Related papers: Nonlocalization of singular potentials in quantum …
"action at a distance" is a weird concept in quantum theory which people always avoid mentioning in most occasions. In this work, without involving any concept about "action at a distance", we naturally construct a physical structure that…
An n-particle 3-dimensional Wigner quantum oscillator model is constructed explicitly. It is non-canonical in that the usual coordinate and linear momentum commutation relations are abandoned in favour of Wigner's suggestion that Hamilton's…
In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein-Gordon wavefunctions, as special cases; and then in turn for non-relativistic…
We demonstrate that the Wigner function of the Einstein-Podolsky-Rosen state, though positive definite, provides a direct evidence of the nonlocal character of this state. The proof is based on an observation that the Wigner function…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
Wannier functions provide a localized representation of spectral subspaces of periodic Hamiltonians, and play an important role for interpreting and accelerating Hartree-Fock and Kohn-Sham density functional theory calculations in quantum…
Nonlocality is a key feature of quantum theory and is reflected in the violation of Bell inequalities for entangled systems. The experimental tests beyond the electromagnetism and massless quanta are of great importance for understanding…
Whether the quantum mechanics (QM) is non-local is an issue disputed for a long time. The violation of the Bell-type inequalities was considered as proving this non-locality. However, these inequalities are constructed on a class of local…
Virtual massless particles in quantum loops lead to nonlocal effects which can have interesting consequences, for example, for primordial magnetogenesis in cosmology or for computing finite $N$ corrections in holography. We describe how the…
Quantum nonlocality, pioneered in Bell's seminal work and subsequently verified through a series of experiments, has drawn substantial attention due to its practical applications in various protocols. Evaluating and comparing the extent of…
Doubly special relativity (DSR) is usually regarded as a low-energy limit of a quantum gravity theory with testable predictions. On the other hand, non-local quantum field theories have been presented as a solution to the inconsistencies…
We study the local behavior of weak solutions, with possible singularities, of nonlocal nonlinear equations. We first prove that sets of capacity zero are removable for weak solutions under certain integrability conditions. We then…
Nonlocality is a defining feature of quantum mechanics and has long served as a key indicator of quantum resources since the formulation of Bell's inequalities. Identifying the contribution of nonlocality to extractable work remains a…
We present the Wigner-Lohe model for quantum synchronization which can be derived from the Schr\"{o}dinger-Lohe model using the Wigner formalism. For identical one-body potentials, we provide a priori sufficient framework leading the…
Active scalars appear in many problems of fluid dynamics. The most common examples of active scalar equations are 2D Euler, Burgers, and 2D surface quasi-geostrophic equations. Many questions about regularity and properties of solutions of…
We formulate the inverse spectral theory for a non-self-adjoint one-dimensional Dirac operator associated periodic potentials via a Riemann-Hilbert problem approach. We use the resulting formalism to solve the initial value problem for the…
It is shown that when properly analyzed using principles consistent with the use of a Hilbert space to describe microscopic properties, quantum mechanics is a local theory: one system cannot influence another system with which it does not…
Using the formalism of generalized fractional derivatives, a two-dimensional non-relativistic meson system is studied. The mesons are interacting by a Cornell potential. The system is formulated in the domain of the symplectic quantum…
We examine inverse problems for the variable-coefficient nonlocal parabolic operator $(\partial_t - \Delta_g)^s$, where $0 < s < 1$. This article makes two primary contributions. First, we introduce a novel entanglement principle for these…
The Extended Wigner's Friend thought experiment, which involves a quantum system with an agent who draws conclusions based on the results of a measurement of a quantum state provided in two nonorthogonal versions by another agent, led its…