相关论文: Bohr-Sommerfeld Quantization of Periodic Orbits

Since its first appearance in 1971, Gutzwiller's trace formula has been extended to systems with continuous symmetries, in which not all periodic orbits are isolated. In order to avoid the divergences occurring in connection with symmetry…

Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…

We place the hyperbolic quantum Ruijsenaars-Schneider system with an exponential Morse term on a lattice and diagonalize the resulting $n$-particle model by means of multivariate continuous dual $q$-Hahn polynomials that arise as a…

A series of quantization identities are established for static vortex solutions governed by the Born--Infeld type actions. These identities are of a universal nature which are indifferent to the details of the models and provide refined…

In this work, the conformable Bateman Lagrangian for the damped harmonic oscillator system is proposed using the conformable derivative concept. In other words, the integer derivatives are replaced by conformable derivatives of order…

A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…

The $\gamma$-metric, also known as Zipoy-Voorhees spacetime, is a static, axially symmetric vacuum solution to Einstein's field equations characterized by two parameters: mass and the deformation parameter $\gamma$. It reduces to the…

We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor using a discrete Hubbard-Stratonovich transformation, which allows us to express the Gutzwiller factor as a linear combination of unitary…

Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there…

Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical…

We present new periodograms that are effective in distinguishing Doppler shift from spectral shape variability in astronomical spectra. These periodograms, building upon the concept of partial distance correlation, separate the periodic…

We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…

Just like decent classical difference-difference systems define symplectic maps on suitable phase spaces, their counterparts with properly ordered noncommutative entries come as Heisenberg equations of motion for corresponding quantum…

The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…

A versatile and numerically inexpensive method is presented allowing the accurate calculation of phase diagrams for bosonic lattice models. By treating clusters within the Gutzwiller theory, a surprisingly good description of quantum…

We study baryon-baryon scattering by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. We derive the corresponding diagrammatic rules paying special…

We perform the canonical quantization of a relativistic spinless particle moving in a curved and static spacetime. We show that the classical theory already describes at the same time both particle and antiparticle. The analyses involves…

The efficacy and accuracy of Bogomolny's method of the quantum surface of section is evaluated by applying it to the quantization of the motion of a particle in a smooth 2-D potential. This method defines a transfer operator T in terms of…

We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally…

We show that for a particular model, the quantum mechanical bootstrap is capable of finding exact results. We consider a solvable system with Hamiltonian $H=SZ(1-Z)S$, where $Z$ and $S$ satisfy canonical commutation relations. While this…