相关论文: Exact Bohr-Sommerfeld Conditions for the Quantum P…

We analyze the spectrum of the 3-site Bose-Hubbard model with periodic boundary conditions using a semiclassical method. The Bohr-Sommerfeld quantization is applied to an effective classical Hamiltonian which we derive using resonance…

In this paper we demonstrate the integrability of the Hamilton-Jacobi equation for two non-central potentials in spherical polar coordinates, and present complete solutions for the classically bound orbits. We then show that the…

A semiclassical Bohr-Sommerfeld approximation is derived for an N-particle, two-mode Bose-Hubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the `classical' dynamics of…

The stationary 1D Schr\"odinger equation with a polynomial potential $V(q)$ of degree N is reduced to a system of exact quantization conditions of Bohr-Sommerfeld form. They arise from bilinear (Wronskian) functional relations pairing…

The transfer operator due to Bogomolny provides a convenient method for obtaining a semiclassical approximation to the energy eigenvalues of a quantum system, no matter what the nature of the analogous classical system. In this paper, the…

We review an "exact semiclassical" resolution method for the general stationary 1D Schr\"odinger equation with a polynomial potential. This method avoids having to compute any Stokes phenomena directly; instead, it basically relies on an…

We present a complete, self-contained formulation of the Bohr--Sommerfeld quantization rule for a semiclassical self-adjoint $2 \times 2$ system on the real line, arising from a simple closed curve in phase space. We focus on the case where…

In this paper we characterize the Nazarov-Sklyanin hierarchy for the classical periodic Benjamin-Ono equation in two complementary degenerations: for the multi-phase initial data (the periodic multi-solitons) at fixed dispersion and for…

The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the…

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…

The bound-state problem for an uncharged massive scalar particle in the field of a naked Reissner-Nordstr\"om singularity is approached by means of the quasiclassical Bohr-Sommerfeld quantization. An approximate analytical expression for…

We consider a class of simple quasi one-dimensional classically non-integrable systems which capture the essence of the periodic orbit structure of general hyperbolic nonintegrable dynamical systems. Their behavior is simple enough to allow…

We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…

We present a generic Markovian master equation inducing the gradual classicalization of a bosonic quantum field. It leads to the decoherence of quantum superpositions of field configurations, while leaving the Ehrenfest equations for both…

We prove the existence of time-periodic, small amplitude solutions of autonomous quasilinear or fully nonlinear completely resonant pseudo-PDEs of Benjamin-Ono type in Sobolev class. The result holds for frequencies in a Cantor set that has…

The semiclassical quantization conditions for all partial waves are derived for bound states of two interacting anyons in the presence of a uniform background magnetic field. Singular Aharonov-Bohm-type interactions between the anyons are…

Bohr-Sommerfeld type quantization conditions of semiclassical eigenvalues for the non-selfadjoint Zakharov-Shabat operator on the circle are derived using an exact WKB method. The conditions are given in terms of the action associated with…

We present a method for computing first order asymptotics of semiclassical spectra for 1-D Bogoliubov-de Gennes (BdG) Hamiltonian from Supraconductivity, which models the electron/hole scattering through two SNS junctions. This involves: 1)…

We construct local solutions to the Benjamin-Ono equation for quasi-periodic initial data. The solution is unique among limits of smooth solutions and depends continuously on the data. Our result applies to a richer class of quasi-periodic…

Can classical systems be described analytically at all orders in their interaction strength? For periodic and approximately periodic systems, the answer is yes, as we show in this work. Our analytical approach, which we call the…