Related papers: On the long time behavior of stochastic Schroeding…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
We analyze the non-Markovian stochastic Schroedinger equation describing a particle subject to spontaneous collapses in space (in the language of collapse models), or subject to a continuous measurement of its position (in the language of…
We show a new method for analyzing the time evolution of the Schrodinger wave function Psi(x,t). We propose the decomposition of the Hamiltonian as: H(t)=Hp(t)+Hc(t), where Hp(t) is the Hamiltonian such that Psi(x,t) is its instantaneous…
Erwin Schrodinger (1939) proved that quantum wave functions coevolve with the curved spacetime of the Friedmann universe. Schrodinger's derivation explains the Hubble redshift of photons in an expanding universe, the energy changes of…
I impose the Newtonian criteria of inertial frames on the c.o.m. trajectories of massive objects undergoing spontaneous collapse of their wave function. The corresponding modification of the so far used stochastic Schr\"odinger equation…
The recent observation of gravitational waves, stimulates the question of the longtime evolution of the space-time fluctuations. Gravitational waves interact themselves through the nonlinear character of Einstein's equations of general…
Time evolution is formulated and discussed in the framework of Schroeder's functional equation. The proposed method yields smooth, continuous dynamics without the prior need for local propagation equations.
We study stochastic evolution equations describing the dynamics of open quantum systems. First, using resolvent approximations, we obtain a sufficient condition for regularity of solutions to linear stochastic Schroedinger equations driven…
A stochastic Schr\"odinger equation is presented to describe simultaneous continuous measurement of the position and momentum of a non-relativistic particle. The equation is solved to yield a state localised in position and momentum…
We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
A consistent classical and quantum relativistic mechanics can be constructed if Einstein's covariant time is considered as a dynamical variable. The evolution of a system is then parametrized by a universal invariant identified with…
We study the Schroedinger equation of a class of two-level systems under the action of a periodic time-dependent external field in the situation where the energy difference 2epsilon between the free energy levels is sufficiently small with…
We consider the relation between so called continuous localization models - i.e. non-linear stochastic Schr\"odinger evolutions - and the discrete GRW-model of wave function collapse. The former can be understood as scaling limit of the GRW…
A quantum system S undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a stochastic master equation and its solution is called a quantum trajectory.…
The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and…
The existence of local, classical solutions is proved, for a system of two coupled equations that describe, in the framework of the wave turbulence theory, the fluctuations around an equilibrium, of a system of nonlinear waves satisfying…
We analyze the emergence of diffractive focusing in the transition from discrete to continuous space-time variables. Three types of dynamical equations are studied in a top-to-bottom approach, starting with the most general system. First we…
Quantum mechanics is an extremely successful theory that agrees with every experiment. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are…
Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to…