Related papers: Schroedinger uncertainty relation and its minimiza…
A model Hamiltonian dynamical system has been derived to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger equation on the torus. Here, we explore the framework for exploring a canonical ensemble formulation of the…
Calling the quantity; 2delta(A)delta(B)/|<[A, B]>|, with non-zero denominator, the uncertainty product ratio or UPR for the pair of observables, (A, B), it is shown that any non-zero correlation coefficient between two observables raises,…
We study Bohr-Sommerfeld states in the context of the irreducible representations of SU(2). These states offer a precise bridge between the classical and quantum descriptions of angular momentum. We show that they recover the usual basis of…
Generalizing the well-known spin-squeezing inequalities, we study the relation between squeezing of collective $N$-particle $su(d)$ operators and many-body entanglement geometry in multi-particle systems. For that aim, we define the set of…
We propose a definition of microcanonical and canonical statistical ensembles based on the concept of density of states. This definition applies both to the classical and the quantum case. For the microcanonical case this allows for a…
We extend recent results on expectation values of coherent oscillator states and SU(2) coherent states to the case of the discrete representations of su(1,1). Systematic semiclassical expansions of products of arbitrary operators are…
Joint measurements of two observables reveal that every state is nonclassical, with the only trivial exception of the state with density matrix proportional to the identity. This naturally includes states considered universally as…
We consider a class of nonlinear Schroedinger equation in three space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
Linear superpositions of macroscopically distinct quantum states (sometimes also called Schr\"odinger cat states) are usually almost immediately reduced to a statistical mixture if exposed to the dephasing influence of a dissipative…
Using the Klauder approach the stable evolution of generalized coherent states (GCS) for some groups (SU(2), SU(1,1) and SU(N)) is considered and it is shown that one and the same classical solution z(t) can correctly characterize the…
We study a 1D nonlinear Schr{\"o}dinger equation appearing in the description of a particle inside an atomic nucleus. For various nonlinearities, the ground states are discussed and given in explicit form. Their stability is studied…
Robertson intelligent states which minimize the Schr\" odinger-Robertson uncertainty relation are constructed as eigenstates of a linear combination of Weyl generators of the $su(3)$ algebra. The construction is based on the analytic…
We prove the existence of normalized ground state solutions for the biharmonic Schr\"odinger equation with combined nonlinearities and show that all ground states correspond to the local minima of the associated energy functional restricted…
We develop a new abstract derivation of the observability inequalities at two points in time for Schr\"odinger type equations. Our approach consists of two steps. In the first step we prove a Nazarov type uncertainty principle associated…
In this paper we will continue the analysis of two dimensional Schr\"odinger equation with a fixed, pointwise, nonlinearity started in [2, 13]. In this model, the occurrence of a blow-up phenomenon has two peculiar features: the energy…
The modified discrete nonlinear Schr\"odinger equation is used to study the formation of stationary localized states in a one-dimensional lattice with a single impurity and an asymmetric dimer impurity. A periodically modulated and a…
Introductory courses on quantum mechanics usually include lectures on uncertainty relations, typically the inequality derived by Robertson and, perhaps, other statements. For the benefit of the lecturers, we present a unified approach --…
We provide an explicit construction for Gazeau-Klauder coherent states related to non-Hermitian Hamiltonians with discrete bounded below and nondegenerate eigenspectrum. The underlying spacetime structure is taken to be of a noncommutative…
The squeezed states are states of minimum uncertainty, but unlike the coherent states, in which the uncertainty in the position and the momentum are the same, these allow to reduce the uncertainty, either in the position or in the momentum,…
In this paper, we are concerned with solutions to the following nonlinear Schr\"odinger equation with combined inhomogeneous nonlinearities, $$ -\Delta u + \lambda u= \mu |x|^{-b}|u|^{q-2} u + |x|^{-b}|u|^{p-2} u \quad \mbox{in} \,\, \R^N,…