Related papers: Comment on "Evolution Operator Can Always Be Separ…
Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an…
We present a new setting of the geometric Hamilton-Jacobi theory by using the so-called time-evolution operator K. This new approach unifies both the Lagrangian and the Hamiltonian formulation of the problem developed in a previous paper…
In this note we present a framework which allows to prove an abstract existence result for evolution equations with pseudo-monotone operators. The assumptions on the spaces and the operators can be easily verified in concrete examples.
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the…
The time evolution operator (Schr\"odinger functional) of quantum field theory can be expressed in terms of first quantised particles moving on the orbifold $S^1/Z_2$. We give a graphical derivation of this that generalises to second…
By using dynamical invariants theory, Hassoul et al. [1,2] investigate the quantum dynamics of two (2D) and three (3D) dimensional time-dependent coupled oscillators. They claim that, in the 2D case, introducing two pairs of annihilation…
We argue that refining, coarse graining and entangling operators can be obtained from time evolution operators. This applies in particular to geometric theories, such as spin foams. We point out that this provides a construction principle…
In this article the time evolution operator of two interacting quantum oscillators, whose Hamiltonian is an element of the complex $\left\{ h(1) \oplus h(1) \right\} \uplus u(2)$ algebra, is analyzed using the Feynman time ordering operator…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
We revisit the formulation of quantum mechanics over the quaternions and investigate the dynamical structure within this framework. Similar to standard complex quantum mechanics, time evolution is then mediated by a unitary operator which…
We attract attention to an interesting family of quantum systems where the generator $H_{(gen)}$ of time-evolution of wave functions is not equal to the Hamiltonian $H$. We describe the origin of the difference $H_{(gen)}-H$ and interpret…
In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the…
We study the quantum evolution under the combined action of the exponentials of two not necessarily commuting operators. We consider the limit in which the two evolutions alternate at infinite frequency. This case appears in a plethora of…
An automorphism defined on an evolution algebra can provide both a finite number and an infinite number of evolution operators on it. This question is dealt with in the paper, as well as others more related to the evolution operators of…
Completely integrable Hamiltonian systems look promising for controllability since their first integrals are stable under an internal evolution, and one may hope to find a perturbation of a Hamiltonian which drives the first integrals at…
The analogy between the quantum evolution and that of the master equation is explored. By stressing the stochastic nature of quantum evolution a number of conceptual difficulties in the interpretation of quantum mechanics are avoided.
We define the action operator in the consistent histories formalism, as the quantum analogue of the classical action functional, for the simple harmonic oscillator case. The action operator is shown to be the generator of time…
In his fresh "Comment" (arXiv:0711.0137v1), A. Mostafazadeh reacts on my very recent letter (arXiv:0710.5653v1) where I tried to clarify certain misunderstandings which occurred in A. M., Phys. Lett. B \textbf{650}, 208 (2007)…
The vacuum expectation value of the evolution operator for a general class of Hamiltonians used in quantum field theory and statistical physics and which include unstable particles is considered. An exact formula which describes the large…