Related papers: Jensen Inequalities for Tunneling Probabilities in…
We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the…
The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite…
Some tunneling phenomena are described, in the semiclassical approximation, by unstable complex trajectories. We develop a systematic procedure to stabilize the trajectories and to calculate the tunneling probability, including both the…
We prove a matrix inequality for convex functions of a Hermitian matrix on a bipartite space. As an application we reprove and extend some theorems about eigenvalue asymptotics of Schr\"odinger operators with homogeneous potentials. The…
A simple example of especially constructed potential barrier enables to show analytically (not numerically) the existence of tunneling effect for a Sommerfeld particle.
We investigate the tunneling process between two symmetric stable islands of a forced pendulum Hamiltonian in the weak chaos regime. We show that when the tunneling doublet is quantized over a classical non-linear resonance the tunneling…
We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the…
We consider in what sense quantum tunnelling is associated with non-classical probabilistic behaviour. We use the Wigner function quasi-probability description of quantum states. We give a definition of tunnelling that allows us to say…
In this note we prove Jensen-type inequality for certain non-convex functions. We apply our idea to prove some inequalities which were suggested at some high-level math olympiades.
Jensen's inequality, attributed to Johan Jensen -- a Danish mathematician and engineer noted for his contributions to the theory of functions -- is a ubiquitous result in convex analysis, providing a fundamental lower bound for the…
We give a general formulation of Jensen's operator inequality for unital fields of positive linear mappings, and we consider different types of converse inequalities.
The probabilities of tunnel ionization of particles confined by one-dimensional power-law and logarithmic potentials are calculated for constant and low-frequency electric fields.
The tunneling effect is the most popular phenomenon of quantum physics and is present in modern physical theories. Still, the most important features of this effect are already present in toy models - low dimensional quantum mechanics with…
Time evolution of tunneling phenomena in medium is studied using a standard model of environment interaction. A semiclassical formula valid at low, but finite temperatures is derived in the form of integral transform for the reduced Wigner…
A semiclassical method for the calculation of tunneling exponent in systems with many degrees of freedom is developed. We find that corresponding classical solution as function of energy form several branches joint by bifurcation points. A…
Despite quantum tunneling has been studied since the advent of quantum mechanics, the literature appears to contain no simple (textbook) formula for tunneling in generic asymmetric double-well potentials. In the regime of strong…
We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a…
It was found recently that processes of multidimensional tunneling are generally described at high energies by unstable semiclassical trajectories. We study two observational signatures related to the instability of trajectories. First, we…
Let $\mathcal{A}$ be a $C^*$-algebra and $\phi:\cA\to L(H)$ be a positive unital map. Then, for a convex function $f:I\to \mathbb{R}$ defined on some open interval and a self-adjoint element $a\in \mathcal{A}$ whose spectrum lies in $I$, we…
Classically allowed transport is shown to compete with quantum tunneling during the ionization of atoms by ultrashort and intense laser pulses, despite Keldysh parameters smaller than unity. This is done by comparing exact probability…