Related papers: Position-Momentum Uncertainty Relation for an Open…
We propose a trade-off between the Lipschitz constants of the position and momentum probability distributions for arbitrary quantum states. We refer to the trade-off as a quantum reciprocity relation. The Lipschitz constant of a function…
Quantum superposition is normally sustained in a microscopic regime governed by Heisenberg uncertainty principle applicable to a single particle. Quantum correlation between paired particles implies the violation of local realism governed…
Some predictions of quantum mechanics are in contrast with the macroscopic realm of everyday experience, in particular those originated by the Heisenberg uncertainty principle, encoded in the non-commutativity of some measurable operators.…
We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…
We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional…
We show that quantum mechanical entanglement can prevail even in noisy open quantum systems at high temperature and far from thermodynamical equilibrium, despite the deteriorating effect of decoherence. The system consists of a number N of…
We investigate a two-level system in resonant contact with a larger environment. The environment typically is in a canonical state with a given temperature initially. Depending on the precise spectral structure of the environment and the…
The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable…
It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We…
Minimum uncertainty states of the conventional Heisenberg uncertainty relation have been extensively studied and are often regarded as the most classical quantum states from the perspective of uncertainty, providing valuable insight into…
We establish a rigorous quantitative connection between (i) the interferometric duality relation for which-way information and fringe visibility and (ii) Heisenberg's uncertainty relation for position and modular momentum. We apply our…
It is shown that the well-defined unbiased measurement or disturbance of a dynamical variable is not maintained for the precise measurement of the conjugate variable, independently of uncertainty relations. The conditionally valid…
For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as eigenstates of the annihilation operator). We…
We examine error-disturbance relations in the quantum measurement of spin systems using an atom-light interface scheme. We model a single spin-1/2 system that interacts with a polarized light meter via a Faraday interaction. We formulate…
It is shown that quantum uncertainty of motion in systems controlled mainly by gravity generally grows with orbital timescale $H^{-1}$, and dominates classical motion for trajectories separated by distances less than $\approx H^{-3/5}$ in…
Interaction between a quantum system and its environment can induce stationary coherences -- off-diagonal elements in the reduced system density matrix -- even at equilibrium. This work investigates the ``quantumness'' of such phenomena by…
A finite number of harmonic oscillators coupled to infinitely many environment oscillators is fundamental to the problem of understanding quantum dissipation of a small system immersed in a large environment. Exact operator solution as a…
We point out that the Gaussian wave-packet formalism can serve as a concrete realization of the joint measurement of position and momentum, which is an essential element in understanding Heisenberg's original philosophy of the uncertainty…
We have studied a $\mathcal{P}\mathcal{T}$-symmetric quantum system for a class of position-dependent effective mass. Formalisms of supersymmetric quantum mechanics are utilized to construct the partner potentials. Since the system under…
We investigate the effects of space noncommutativity and the generalized uncertainty principle on the stability of circular orbits of particles in both a central force potential and Schwarzschild spacetime. We find noncommutative form of…