Related papers: Position and momentum cannot both be lazy: Quantum…
A transfer matrix formalism applicable to certain reparametrization invariant theories, including quantum gravity, is proposed. In this formulation it is found that every stationary state in quantum gravity satisfies a Wheeler-DeWitt…
The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements,…
Exchangeability is a fundamental concept in probability theory and statistics. It allows to model situations where the order of observations does not matter. The classical de Finetti's theorem provides a representation of infinitely…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
A quantum-mechanical framework is set up to describe the full counting statistics of particles flowing between reservoirs in an open system under time-dependent driving. A symmetry relation is obtained which is the consequence of…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…
Quantum coherence is an important quantum resource and it is intimately related to various research fields. The geometric coherence is a coherence measure both operationally and geometrically. We study the trade-off relation of geometric…
We consider the frog model with Bernoulli initial configuration, which is an interacting particle system on the multidimensional lattice consisting of two states of particles: active and sleeping. Active particles perform independent simple…
The Einstein relation describes the response of a diffusing particle to a small constant external force. It states that, as the force tends to zero, the ratio of the limiting velocity to the force magnitude converges to the diffusivity…
Common misconceptions on the Heisenberg principle are reviewed, and the original spirit of the principle is reestablished in terms of the trade-off between information retrieved by a measurement and disturbance on the measured system. After…
Wigner function is a quasi-distribution that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between Wigner function and appropriate…
Heisenberg's uncertainty relation for measurement noise and disturbance states that any position measurement with noise epsilon brings the momentum disturbance not less than hbar/2epsilon. This relation holds only for restricted class of…
Nonreciprocal interactions are known to produce distinctive dynamics in active matter. To shed light on how the stationary state of such systems is affected by breaking reciprocity, we consider active Ornstein-Uhlenbeck particles coupled…
Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the…
We present the uncertainty relation for the characteristic functions (ChUR) of the quantum mechanical position and momentum probability distributions. This inequality is more general than the Heisenberg Uncertainty Relation, and is…
The problem of the position and spin in relativistic quantum mechanics is analyzed in detail. It is definitively shown that the position and spin operators in the Foldy-Wouthuysen representation (but not in the Dirac one) are…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…
The canonical commutation relation is a cornerstone of quantum theory and underlies the Heisenberg uncertainty principle. Although uncertainty relations have been extensively tested, direct verifications of the underlying commutation…
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…
The Landau--Lifshitz--Gilbert equations for the evolution of the magnetization, in presence of an external torque, can be cast in the form of the Lorenz equations and, thus, can describe chaotic fluctuations. To study quantum effects, we…