Related papers: Inverse momentum expectation values for hydrogenic…
We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.
The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
We study the phenomenon of quantum backflow in tight-binding systems with complex couplings, considering different boundary conditions and lattice sizes. Backflow is an intrinsically non-classical effect where the density flux associated…
Complex and spinorial techniques of general relativity are used to determine all the states of the $SU(2)$ invariant quantum mechanical systems in which the equality holds in the uncertainty relations for the components of the angular…
We show spurious effects in perturbative calculations due to different orderings of inhomogeneous terms while computing corrections to Green functions for two different metrics. These effects are not carried over to physically measurable…
In this paper, we obtain almost sure invariance principles with rate of order $n^{1/p}\log^\beta n$, $2< p\le 4$, for sums associated to a sequence of reverse martingale differences. Then, we apply those results to obtain similar…
A ubiquitous feature of quantum mechanical theories is the existence of states of superposition. This is expected to be no different for a quantum gravity theory. Guided by this consideration and others we consider a framework in which…
Take a random variable X with some finite exponential moments. Define an exponentially weighted expectation by E^t(f) = E(e^{tX}f)/E(e^{tX}) for admissible values of the parameter t. Denote the weighted expectation of X itself by r(t) =…
In this paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of…
We provide a posteriori error estimates in the energy norm for temporal semi-discretisations of wave maps into spheres that are based on the angular momentum formulation. Our analysis is based on novel weak-strong stability estimates which…
We propose the skewness of mean transverse momentum, $\langle p_t \rangle$, fluctuations as a fine probe of hydrodynamic behavior in relativistic nuclear collisions. We describe how the skewness of the $\langle p_t \rangle$ distribution can…
We study fluctuations and correlations of the average transverse momentum of particles emitted in heavy-ion collisions. Fluctuations of the average transverse momentum are related to event-by-event fluctuations of the size and entropy of…
Two estimates for the inverse binary entropy function are derived using the property of information entropy to estimate combinatorics of sequences as well as related formulas from population genetics for the effective number of alleles. The…
Quantum mechanics relates probability of an observable event to the absolute square of the corresponding probability amplitude. It may, therefore, seem that the information about the amplitudes' phases must be irretrievably lost in the…
The vacuum expectation values of conserved currents play an essential role in the generalized hydrodynamics of integrable quantum field theories. We use analytic continuation to extend these results for the excited state expectation values…
The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator…
Exact solution of Schrodinger equation for the Mie potential is obtained for an arbitrary angular momentum. The energy eigenvalues and the corresponding wavefunctions are calculated by the use of the Nikiforov-Uvarov method. Wavefunctions…
We consider an inverse boundary problem for the dynamical Maxwell's equations. We show that the electric permittivity, conductivity, and magnetic permeability can be uniquely determined locally if there is a strictly convex foliation with…
Weconsider Markov decision processes arising from a Markov model of an underlying natural phenomenon. Such phenomena are usually periodic (e.g. annual) in time, and so the Markov processes modelling them must be time-inhomogeneous, with…