Related papers: $\hbar$ corrections in semi-classical formula for …
We consider Schr\"odinger equations and Fokker-Planck equations in one dimension, and study the low-energy asymptotic behavior of the Green function using a new method. In this method, the coefficient of the expansion in powers of the wave…
We report on the experimental investigation of the properties of the eigenvalues and wavefunctions and the fluctuation properties of the scattering matrix of closed and open billiards, respectively, of which the classical dynamics undergoes…
We have derived several relations, which allow the evaluation of the system free energy changes in the leading order in $\hbar^{2}$ along classically generated trajectories. The results are formulated in terms of purely classical…
An $\hbar$-expansion is presented for the ensemble-averaged spectral function of noninteracting matter waves in random potentials. We obtain the leading quantum corrections to the deep classical limit at high energies by the Wigner-Weyl…
An end-to-end strategy for hybrid quantum-classical computations of Green's functions in many-body systems is presented and applied to the pairing model. The scheme makes explicit use of the spectral representation of the Green's function,…
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…
A way of construction of semiclassical wave function (SWF) based on the Maslov - Fedoriuk approach is proposed which appears to be appropriate also for systems with chaotic classical limits. Some classical constructions called skeletons are…
We present a method for analytic continuation of retarded Green functions, including Euclidean Green functions computed using lattice QCD. The method is based on conformal maps and construction of an interpolation function which is analytic…
In this article, we consider fixed spin 1/2 particles interacting through the quantized electromagnetic field in a constant magnetic field. We give some asymptotic expansions for the ground state and the ground state energy of the…
We develop a formula for the diagonal values of the Hadamard coefficients associated to a normally hyperbolic operator on a globally hyperbolic spacetime in terms of the advanced and retarded Green's operators. We develop a local formula as…
An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…
We introduce an improved semiclassical dynamics approach to quantum vibrational spectroscopy. In this method, a harmonic-based phase space sampling is preliminarily driven toward non-harmonic quantization by slowly switching on the actual…
We propose a causality-based divide-and-conquer algorithm for nonequilibrium Green's function calculations with quantics tensor trains. This algorithm enables stable and efficient extensions of the simulated time domain by exploiting the…
The semiclassical formula for the quantum propagator in the coherent state representation $<\mathbf{z}'' | e^{-i\hat{H}T/\hbar} | \mathbf{z}'>$ is not free from the problem of caustics. These are singular points along the complex classical…
We consider a fractional Laplace equation and we give a self-contained elementary exposition of the representation formula for the Green function on the ball. In this exposition, only elementary calculus techniques will be used, in…
We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence…
We work out the perturbative expansion of quantum Liouville theory on the pseudosphere starting from the semiclassical limit of a background generated by heavy charges. By solving perturbatively the Riemann-Hilbert problem for the Poincare'…
We study scalar perturbations to a Robertson-Walker cosmological metric in terms of a pseudo-Newtonian potential, which emerges naturally from the solution of the field equations. This potential is given in terms of a Green function for…
The trace formula for the density of single-particle levels in the two-dimensional radial power-law potentials, which nicely approximate the radial dependence of the Woods-Saxon potential and quantum spectra in a bound region, was derived…
The quantum partition function at finite temperature requires computing the trace of the imaginary time propagator. For numerical and Monte Carlo calculations, the propagator is usually split into its kinetic and potential parts. A higher…