Related papers: Acceleration deforms exponential decays into gener…
One characterization of a chaotic system is the quick delocalization of quantum information (fast scrambling). One therefore expects that in such a system a state quickly becomes locally indistinguishable from its perturbations. In this…
It is known that a relative translational motion between the deflector and the observer affects gravitational lensing. In this paper, a lens equation is obtained to describe such effects on actual lensing observables. Results can be easily…
An important body of quantitative linguistics is constituted by a series of statistical laws about language usage. Despite the importance of these linguistic laws, some of them are poorly formulated, and, more importantly, there is no…
The essential decorrelation rate of a hyperbolic dynamical system is the decay rate of time-correlations one expects to see stably for typical observables once resonances are projected out. We define and illustrate these notions and study…
The first photon emission and the disentanglement of a pair of identical bosonic atoms in excited entangled states follow an exponential law. We extend the theory to distinguishable and identical fermionic two-atom systems. As a byproduct…
We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or…
A degenerate dynamical system is characterized by a state-dependent multiplier of the time derivative of the state in the time evolution equation. It can give rise to Hamiltonian systems whose symplectic structure possesses a non-constant…
Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank. It is very robust as an experimental observation, but to date it escaped…
Non-adiabatic molecular phenomena, arising from the breakdown of the Born-Oppenheimer approximation, govern the fate of virtually all photo-physical and photochemical processes and limit the quantum efficiency of molecules and other…
A new look at the so-called effect of an accelerating matter is presented. It was previously stated that the effect is optical in nature and consists in changing the frequency of the wave passing through a refractive sample moving with…
The time-domain response of highly conducting targets following a rapidly terminated electromagnetic pulse displays three distinct regimes: early, intermediate and late time. The intermediate and late times are characterized by a…
In this paper, it is shown why Lorentz Transformation implies the general case where observed events are not necessarily in the inertia frame of any observer but assumes a special scenario when determining the length contraction and time…
We study the entanglement dynamics of accelerated atoms using the theory of open quantum systems. We consider two atoms travelling along different hyperbolic trajectories with different proper times. We use the generalized master equation…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
The Zipf's law establishes that if the words of a (large) text are ordered by decreasing frequency, the frequency versus the rank decreases as a power law with exponent close to $-1$. Previous work has stressed that this pattern arises from…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
Grammatical forms are said to evolve via two main mechanisms. These are, respectively, the `descent' mechanism, where current forms can be seen to have descended (albeit with occasional modifications) from their roots in ancient languages,…
The motion of electrons under homogeneously applied electric fields in low-dimensional systems with non-zero off-diagonal effective mass (ODEM) is studied. The equation describing the time evolution of a probability coefficient of finding…
Zipf's law seems to be ubiquitous in human languages and appears to be a universal property of complex communicating systems. Following the early proposal made by Zipf concerning the presence of a tension between the efforts of speaker and…
We present here a general iterative formula which gives a (formal) series expansion for the time autocorrelation of smooth dynamical variables, for all Hamiltonian systems endowed with an invariant measure. We add some criteria, theoretical…