Related papers: Energy-time and frequency-time uncertainty relatio…
The quantum variables that can be accessed directly by experiments are described by observables. Therefore, physical parameters can only be evaluated indirectly, via estimations based on experimental measurement results. I show that the…
Difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$ and $\beta$ are considered. By the method of energy inequalities, for the solution…
The paper contains a proposal for an energy and time representation. We construct modes that correspond to fuzzy distributions around discrete values of energy or time. The modes form an orthogonal and complete set in the space of square…
Using the Mandelstam-Tamm method we derive time-energy uncertainty relations for neutrino oscillations. We demonstrate that the small energy uncertainty of antineutrinos in a recently considered experiment with recoilless resonant…
We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [Tsang, Shapiro, and Lloyd, Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to…
An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit…
We propose a method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a "slow" detector. Such a detector is only sensitive to slowly-changing variables, e. g. energy, while its back-action can…
Using a \emph{gedanken} experiment providing presumably a minimal inaccuracy the uncertainty contributions to the space-time measurement are precisely evaluated for clock and mirror respectively. The resulting expression of minimal…
Multi-time quantum processes are endowed with the same richness as multipartite states, including temporal entanglement and exotic causal structures. However, experimentally probing these rich phenomena leans heavily on fast and clean…
Quantum gravitational effects may induce stochastic fluctuations in the structure of space-time, to produce a characteristic foamy structure. It has been known for some time now that these fluctuations may have observable consequencies for…
Sub-Gaussian and subexponential distributions are introduced and applied to study the fluctuation-response relation out of equilibrium. A bound on the difference in expected values of an arbitrary sub-Gaussian or subexponential physical…
The problem of estimating the frequency of a two-level atom in a noisy environment is studied. Our interest is to minimise both the energetic cost of the protocol and the statistical uncertainty of the estimate. In particular, we prepare a…
We study the quantum properties of an oscillator in proper time. This proper time oscillator is a particle model with mass that is on shell. Its internal time can be treated as a self-adjoint operator. The displaced time and displaced time…
We investigate dynamical systems with time-dependent mass and frequency, with particular attention on models attaining the minimum value of uncertainty formula. A criterium of minimum uncertainty is presented and illustrated by means of…
We consider time-harmonic elastodynamic problems in heterogeneous media.cWe focus on scattering problems in the high-frequency regime and incnearly incompressible media, where the the angular frequency $\omega$ and ratio of the Lam\'e…
Quantum mechanics requires that identical particles are treated as indistinguishable. This requirement leads to correlations in the fluctuating properties of a system. Theoretical predictions are made for an experiment on a multi-lead…
We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clocks and find its general solution. This…
Lower bounds on fluctuations of thermodynamic currents depend on the nature of time: discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master…
Five previously unknown inequalities relating equilibrium free energy differences and non-equilibrium work fluctuations are derived, and lucid path to derivation of many similar inequalities is presented. These results are based upon…
Quantum non-local correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in…