Related papers: Exact solutions of time-dependent three-generator …
We explore the problem of time in quantum gravity in a point-particle analogue model of scale-invariant gravity. If quantized after reduction to true degrees of freedom, it leads to a time-independent Schr\"odinger equation. As with the…
A Charged harmonic oscillator in a magnetic field, Landau problems, and an oscillator in a noncommutative space, share the same mathematical structure in their Hamiltonians. We have considered a two-dimensional anisotropic harmonic…
In this second in a series of four articles we create a mathematical formalism sufficient to represent nontrivial hamiltonian quantum dynamics, including resonances. Some parts of this construction are also mathematically necessary. The…
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…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
In this paper we use a similarity transformation connecting some families of Nonlinear Schrodinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrodinger equation. This transformation allows one to apply…
We outline a general method for obtaining exact solutions of Schr\"{o}dinger equations with a position dependent effective mass and compare the results with those obtained within the frame of supersymmetric quantum theory. We observe that…
Consideration of the asteroid belt (Kuiper belt) as a jammed-granular media establishes a bridge between condensed matter physics and astrophysics. It opens up an experimental possibility to determine the deformation parameters for…
Semigroups describing the time evolution of open quantum systems in finite-dimensional spaces have generators of a special form, known as Lindblad generators. These generators and the corresponding processes of time evolution are analyzed,…
The approach of multi-dimensional SUSY Quantum Mechanics is used in an explicit construction of exactly solvable 3-body (and quasi-exactly-solvable $N$-body) matrix problems on a line. From intertwining relations with time-dependent…
Systems invariant under the reparametrization of time were treated as constrained systems within Hamilton-Jacobi formalism. After imposing the integrability conditions the time-dependent Schr\"odinger equation was obtained. Three examples…
The time-dependent variational principle is used to optimize the linear and nonlinear parameters of Gaussian basis functions to solve the time-dependent Schrodinger equation in 1 and 3 dimensions for a one-body soft Coulomb potential in a…
We show that Liouville-von Neumann approach to quantum mechanical systems, which demands the existence of invariant operators, reproduces the time-dependent variational Gaussian approximation. We find the effective action of the…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…
Quantum-mechanical WKB-method is elaborated for the known quantum oscillator problem in curved 3-spaces models Euclid, Riemann, and Lobachevsky E_{3}, H_{3}, S_{3} in the framework of the complex variable function theory. Generalized…
We focus on three-dimensional QRLG with the purpose of shedding light on the link between reduced LQG and LQC in four space-time dimensions. Considering homogeneous three-dimensional LQG, the theory simplifies to QRLG. We then implement…
It might seem that a choice of a time coordinate in Hamiltonian formulations of general relativity breaks the full four-dimensional diffeomorphism covariance of the theory. This is not the case. We construct explicitly the complete set of…
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…
The construction of exactly-solvable models has recently been advanced by considering integrable $T\bar{T}$ deformations and related Hamiltonian deformations in quantum mechanics. We introduce a broader class of non-Hermitian Hamiltonian…
New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.