相关论文: Quantization via Classical Orbits
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
Let $\C$ be a sequence of multisets of subspaces of a vector space $\F_q^k$. We describe a practical algorithm which computes a canonical form and the stabilizer of $\C$ under the group action of the general semilinear group. It allows us…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
We review recent progress in the computation of leading quantum corrections to the energies of classical solitons with topological structure, including multi-soliton models in one space dimension and string configurations in three space…
Most modern calculations of many-electron atoms use basis sets of atomic orbitals. An accurate account for the electronic correlations in heavy atoms is very difficult computational problem and optimization of the basis sets can reduce…
Classical mechanics involves position and momentum variables that must be special coordinates chosen to promote to suitable quantum operators. Since classical variables may be broadly chosen, only unique variables should be chosen. We will…
Semiclassical quantization is exact only for the so called \emph{solvable} potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the semiclassical phase, given by a series in $\hbar$, yields more or less approximate…
We study the quantum probability to survive in an open chaotic system in the framework of the van Vleck-Gutzwiller propagator and present the first such calculation that accounts for quantum interference effects. Specifically we calculate…
Semiclassical spectra weighted with products of diagonal matrix elements of operators A_{alpha}, i.e., g_{alpha alpha'}(E) = sum_n <n|A_{alpha}|n><n|A_{alpha'}|n>/(E-E_n) are obtained by harmonic inversion of a cross-correlation signal…
We investigate quantum corrections to the classical work characteristic function (CF) as a semiclassical approximation to the full quantum work CF. In addition to explicitly establishing the quantum-classical correspondence of the…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
We compute the inclusive jet spectrum in the presence of a dense QCD medium by going beyond the single parton energy loss approximation. We show that higher-order corrections are important yielding large logarithmic contributions that must…
When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods…
The Planck or the quantum gravity scale, being $16$ orders of magnitude greater than the electroweak scale, is often considered inaccessible by current experimental techniques. However, it was shown recently by one of the current authors…
In the periodic orbit quantization of physical systems, usually only the leading-order hbar contribution to the density of states is considered. Therefore, by construction, the eigenvalues following from semiclassical trace formulae…
We make a critical review of the semiclassical interpretation of quantum cosmology and emphasise that it is not necessary to consider that a concept of time emerges only when the gravitational field is (semi)classical. We show that the…
The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One example of such a hybrid quantum-classical approach is the variational quantum eigensolver (VQE) built to…
For certain situations we give a geometrical background for quasiclassical KP calculations based on an explicit connection to quantum mechanics and the collapse of coherent states to coadjoint orbits for classical operators.