Related papers: Effective nonlinear Ehrenfest hybrid quantum-class…
We find that the quantum-classical correspondence in integrable systems is characterized by two time scales. One is the Ehrenfest time below which the system is classical; the other is the quantum revival time beyond which the system is…
Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…
The article explores challenges presented by revelations in physics and the questions they provoke concerning reality. It sheds light on the disparity between the indefinite nature of quantum reality and our perception of classical reality.…
The Ehrenfest time scale in quantum transport separates essentially classical propagation from wave interference and here we consider its effect on the transmission and reflection through quantum dots. In particular we calculate the…
We studied the Ehrenfest urn model in which particles in the same urn interact with each other. Depending on the nature of interaction, the system undergoes a first-order or second-order phase transition. The relaxation time to the…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
We analyze the decay of classically chaotic quantum systems in the presence of fast ballistic escape routes on the Ehrenfest time scale. For a continuous excitation process, the form factor of the decay cross section deviates from the…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…
A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a…
Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail)…
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement…
The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve.…
We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We study data-driven decision problems where historical observations are generated by a time-evolving distribution whose consecutive shifts are bounded in Wasserstein distance. We address this nonstationarity using a distributionally robust…
We describe a study motivated by our interest to examine the incompleteness of the Ehrenfest's theorem in quantum mechanics and to resolve a doubt regarding whether or not the hermiticity of the hamiltonian operator is sufficient to justify…
How well can quantum computers simulate classical dynamical systems? There is increasing effort in developing quantum algorithms to efficiently simulate dynamics beyond Hamiltonian simulation, but so far exact resource estimates are not…
Stochastic systems feature, in general, both coherent dynamics and incoherent transitions between different states. We propose a method to identify the coherent part in the full counting statistics for the transitions. The proposal is…