Related papers: A variational approach for linearly dependent movi…
The Meta-Schr\"odinger algebra arises as the dynamical symmetry in transport processes which are ballistic in a chosen `parallel' direction and diffusive and all other `transverse' directions. The time-space transformations of this Lie…
For the unitary operator, solution of the Schroedinger equation corresponding to a time-varying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first order…
We study the time evolution of a density matrix in a quantum mechanical system described by an ergodic magnetic Schr\"odinger operator with singular magnetic and electric potentials, the electric field being introduced adiabatically. We…
By making use of the Lewis-Riesenfeld invariant theory, the solution of the Schr\"{o}dinger equation for the time-dependent linear potential corresponding to the quadratic-form Lewis-Riesenfeld invariant $I_{\rm q}(t)$ is obtained in the…
Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time dependent Schr\"odinger equation is an important and challenging problem in quantum mechanics and…
We have derived a variational principle that defines the nonequilibrium steady-state transport across a correlated impurity mimicking, e.g., a quantum dot coupled to biased leads. This variational principle has been specialized to a…
We propose a new approach that allows one to reduce nonlinear equations on Lie groups to equations with a fewer number of independent variables for finding particular solutions of the nonlinear equations. The main idea is to apply the…
We consider time-dependent Schr\"{o}dinger equations for a free nonrelativistic particle on the three-dimensional $q$-deformed Euclidean space. We determine plane wave solutions to these Schr\"{o}dinger equations and show that they form a…
The functional Schrodinger picture formulation of quantum field theory and the variational Gaussian approximation method based on the formulation are briefly reviewed. After presenting recent attempts to improve the variational…
Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a $d$-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new…
I point out that if one defines the operator $U_R(t)$ as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of $U_R(t)$ as given in his paper…
We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schroedinger equation with variable quadratic Hamiltonians. The Green…
The scaling functions of single-time and two-time correlators in systems undergoing non-equilibrium critical dynamics with dynamical exponent ${z}=2$ are predicted from a new time-dependent non-equilibrium representation of the…
We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time.…
The Schroedinger operator on the Newtonian space-time is defined in a way which is independent on the class of inertial observers. In this picture the Schroedinger operator acts not on functions on the space-time but on sections of certain…
A closed expression for the harmonic oscillator wave function after the passage of a linear signal with arbitrary time dependence is derived. Transition probabilities are simple to express in terms of Laguerre polynomials. Spontaneous…
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained…
In this paper, the trial function method is employed to find the exact solutions for high-order nonlinear Schr\"odinger equations with time-dependent coefficients. This system describes the propagation of ultrashort light pulses in…
We obtain time dependent $q$-Gaussian wave-packet solutions to a non linear Schr\"odinger equation recently advanced by Nobre, Rego-Montero and Tsallis (NRT) [Phys. Rev. Lett. 106 (2011) 10601]. The NRT non-linear equation admits plane…
Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…