相关论文: Finite-time stochastic reduction models

Exact boundary conditions at finite distance for the solutions of the time-dependent Schrodinger equation are derived. A numerical scheme based on Crank-Nicholson method is proposed to illustrate its applicability in several examples.

We provide a scenario for a singularity-mediated turbulence based on the self-focusing non-linear Schr\"odinger equation, for which sufficiently smooth initial states leads to blow-up in finite time. Here, by adding dissipation, these…

We set up a general formalism for models of spontaneous wave function collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white in time. In particular, we show that the…

Modified versions of the Schr\"{o}dinger equation have been proposed in order to incorporate the description of measurement processes into the mathematical structure of quantum theory. Typically, these proposals introduce new physical…

We use a change of variables that turns the critical nonlinear Schroedinger equation into the critical nonlinear Schroedinger equation with isotropic harmonic potential, in any space dimension. This change of variables is isometric on…

We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schr\"odinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this…

Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…

A quantum many-body model is presented with features similar to those of certain particle detectors. The energy spectrum contains a single metastable 'ready'-state and macroscopically-distinct 'pointer' states. Measurements do not pose…

A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…

Quantum theory depends on an external classical time, and there ought to exist an equivalent reformulation of the theory which does not depend on such a time. The demand for the existence of such a reformulation suggests that quantum theory…

The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…

A simple and natural introduction to the concept and formalism of spontaneous wave function collapse can and should be based on textbook knowledge of standard quantum state collapse and monitoring. This approach explains the origin of noise…

Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…

Abstract: Models for studying systems in stationary states but out of equilibrium have often empirical nature and very often break the fundamental time reversal symmetry. Here a formal interpretation will be discussed of the widespread idea…

It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr\"odinger equation are derived from the causal action principle. The…

Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized…

It has been suggested by Diosi and Penrose that the occurrence of quantum state reduction in macroscopic objects is related to a manifestation of gravitational effects in quantum mechanics. Although within Penrose's framework the dynamics…

Solutions to the Schr\"{o}dinger equation are examined for a particle inside a cylindrical trap of a circular time-dependent cross-section. Analytical expressions for energy and momentum expectation values are derived with respect to the…

Based on the assumption that the standard Schr\"odinger equation becomes gravitationally modified for massive macroscopic objects, two independent proposals has survived from the nineteen-eighties. The Schr\"odinger--Newton equation (1984)…

Recently, Josserand et al. proposed a stochastic nonlinear Schroedinger model for finite-time singularity-mediated turbulence [Phys. Rev. Fluids 5, 054607 (2020)]. Here, we use instanton calculus to quantify the effect of extreme…