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We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the…
Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law…
We address the time decay of the Loschmidt echo, measuring sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using semiclassical analysis, we show that the Loschmidt echo may exhibit…
We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses…
We study the time evolution of two wave packets prepared at the same initial state, but evolving under slightly different Hamiltonians. For chaotic systems, we determine the circumstances that lead to an exponential decay with time of the…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
The Einstein-Hilbert (EH) action is peculiar in many ways. Some of the Peculiar features have already been highlighted in literature. In the present article, we have discussed some peculiar features of EH action which has not been discussed…
Molecular dynamics simulations are used to investigate the effects of deformation on the segmental dynamics in an aging polymer glass. Individual particle trajectories are decomposed into a series of discontinuous hops, from which we obtain…
When applied to a dipole source subjected to acceleration which is violent and long lasting (``extreme acceleration''), Maxwell's equations predict radiative power which augments Larmor's classical radiation formula by a nontrivial amount.…
Imagine a swarm of free particles near a point P outside a gravitating mass M and a free reference particle at P that is on a radial escape trajectory away from M. Relative to this reference particle and in a Fermi normal coordinate system…
We show that a short-time regime, in which a deviation from the exponential decay law occurs, exists also in the framework of a superrenormalizable relativistic quantum field theory. This, in turn, implies the possibility of a quantum Zeno…
In models in statistical physics, the dynamics often slows down tremendously near the critical point. Usually, the correlation time $\tau$ at the critical point increases with system size $L$ in power-law fashion: $\tau \sim L^z$, which…
This work is devoted to the study of the scaling, and the consequent power-law behavior, of the correlation function in a mutation-replication model known as the expansion-modification system. The latter is a biology inspired random…
Based on the generalized principle of relativity and the ensuing symmetry, we have shown that there are only two possible types of transformations between uniformly accelerated systems. The first allowable type of transformation holds if…
Many applications require that we learn the parameters of a model from data. EM is a method used to learn the parameters of probabilistic models for which the data for some of the variables in the models is either missing or hidden. There…
Systems evolving according to the standard concept of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find a deep relationship to classical…
We consider two-level detectors coupled to a scalar field and moving on arbitrary trajectories in Minkowski space-time. We first derive a generic expression for the response function using a (novel) regularization procedure based on the…
We modify the theory of the Quantum Zeno Effect to make it consistent with the postulates of quantum mechanics. This modification allows one, throughout a sequence of observations of an excited system, to address the nature of the…
Decay laws of moving unstable quantum systems with oscillating decay rates are analyzed over intermediate times. The transformations of the decay laws at rest and of the intermediate times at rest, which are induced by the change of…
A random walk $w_n$ on a separable, geodesic hyperbolic metric space $X$ converges to the boundary $\partial X$ with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes…