Related papers: Unitary quantum evolution for time-dependent quasi…
We introduce time-dependent variational principles to study the non-unitary dynamics of open quantum many-body systems, including dynamics described by the full Lindblad master equation, the non-Hermitian dynamics corresponding to the…
The recursion operators and symmetries of non-autonomous, (1+1)-dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their…
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…
In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below by a strictly positive constant uniformly in time. Allowing…
A class of non-Dirac-hermitian many-particle quantum systems admitting entirely real spectra and unitary time-evolution is presented. These quantum models are isospectral with Dirac-hermitian systems and are exactly solvable. The general…
We give a simple proof of the fact that every diagonalizable operator that has a real spectrum is quasi-Hermitian and show how the metric operators associated with a quasi-Hermitian Hamiltonian are related to the symmetry generators of an…
We address the problem of coupling non-Hermitian systems, treated as fundamental rather than effective theories, to the electromagnetic field. In such theories the observables are not the $\bs{x}$ and $\bs{p}$ appearing in the Hamiltonian,…
We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations…
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…
A stable and fast path linking two arbitrary states of a quantum system is generally required for state-engineering protocols, such as stimulated Raman adiabatic passage, shortcuts to adiabaticity, and holonomic transformation. Such a path…
The notion of non-Hermitian PT symmetric quantum theory has recently been generalized to the gauge/gravity duality. We study the evolution of such non-Hermitian holographic field theories when the couplings are varied with time with…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectrum, and transit to the Hermitian…
Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an…
The self adjoint operator of time in non-relativistic quantum mechanics is found within the approach where the ordinary Hamiltonian is not taken to be conjugate to time. The operator version of the reexpressed Liouville equation with the…
We investigated the quantum speed limit time of a qubit system with non-Hermitian detuning. Our results show that, with respect to two distinguishable states of the non-Hermitian system, the evolutionary time does not have a nonzero lower…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…
A condition on the Hamiltonian of a time-dependent quantum mechanical system is derived which, if satisfied, implies optimal adiabaticity (defined below). The condition is expressed in terms of the Hamiltonian and in terms of the evolution…
We address the problem of integrating operator equations concomitant with the dynamics of non autonomous quantum systems by taking advantage of the use of time-dependent canonical transformations. In particular, we proceed to a discussion…