相关论文: On a Class of Quantum Canonical Transformations an…
This paper develops a systematic strong coupling spin wave expansion of itinerant Kondo lattice magnets, magnets in which local moment spins are Kondo coupled to itinerant charge degrees of freedom. The strong coupling expansion is based on…
We show that the isotropic harmonic oscillator in the ordinary euclidean space ${\bf R}^N$ ($N\ge 3$) admits a natural q-deformation into a new quantum mechanical model having a q-deformed symmetry (in the sense of quantum groups),…
Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model…
The Schr\"{o}dinger equation and ladder operators for the harmonic oscillator are shown to simplify through the use of an isometric conformal transformation. These results are discussed in relation to the Bargmann representation. It is…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and…
Linear Canonical Transformations (LCTs) are known in signal processing and optics as the generalization of certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the…
Two quantum theories are physically equivalent if they are related, not by a unitary transformation, but by an isometric transformation. The conditions under which a quantum canonical transformation is an isometric transformation are given.
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…
Recently\cite{BQG}, it was shown that quantum effects of matter could be identified with the conformal degree of freedom of the space-time metric. Accordingly, one can introduce quantum effects either by making a scale transformation (i.e.…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
The calculation of quantum canonical time correlation functions is considered in this paper. Transport properties, such as diffusion and reaction rate coefficients, can be determined from time integrals of these correlation functions.…
The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri…
The quantum harmonic oscillator is one of the most fundamental objects in physics. We consider the case where it is extended to an arbitrary number modes and includes all possible terms that are bilinear in the annihilation and creation…
The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time…
The Snyder model is an example of noncommutative spacetime admitting a fundamental length scale $\beta$ and invariant under Lorentz transformations, that can be interpreted as a realization of the doubly special relativity axioms. Here, we…
We consider a radiation from a uniformly accelerating harmonic oscillator whose minimal coupling to the scalar field changes suddenly. The exact time evolutions of the quantum operators are given in terms of a classical solution of a forced…
A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
In this work we take a closer look at the algebraic-operator correspondence between the momentum space and the position space which defines the form of the canonical momentum operator in position space in Quantum Mechanics (QM). Starting…