Related papers: Exact solutions for time-dependent non-Hermitian o…
Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the…
An exact analytical treatment of the dynamical problem for time-dependent 2x2 pseudo-hermitian su(1,1) Hamiltonians is reported. A class of exactly solvable and physically transparent new scenarios are identified within both classical and…
It is shown that for a given Hermitian Hamiltonian possessing supersymmetry, there is alwayas a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the…
The ordinary Landau problem consists of describing a charged particle in time-independent magnetic field. In the present case the problem is generalized onto time-dependent uniform electric fields with time-dependent mass and harmonic…
We systematically study the non-Hermitian version of the one-dimensional anisotropic XY model, which in its original form, is a unique exactly solvable quantum spin model for understanding the quantum phase transition. The distinguishing…
We investigate a quantum mechanical system on a noncommutative space for which the structure constant is explicitly time-dependent. Any autonomous Hamiltonian on such a space acquires a time-dependent form in terms of the conventional…
We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form $\hat{H}(t) = \hat{A} +\hat{B} t + \hat{C}/t$, where $t$ is time and $\hat{A}$, $\hat{B}$, $\hat{C}$ are Hermitian $N\times N$ matrices.…
We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with…
We consider the quantum dynamics of a harmonic oscillator in noncommutative space under the influence of linearized gravitational waves (GW) in the long wave-length and low-velocity limit. Following the prescription in \cite{ncgw1} we…
The Swanson model is an exactly solvable model in quantum mechanics with a manifestly non self-adjoint Hamiltonian whose eigenvalues are all real. Its eigenvectors can be deduced easily, by means of suitable ladder operators. This is…
In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case.…
In this work we address the problem of the quantization of a simple harmonic oscillator that is perturbed by a time dependent force. The approach consists of removing the perturbation by a canonical change of coordinates. Since the…
Over the past decade, parity-time ($\mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the…
We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner by constructing an appropriate open quantum system. We focus on the quantum steady states of such…
In position dependent mass (PDM) problems, the quantum dynamics of the associated systems have been understood well in the literature for particular orderings. However, no efforts seem to have been made to solve such PDM problems for…
A system of a quantum harmonic oscillator bi-linearly coupled with a Glauber amplifier is analysed considering a time-dependent Hamiltonian model. The Hilbert space of this system may be exactly subdivided into invariant finite dimensional…
Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator…
For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as…
We present an asymptotically exact solution of a paradigmatic non-Hermitian model: the disordered interacting fermionic Hatano-Nelson model, or equivalently, the non-Hermitian spin-1/2 XXZ model. We use a renormalization group method suited…