Related papers: Solving the von Neumann equation with time-depende…
In this paper, time-independent Hamiltonian systems are investigated via a Lie-group/algebra formalism. The (unknown) solution linked with the Hamiltonian is considered to be a Lie-group transformation of the initial data, where the group…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
Hamiltonian simulation becomes more challenging as the underlying unitary becomes more oscillatory. In such cases, an algorithm with commutator scaling and a weak dependence, such as logarithmic, on the derivatives of the Hamiltonian is…
The Lindblad equation is widely employed in studies of Markovian quantum open systems. Here, firstly, a simple result is presented on the time evolution of the non Neumann entropy under the Lindblad equation, which enables one to examine if…
We study in this paper the time evolution of $PT$-symmetric non-Hermitian Hamiltonian consisting of periodically driven $SU(1,1)$ generators. A non-Hermitian invariant operator is adopted to solve the Schr\"{o}dinger equation, since the…
In this paper, we present a variational treatment of the linear dependence for a non-orthogonal time-dependent basis set in solving the Schr\"odinger equation. The method is based on: i) the definition of a linearly independent working…
The time-evolution operator for an explicitly time-dependent Hamiltonian is expressed as the product of a sequence of unitary operators. These are obtained by successive time-dependent unitary transformations of the Hilbert space followed…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
The properties of SU(1,1) SU(2),SU(2,1) and SU(3) have often been used in quantum optics. In this paper we demonstrate the use of these symmetries. The group properties of SU(1,1) SU(2), and SU(2,1) are used to find the transition…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
We build an efficient and unitary (hence stable) method for the solution of the semi-classical Schr\"odinger equation subject with explicitly time-dependent potentials. The method is based on a combination of the Zassenhaus decomposition…
An extension of standard quantum mechanics is proposed in which the Newtonian time appearing as a parameter in the unitary evolution operator is replaced with the time shown by a `quantum clock'. Such a clock is defined by the following…
We construct Lewis-Riesenfeld invariants from two dimensional point transformations for two oscillators that are coupled to each other in space in a PT-symmetrical and time-dependent fashion. The non-Hermitian Hamiltonian of the model is…
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…
Mathematical aspects of the SU(1,1) group parameter x dynamics governed by Hamiltonians exhibiting some special types of time dependence has been presented on an elementary level from the point of view of Moebius transformation of complex…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
We investigate quantum mechanical Hamiltonians with explicit time dependence. We find a class of models in which an analogue of the time independent \S equation exists. Among the models in this class is a new exactly soluble model, the…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…
Quantum mechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem…