Nonlocal Quantum Mechanics Research Articles

Solutions of Nonlocal Schrödinger Equation via the Caputo-Fabrizio Definition for Some Quantum Systems

The aim of this work is to treat the time-independent one-dimensional nonlocal Schrodinger equation. The nonlocality is described by a kernel with a noninteger power α between 1 and 2. At first stage, by using Caputo–Fabrizio definition and other known results, we have transformed the nonlocal Schrodinger equation to an ordinary linear differential equation. Secondly, we have applied the last result to solve two problems in nonlocal quantum mechanics: the Coulomb-type and Hulthen-type potentials in one dimension. The eigenenergies and eigenfunctions are calculated. As expected, when the power α tends to two, the resulting solutions go to the standard case.

Multiplicity and concentration of solutions for a fractional Schrödinger equation via Nehari method and pseudo-index theory

We study a nonlinear fractional Schrödinger equation motivated by nonlocal quantum mechanics. Under suitable assumptions on the potentials, we explore the existence, concentration, convergence, and decay estimates of ground state solutions for this equation. Moreover, the multiplicity of solutions is constructed via pseudo-index theory, and the existence of sign-changing solutions is obtained via the Nehari method.

Electromagnetic coupling of strongly non-local quantum mechanics

Although standard quantum mechanics has some non-local features, the probability current of the Schrödinger equation is locally conserved, and this allows minimal electromagnetic coupling. For some important extensions of the Schrödinger equation, however, the probability current is not locally conserved. We show that in these cases the correct electromagnetic coupling requires a relatively simple extension of Maxwell theory which has been known for some time and recently improved by covariant integration of a scalar degree of freedom. We discuss some general properties of the solutions and examine in particular the case of an oscillating dipolar source. Remarkable mathematical and physical differences emerge with respect to Maxwell theory, as a consequence of additional current terms present in the equations for ∇·E and ∇×B. Several possible applications are mentioned.

RELATIVISTIC, CAUSAL DESCRIPTION OF QUANTUM ENTANGLEMENT AND GRAVITY

A possible solution to the problem of providing a spacetime description of the transmission of signals for quantum entangled states is obtained by using a bimetric spacetime structure, in which quantum entanglement measurements alter the structure of the classical relativity spacetime. A bimetric gravity theory locally has two lightcones, one which describes classical special relativity and a larger lightcone which allows light signals to communicate quantum information between entangled states, after a measurement device detects one of the entangled quantum states. This theory would remove the tension that exists between macroscopic classical, local gravity and macroscopic nonlocal quantum mechanics.