Related papers: Nonlocal looking equations can make nonlinear quan…
We consider a quantum system subject to superselection rules, for which certain restrictions apply to the quantum operations that can be implemented. It is shown how the notion of quantum-nonlocality has to be redefined in the presence of…
Unitary representations of the Galilei group are studied in phase space, in order to describe classical and quantum systems. Conditions to write in general form the generator of time translation and Lagrangians in phase space are then…
We obtain conditions for the differentiability of weak solutions for a second-order uniformly elliptic equation in divergence form with a homogeneous co-normal boundary condition. The modulus of continuity for the coefficients is assumed to…
In this paper, symmetry analysis is extended to study nonlocal differential equations, in particular two integrable nonlocal equations, the nonlocal nonlinear Schr\"odinger equation and the nonlocal modified Korteweg--de Vries equation. Lie…
We extend the variational problem of Wheeler-Feynman electrodynamics by putting the electromagnetic functional in a local space of absolutely continuous trajectories possessing a derivative (velocities) of bounded variation. Generalizing…
Entanglement is an useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and is not locally possible. We focus on orthogonal states, which can…
In this paper we consider the local well-posedness theory for the quadratic nonlinear Schr\"odinger equation with low regularity initial data in the case when the nonlinearity contains derivatives. We work in 2+1 dimensions and prove a…
When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the…
We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schr\"odinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of…
Is wave function collapse a prediction of the Schr\"odinger equation? This unusual problem is explored in an enlarged framework of interpretation, where quantum dynamics is considered exact and its interpretation is extended to include…
Local and global existence of localized solutions of a discrete nonlinear Schrodinger (DNLS) equation, with arbitrary on-site nonlinearity, is proved. In particular, it is shown that an initially localized excitation persists localized…
We consider the periodic fractional nonlinear Schr\"{o}dinger equation $$ iu_t -(-\Delta)^{\frac{s}{2}} u + \mathcal{N}(|u|)u=0, \quad x\in \mathbb{T}^N,\, \, t \in \mathbb R, \, \, s>0, $$ where the nonlinearity term is expressed in two…
According to a fundamental result in quantum computing, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two subsystems. Beyond its importance in quantum computing, this…
Unlike in the case of distinguishable particles, the concept of entanglement-- not to mention, nonlocality-- remains debated in case of indistinguishable particles. Here, we show that certain existing all-versus-nothing type of proofs of…
A set of orthogonal states possesses the strongest quantum nonlocality if only a trivial orthogonality-preserving positive operator-valued measure (POVM) can be performed for each bipartition of the subsystems. This concept originated from…
Existence and uniqueness theorems for quantum stochastic differential equations with nontrivial initial conditions are proved for coefficients with completely bounded columns. Applications are given for the case of finite-dimensional…
It is well-known that the Liouville equation of statistical mechanics is restricted to systems where the total number of particles (N) is fixed. In this paper, we show how the Liouville equation can be extended to systems where the number…
In this paper, we establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum…
We study the derivative nonlinear wave equation \( - \partial_{tt} u + \Delta u = |\nabla u|^2 \) on \( \mathbb{R}^{1+3} \). The deterministic theory is determined by the Lorentz-critical regularity \( s_L = 2 \), and both local…
An orthogonal set of states in multipartite systems is called to be strong quantum nonlocality if it is locally irreducible under every bipartition of the subsystems…