相关论文: Ermakov approach for the one-dimensional Helmholtz…

We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we…

In this note we address the exact solutions of a time-dependent Hamiltonian composed by an oscillator-like interaction with both a frequency and a mass term that depend on time. The latter is achieved by constructing the appropriate point…

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…

We propose an approach to quantum cosmology of integrable models. To analyze the models with two dynamical variables, we introduce equivalent Hamiltonians in reduced phase spaces, which are obtained with the aid of the Faddeev--Jackiw…

Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between…

In this paper, we attack the specific time-dependent Hamiltonian problem H=-{1/2}e^{\Upsilon(t-t_o)}\partial_{xx} +\lfrac{1}{2}\omega^2e^{-\Upsilon(t-t_o)}x^2. This corresponds to a time-dependent mass (TM) Schr\"odinger equation. We give…

This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…

We analyze the consistency of the ADM approach to KK model; we prove that KK reduction commute with ADM splitting. This leads to a well defined Hamiltonian; we provide the outcome. The electromagnetic constraint is derived from a…

We consider the $m$-dimensional modified Helmholtz equation and establish two relations between its solutions in a bounded domain and harmonic functions. Both relations essentially rely on properties of the Newtonian potential. Some other…

Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…

We investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schreodinger time-evolution…

Positive-energy solutions of the Klein-Gordon equation form a Hilbert space of holomorphic functions on the future tube. This domain is interpreted as an extended phase space for the associated classical particle, the extra dimensions being…

Time-dependent quantities are calculated in the linear response limit for a correlated one dimensional model atom driven by an external quadrupolar time-dependent field. Besides the analysis of the time-evolving energy change in the…

The Hamiltonian dynamics associated to classical, planar, Heisenberg XY models is investigated for two- and three-dimensional lattices. Besides the conventional signatures of phase transitions, here obtained through time averages of…

In this paper, we present the point symmetry group of three-dimensional homogeneous Helmholtz equation, when we consider the cylindrical coordinate system. In continuation, we present a complete set of functionally independent invariants of…

We construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time-independent, local, one-dimensional, and translation invariant. As a…

We write the Hamiltonian for a gravitational spherically symmetric scalar field collapse with massive scalar field source, and we discuss the application of Wheeler De Witt equation as well as the appearence of time in this context. Using…

The web page contains both the dvi and postscript version of the paper. This paper presents the method of applying the Melnikov method to autonomous Hamiltonian systems in dimension four. Besides giving an application to Celestial…

The common treatment of time-dependent potentials, such as those used for radio frequency cavities, is to average a potential's time component through the interval that the reference particle spends in the cavity. Such an approach, using…

The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present…