相关论文: Stochastic Quantization of the Time-Dependent Harm…
We outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general (possibly non-Hermitian) Hamiltonian. For a class of such Hamiltonians this expansion involves a…
Time dependent entropy of harmonic oscillator with time dependent mass and frequency are investigated. The joint entropy so called Leipnik's entropy is calculated by using time dependent wave function obtained by the Feynman path integral…
We take a qualitative comparative look at quantum and classical quartic anharmonic oscillators. It has been shown that the behavior of the quantum anharmonic oscillator mimics that of the classical anharmonic oscillators with the…
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 present quantum algorithms for simulating the dynamics of a broad class of classical oscillator systems containing $2^n$ coupled oscillators (Eg: $2^n$ masses coupled by springs), including those with time-dependent forces, time-varying…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
We construct a relativistically covariant stochastic model for systems of non-interacting spinless particles whose number undergoes random fluctuations. The model is compared with the canonical quantization of the free scalar field in the…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
The dynamics of qubits coupled to a harmonic oscillator with time-periodic coupling is investigated in the framework of Floquet theory. This system can be used to model nonadiabatic phenomena that require a periodic modulation of the…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions is proved by an extension of the Ovsyannikov method. This…
We study a pair of canonoid (fouled) Hamiltonians of the harmonic oscillator which provide, at the classical level, the same equation of motion as the conventional Hamiltonian. These Hamiltonians, say $K_{1}$ and $K_{2}$, result to be…
We study the treatment of the constraints in stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking account of the Ito calculus. Then we obtain an…
The procedure of the "quantum" linearization of the Hamiltonian ordinary differential equations with one degree of freedom is introduced. It is offered to be used for the classification of integrable equations of the Painleve type. By this…
We present a theory of resonances for a class of non-autonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed autonomous Hamiltonian. The mechanism of…
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…
We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the…
Recently, an application of the numerical bootstrap method to quantum mechanics was proposed, and it successfully reproduces the eigenstates of various systems. However, it is unclear why this method works. In order to understand this…
It is desirable to observe synchronization of quantum systems in the quantum regime, defined by low number of excitations and a highly non-classical steady state of the self-sustained oscillator. Several existing proposals of observing…
Quantization of electromagnetic fields is investigated in the framework of stochastic variational method (SVM). Differently from the canonical quantization, this method does not require canonical form and quantization can be performed…
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…