Related papers: Quantal Overlapping Resonance Criterion in the Pul…

Here we investigate the accuracy of the overlap criterion when applied to a simple near-integrable model in both its 2D and 3D version. To this end, we consider respectively, two and three quartic oscillators as the unperturbed system, and…

The chaotic dynamics in a cell of particles' chain interacting by means of Lennard-Jones potential is considered. Chirikov criterion of resonance over- lapping is used as the condition of chaos. The asymptotic representation for this…

We prove upper and lower bounds for the threshold of the q-overlap-k-Exact cover problem. These results are motivated by the one-step replica symmetry breaking approach of Statistical Physics, and the hope of using an approach based on that…

The overlap measurement scheme accomplishes to evaluate the overlap of two input quantum states by only measuring an introduced auxiliary qubit, irrespective of the complexity of the two input states. We find a counterintuitive phenomenon…

An ideal system of $n$ qubits has $2^n$ dimensions. This exponential grants power, but also hinders characterizing the system's state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can…

I study the scaling behavior in the physical parameters of dynamical entropies, classical and quantum, in a specifically devised model of collision-induced decoherence in a chaotic system. The treatment is fully canonical and no…

Chirikov's celebrated criterion of resonance overlap has been widely used in celestial mechanics and Hamiltonian dynamics to detect global instability, but is rarely rigourous. We introduce two simple Hamiltonian systems, each depending on…

The relation between the onset of chaos and critical phenomena, like Quantum Phase Transitions (QPT) and Excited-State Quantum Phase transitions (ESQPT), is analyzed for atom-field systems. While it has been speculated that the onset of…

We consider a toy model for emergence of chaos in a quantum many-body short-range-interacting system: two one-dimensional hard-core particles in a box, with a small mass defect as a perturbation over an integrable system, the latter…

The Chirikov resonance-overlap criterion predicts the onset of global chaos if nonlinear resonances overlap in energy, which is conventionally assumed to require a non-small magnitude of perturbation. We show that, for a time-periodic…

We investigate how to experimentally detect a recently proposed measure to quantify macroscopic quantum superpositions [Phys. Rev. Lett. 106, 220401 (2011)], namely, "macroscopic quantumness" $\mathcal{I}$. Schemes based on overlap…

We analyze the requirements to test some of the most paradigmatic collapse models with a protocol that prepares quantum superpositions of massive objects. This consists of coherently expanding the wave function of a ground-state-cooled…

We establish a renormalization group approach which is implemented on the degrees of freedom defined by the overlap of two replicas to determine the critical fixed point and to extract four critical exponents for the phase transition of the…

Chaos criterion for quantum field theory is proposed. Its accordance with classical chaos criterion is demonstrated in the semi-classical limit of quantum mechanics.

We consider the problems of chaos in disorder and temperature for coupled copies of the mixed p-spin models. Under certain assumptions on the parameters of the models we will first prove a weak form of chaos by showing that the overlap is…

Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate…

We consider a disordered system obtained by coupling two mixed even-spin models together. The chaos problem is concerned with the behavior of the coupled system when the external parameters in the two models, such as, temperature, disorder,…

Collapse models describe the breakdown of the quantum superposition principle when moving from microscopic to macroscopic scales. They are among the possible solutions to the quantum measurement problem and thus describe the emergence of…

Using the decoherence formalism of Gell-Mann and Hartle, a quantum system is found which is the equivalent of the classical chaotic Duffing oscillator. The similarities and the differences from the classical oscillator are examined; in…

We review several theoretical aspects of the Equivalence Principle (EP). We emphasize the unsatisfactory fact that the EP maintains the absolute character of the coupling constants of physics while General Relativity, and its…