koopman operator that evolves functions on phase space, 4 classical Koopman channels are identified that are analogs of the 4 possible quantum channels in a…
We show the relation between the Heisenberg averaging of regularized 2-point out-of-time ordered correlation function and the 2-point spectral form factor in bosonic quantum mechanics. The generalization to all even-point is also discussed.…
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
Due to the exponential growth of the state space of coupled quantum systems it is not possible, in general, to numerically store the state of a very large number of quantum systems within a classical computer. We demonstrate a method for…
We consider generalized quantum Ising models, including those which could describe disordered materials or quantum annealers, and we prove that for all temperatures above a system-size independent threshold the path integral Monte Carlo…
A semiclassical Bohr-Sommerfeld approximation is derived for an N-particle, two-mode Bose-Hubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the `classical' dynamics of…
A class of time independent and physically meaningful Hamiltonians leads to evolution of observable quantities whose Ehrenfest times are arbitrarily large. This fact contradicts the popular claim that the true chaos is in quantum mechanics…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…
The correspondence principle is investigated in the framework of deterministic predictions for individual systems. Exact analytical results are obtained for the quantum and the Liouvillian dynamics of a nonlinear oscillator coupled to a…
We discuss quantum fidelity decay of classically regular dynamics, in particular for an important special case of a vanishing time averaged perturbation operator, i.e. vanishing expectation values of the perturbation in the eigenbasis of…
Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical…