相关论文: Lower limit in semiclassical form for the number o…

We demonstrate how a certain new form of the quantization condition proposed earlier can be used outside the class of potentials for which this form ensures exact spectra. Taking this form as a base we get an improved interpolating…

We establish new bounds of the Sobolev norms of solutions of semilinear wave equations for data lying in the Hs, s<1, closure of compactly supported data inside a ball of radius R, with R a fixed and positive number. In order to do that we…

In this work, we study the semiclassical limit of cubic Nonlinear Schr\"odinger equations for mixed states. We justify the limit to a singular Vlasov equation (in which the force field is proportional to the gradient of the density), for…

Compact algebraic equations are derived, which connect the binding energy and the asymptotic normalization constant (ANC) of a subthreshold bound state with the effective-range expansion of the corresponding partial wave. These relations…

Using semi-classical formalism and asymptotic proliferation law of periodic orbits, we obtain an analytical expressions for the two-level cluster function, spectral form factor, level spacing distribution and the number variance for…

We derive semiclassical quantization conditions for systems with spin. To this end one has to define the notion of integrability for the corresponding classical system which is given by a combination of the translational motion and…

A certain modification of the semiclassical quantization condition based on the summarization of the known power expansion in the squared Planck constant is proposed. Corresponding deviation from exact spectra arises only together with the…

We use an improved version of the semiclassical method described in Refs. [1,2,3] to evaluate fusion cross sections in collisions of weakly bound nuclei. This version takes into account the static effects of the low breakup threshold, uses…

We consider the semiclassical (zero-dispersion) limit of the one-dimensional focusing Nonlinear Schroedinger equation (NLS) with decaying potentials. If a potential is a simple rapidly oscillating wave (the period has the order of the…

The purpose of this paper is to prove local upper and lower bounds for weak solutions of semilinear elliptic equations of the form $-\Delta u= c u^p$, with $0<p<p_s=(d+2)/(d-2)$, defined on bounded domains of $\RR^d$, $d\ge 3$, without…

This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…

In this paper we study the semiclassical limit of the Schr\"odinger equation. Under mild regularity assumptions on the potential $U$ which include Born-Oppenheimer potential energy surfaces in molecular dynamics, we establish asymptotic…

We consider semiclassically scaled Schrodinger equations with an external potential and a highly oscillatory periodic potential. We construct asymptotic solutions in the form of semiclassical wave packets. These solutions are concentrated…

We study a special kind of semiclassical limit of quantum dynamics on a circle and in a box (infinite potential well with hard walls) as the Planck constant tends to zero and time tends to infinity. The results give detailed information…

Recursion relations for integrals of amplitudes over the phase space, i.e. for partial wave amplitudes, are introduced. In their simplest form these integrals are proportional to the s-wave amplitudes and represent rigorous lower bounds on…

In this work, we study the electromagnetic energy and energy rate spectra produced by a point particle in the presence of plane wave fields. Our approach is based on a semiclassical formulation, in which the current distribution that…

We consider a quasi-classical version of the Alicki-Fannes-Winter technique widely used for quantitative continuity analysis of characteristics of quantum systems and channels. This version allows us to obtain continuity bounds under…

We place limits on semiclassical fluctuations that might be present in the primordial perturbation spectrum. These can arise if some signatures of pre-inflationary features survive the expansion, or could be created by whatever mechanism…

We point out a misleading treatment in the literature regarding to bound-state solutions for the $s$-wave Klein-Gordon equation with exponential scalar and vector potentials. Following the appropriate procedure for an arbitrary mixing of…

By converting the rectangular basis potential V(x,y) into the form as V(r)+V(r, phi) described by the pseudo central plus noncentral potential, particular solutions of the two dimensional Schrodinger equation in plane-polar coordinates have…