Related papers: Exact solutions for time-dependent non-Hermitian o…
A nonlinear quantum-classical transition wave equation is proposed for dissipative systems within the Caldirola-Kanai model. Equivalence of this transition equation to a scaled Schr\"{o}dinger equation is proved. The dissipative dynamics is…
For the models of $N$-body identical harmonic oscillators interacting through potentials of homogeneous degree -2, the unitary operator that transforms a system of time-dependent parameters into that of unit spring constant and unit mass of…
In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians…
We show that, by using the quantum orthogonal functions invariant, we are able to solve a coupled of time dependent harmonic oscillators where all the time dependent frequencies are arbitrary. We do so, by transforming the time dependent…
Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with…
Non-unitary quantum mechanics has been used in the past to study irreversibility, dissipation and decay in a variety of physical systems. In this letter, we propose a general scheme to deal with systems governed by non-Hermitian…
The Snyder model is an example of noncommutative spacetime admitting a fundamental length scale $\beta$ and invariant under Lorentz transformations, that can be interpreted as a realization of the doubly special relativity axioms. Here, we…
The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric…
We provide a time-dependent Dyson map and metric for the two dimensional harmonic oscillator with a non-Hermitian $i xy$ coupling term. This particular time-independent model exhibits spontaneously broken $\mathcal{PT}$-symmetry and becomes…
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 study a class of time-dependent (TD) non-Hermitian Hamiltonians $H(t)$ that can be transformed into a time-independent pseudo-Hermitian Hamiltonian $\mathcal{H}_{0}^{PH}$ using a suitable TD unitary transformation $F(t)$. The latter can…
With the aim to solve the time-dependent Schr\"{o}dinger equation associated to a time-dependent non-Hermitian Hamiltonian, we introduce a unitary transformation that maps the Hamiltonian to a time-independent $\mathcal{PT}$-symmetric one.…
Here we prove that the classical (respectively, quantum) system, consisting of a particle moving in a static electromagnetic field, is canonically (respectively, unitarily) equivalent to a harmonic oscillator perturbed by a spatially…
For $N$-coupled generalized time-dependent oscillators, primary invariants and a generalized invariant are found in terms of classical solutions. Exact quantum motions satisfying the Heisenberg equation of motion are also found. For number…
We transform the time-dependent Schroedinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time-evolution of exact wave functions of generalized harmonic oscillators is…
We propose and explore a scheme that leads to an infinite series of time- dependent Dyson maps which associate different Hermitian Hamiltonians to a uniquely specified time-dependent non-Hermitian Hamiltonian. We identify the underlying…
A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization which gives a general quadratic Hamiltonian system does not…
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…
A general treatment of the quantal time-dependent coupled oscillators in presence of the variable magnetic field is presented. The treatment is based on the use of an alternative canonical transformations, time-dependent unitary…
We elaborate further on the metric representation that is obtained by transferring the time-dependence from a Hermitian Hamiltonian to the metric operator in a related non-Hermitian system. We provide further insight into the procedure on…