Related papers: Crypto-unitary forms of quantum evolution 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…
In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another…
Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a $d$-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new…
Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an…
In quantum mechanics the unitary evolution is most often described in a pre-selected Hilbert space ${\cal H}^{(textbook)}$ in which, due to the Stone theorem, the Schr\"odinger-picture Hamiltonian is self-adjoint,…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
Time-dependent quantum evolution is described by an algebraic connection on a $C^\infty(R)$-module of sections of a $C^*$-algebra (or Hilbert) fibre bundle.
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…
Non-stationary version of unitary quantum mechanics formulated in non-Hermitian (or, more precisely, in hiddenly Hermitian) interaction-picture representation is illustrated via an elementary $N$ by $N$ matrix Hamiltonian $H(t)$ mimicking a…
The time-evolution operator obtained from the fractional-time Schr\"{o}dinger equation (FTSE) is said to be non-unitary since it does not preserve the norm of the vector state in time. As done in the time-dependent non-Hermitian quantum…
One of the axioms of quantum field theory is the property of unitarity of the evolution operator. However, if one considers the quantum electrodynamics in the external field in the leading order of perturbation theory, one will find that…
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…
It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation…
We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that…
For many quantum models an apparent non-Hermiticity of observables corresponds to their hidden Hermiticity in another, physical Hilbert space. For these models we show that the existence of observables which are manifestly time-dependent…
For any Dirac theory of quantum gravity governed by a set of well-defined quantum constraints, we discover a universal formula for the exact form of the evolution Hamiltonian operator in a variable quantum reference frame of our…
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…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…