相关论文: Efficient Simulation of Quantum State Reduction

We provide the exact analytic solution of the stochastic Schr\"odinger equation describing an harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of…

We prove that the quintic Schrodinger equation with Dirichlet boundary conditions is locally well posed for H^{1}_{0} data on any smooth, non-trapping domain of R^3. The key ingredient is a smoothing effect in L^{5}_{x}L^{2}_{t} for the…

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…

It is shown that, for a large class of statistical mixtures, the Wigner-Poisson (or Hartree) system can be reduced to an effective Schroedinger-Poisson system, in which the Schroedinger equation contains a new nonlinearity. For the case of…

Stochastic models for quantum state reduction give rise to statistical laws that are in most respects in agreement with those of quantum measurement theory. Here we examine the correspondence of the two theories in detail, making a…

We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…

By assuming that the kinetic energy,potential energy,momentum,and some other physical quantities of a particle exist in the field out of the particle,the Schrodinger equation is an equation describing field of a particle,but not the…

The consistency of the concept of quantum (quasi)particles possessing effective mass which is both position- and excitation-dependent is analyzed via simplified models. It is shown that the system may be stable even when the effective mass…

This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit…

Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical…

We review a new iterative procedure to solve the low-lying states of the Schroedinger equation, done in collaboration with Richard Friedberg. For the groundstate energy, the $n^{th}$ order iterative energy is bounded by a finite limit,…

We present and analyze large-scale simulation results of a hybrid quantum-classical variational method to calculate the ground state energy of the anti-ferromagnetic Heisenberg model. Using a massively parallel universal quantum computer…

In the probabilistic approach to quantum many-body systems, the ground-state energy is the solution of a nonlinear scalar equation written either as a cumulant expansion or as an expectation with respect to a probability distribution of the…

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…

We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…

A new technique was recently developed to approximate the solution of the Schroedinger equation. This approximation (dubbed ERS) is shown to yield a better accuracy than the WKB-approximation. Here, we review the ERS approximation and its…

We investigate the non-Markovian quantum dynamics of a hybrid open system consisting of one qubit and one qutrit by employing a stochastic Schr\"{o}dinger equation to generate diffusive quantum trajectories. We have established an exact…

We found a simple procedure for the solution of the time - independent Schrodinger equation in one dimension without making any approximation. The wave functions are always periodic. Two difficulties may be encountered: one is to solve the…

The interrelationship between energy and probability conservation is explored from the point of view of statistical physics and non-relativistic quantum mechanics. The simultaneous validity of the law of conservation of energy and the…

The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a…