Related papers: A selfadjoint variant of the time operator

In this paper, we consider partially observable timed automata endowed with a single clock. A time interval is associated with each transition specifying at which clock values it may occur. In addition, a resetting condition associated to a…

One clock alternating timed automata OCATA have been recently introduced as natural extension of (one clock) timed automata to express the semantics of MTL (Ouaknine, Worrell 2005). We consider the application of OCATA to problem of…

In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves…

The clock time t' of an accelerating observer, simultaneous with the measured clock time t of an inertial observer,is easily established in special relativity (as proper time) by the well-known time-dilation formula for t'(t). In this work,…

The main goal of this paper is to show that a (not necessarily densely defined or closed) symmetric operator $A$ acting on a real or complex Hilbert space is selfadjoint exactly when $I+A^2$ is a full range operator.

The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing…

Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associated with a time-dependent Riemannian metric by extremizing…

For a wide class of pairs of unbounded selfadjoint operators with bounded commutator we construct a K-theoretical integer invariant which is continuous, is equal to zero for commuting operators and is equal to one for the pair (x, i d/dx).

There are many different types of time keeping devices. We use the phrase ticking clock to describe those which -- simply put -- "tick" at approximately regular intervals. Various important results have been derived for ticking clocks, and…

This is a survey note of the author's observations on the discrete-time analogues of It\^o formulas.

We give an explicit correspondence between the domains of the self-adjoint extensions of a one-dimensional Schr\"odinger differential operator with symmetric real-valued potential and the boundary conditions the functions in the resulting…

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We consider the setting of component-based design for real-time systems with critical timing constraints. Based on our earlier work, we propose a compositional specification theory for timed automata with I/O distinction, which supports…

Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…

The semijoin algebra is the variant of the relational algebra obtained by replacing the join operator by the semijoin operator. We discuss some interesting connections between the semijoin algebra and the guarded fragment of first-order…

The issue of justifying the eddy current approximation of Maxwell's equations is re-considered in the time-dependent setting. Convergence of the solution operators is shown in the sense of strong operator limits.

We study a homogenization question for stochastic divergence type operator

We shall work with the so called duality triads following kwa\'sniewski. In particular in this note we propose some extensions of them - hence we choose such special class of triads that admit - all at once - a unified combinatorial…

The failure of conventional quantum theory to recognize time as an observable and to admit time operators is addressed. Instead of focusing on the existence of a time operator for a given Hamiltonian, we emphasize the role of the…

The question of self-adjoint realizations of sign-indefinite second order differential operators is discussed in terms of a model problem. Operators of the type $-\frac{d}{dx} \sgn (x) \frac{d}{dx}$ are generalized to finite, not…