Related papers: Trajectory-coherent states and the Heisenberg's un…
We focus on the global semiconcavity of solutions to first-order Hamilton--Jacobi equations with state constraints, especially for the Hamiltonian $H(x, \beta):=|\beta|^p-f(x)$ with $p \in (1, 2]$. We first show that the solution is locally…
We study the existence of patterns (nontrivial, stationary solutions) for one-dimensional Swift-Hohenberg Equation in a directional quenching scenario, that is, on $x\leq 0$ the energy potential associated to the equation is bistable,…
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…
The Heisenberg uncertainty relation is derived for relativistic electrons described by the Dirac equation. The standard nonrelativistic lower bound $3/2\hbar$ is attained only in the limit and the wave function that reproduces this value is…
Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be sharply determined simultaneously. Standard-deviation and entropic formulations capture the spread of the probability distribution but say…
A minimum uncertainty state for position and momentum of a fluid element is obtained. We consider a general fluid described by the Navier-Stokes-Korteweg (NSK) equation, which reproduces the behaviors of a standard viscous fluid, a fluid…
It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a "weak-measurement", this disturbance can be reduced. One…
The main characteristics of the quantum oscillator coherent states including the two-particle Calogero interaction are investigated. We show that these Calogero coherent states are the eigenstates of the second-order differential…
The Koch curve is a self-similar object whose length grows unboundedly when the measuring unit by which is calculated diminishes. If this curve is considered to be the trajectory of a point corpuscle of mass m (a particle) rendering it in a…
We establish the stability under the formations of infimum and of convex combinations of subsolutions of convex Hamilton-Jacobi equations, some comparison and existence results for convex and coercive Hamilton-Jacobi equations with the…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…
A numerical illustration of a universally valid Heisenberg uncertainty relation, which was proposed recently, is presented by using the experimental data on spin-measurements by J. Erhart, et al.[ Nature Phys. {\bf 8}, 185 (2012)]. This…
We prove a few novel state-dependent uncertainty relations for product as well the sum of variances of two incompatible observables. These uncertainty relations are shown to be tighter than the Roberson-Schr\"odinger uncertainty relation…
We study stochastic differential equations(SDEs) with a small perturbation parameter. Under the dissipative condition on the drift coefficient and the local Lipschitz condition on the drift and diffusion coefficients we prove the existence…
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…
To protect a quantum system from decoherence due to interaction with its environment, we investigate the existence of initial states of the environment allowing for decoherence-free evolution of the system. For models in which a two-state…
In this paper, we consider a hierarchical control problem with model uncertainty. Specifically, we consider the following objectives that we would like to accomplish. The first one being of a controllability-type that consists of…
While the slogan "no measurement without disturbance" has established itself under the name Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world…
We present a general method to determine the energy minimum of spin Hamiltonians over separable states when the single-particle reduced density matrices are fixed. For ferromagnetic Ising and Ising-like models with nearest-neighbor…
Consider the dynamics of a two-qubit entangled system in the decoherence environment, we investigate the stability of pairwise entanglement under decoherence. We find that for different decoherence models, there exist some special class of…