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The microcanonical ensemble has long been a starting point for the development of thermodynamics from statistical mechanics. However, this approach presents two problems. First, it predicts that the entropy is only defined on a discrete set…
Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
The stochastic dissipative Schrodinger equation is derived for an open quantum system consisting of a sub-system able to exchange energy with a thermal reservoir. The resultant evolution of the wave function also gives the evolution of the…
We study the diffusion of classical hard-core particles in disordered lattices within the formalism of a quantum spin representation. This analogy enables an exact treatment of non-instantaneous correlation functions at finite particle…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There…
It is shown how the essentials of quantum theory, i.e., the Schroedinger equation and the Heisenberg uncertainty relations, can be derived from classical physics. Next to the empirically grounded quantisation of energy and momentum, the…
We give a partial answer to the question whether the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one…
We discuss two topics that are usually considered to be exclusively "quantum": the Schroedinger equation, and the uncertainty principle. We show (or rather recall) that the Schroedinger equation can be derived from Hamilton's equations…
We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum…
The quantum dynamics of a localized spin-$\frac{1}{2} $ Particle interacting with an absorbing environment is investigated. The quantum Langevin-Schr\"odinger equation for spin-$\frac{1}{2} $ is obtained. The susceptibility function of the…
We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the…
We establish quantum dynamical lower bounds for discrete one-dimensional Schr\"odinger operators in situations where, in addition to power-law upper bounds on solutions corresponding to energies in the spectrum, one also has lower bounds…
The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…
In quantum mechanics, the time evolution of particles is given by the Schr\"odinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not…
We formulate the Schr\"odinger equation as the equation of motion of a small external influence which serves as the initial boundary condition of a physical system in classical laboratory space. The Hilbert space of possible external…
The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…