Related papers: Trajectory-coherent states and the Heisenberg's un…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
When a thermodynamic system is released from any constraint, after some time its evolution will render it into an equilibrium state. Although the description of this relaxation to thermodynamic equilibrium has been attempted through both…
The paper presents a new method of geometric solution of a Schrodinger equation by a construction of an equivalent first-order partial differential equation with a bigger number of variables. The equivalent equation shall be restricted to a…
In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudo-spin observables for an arbitrary non-positive Hermitian…
The quantum trajectory sensing problem seeks quantum sensor states which enable the trajectories of incident particles to be distinguished using a single measurement. For an $n$-qubit sensor state to unambiguously discriminate a set of…
The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal…
A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg's uncertainty principle states that a given function cannot be arbitrarily compact both in time and…
In this paper we discuss some aspects of the Heisenberg uncertainty relation, mostly from the point of view of non self-adjoint operators. Some equivalence results, and some refinements of the inequality, are deduced, and some relevant…
Minimization of the expectation value of energy under the constraints imposed by the uncertainty principle can be a convenient method of solving quantum-mechanical problems.
In this paper, the Higgs-like approach is used to analyze the quantum dynamics of a harmonic oscillator constrained on a circle. We obtain the Hamiltonian of this system as a function of the Cartesian coordinate of the tangent line through…
How systems transit between different stable states under external perturbation is an important practical issue. We discuss here how a recently-developed energy optimization method for identifying the minimal disturbance necessary to reach…
In this paper we show that the existence of a primarily discrete space-time may be a fruitful assumption from which we may develop a new approach of statistical thermodynamics in pre-relativistic conditions. The discreetness of space-time…
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…
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…
The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions…
In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how…
It is generally accepted that the disturbance interpretation cannot explain Heisenberg's uncertainty relation DxDp=h. In this paper a clear distinction will be made between the notions of state preparation and measurement, noting that the…
Heisenberg's original uncertainty relation is related to measurement effect, which is different from the preparation uncertainty relation. However, it has been shown that Heisenberg's error-disturbance uncertainty relation can be violated…
We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. There are studied uncertainty relations for sums of…
This paper has a dual purpose. One aim is to study the evolution of coherent states in ordinary quantum mechanics. This is done by means of a Hamiltonian approach to the evolution of the parameters that define the state. The stability of…