Related papers: Asymptotic formula for quantum harmonic oscillator…
Quantum particle is considered confined in a toy-model potential possessing multiple minima. For the specific choice of the family of potentials (in the form of harmonic oscillator plus several logarithmic infinitely high but penetrable…
In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is…
We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two…
It is shown, by considering the case of the harmonic oscillator, that quantum fluctuations may be the most significant contribution to the random walk of a single molecule. From this point, the controversy on the existence of a standard…
For the PT symmetric potential of Dorey, Dunning and Tateo we show that in the large angular momentum (i.e., strongly spiked) limit the low-lying eigenstates of this popular non-Hermitian problem coincide with the shifted Hermitian harmonic…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
We present a theory of quantum oscillations in insulators that are particle-hole symmetric and non-topological but with arbitrary band dispersion, at both zero and non-zero temperature. At temperatures $T$ less than or comparable to the…
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…
We consider semiclassical self-adjoint operators whose symbol, defined on a two-dimensional symplectic manifold, reaches a non-degenerate minimum $b_0$ on a closed curve. We derive a classical and quantum normal form which allows us, in…
In generic Hamiltonian systems tori of regular motion are dynamically separated from regions of chaotic motion in phase space. Quantum mechanically these phase-space regions are coupled by dynamical tunneling. We introduce a semiclassical…
We calculate the susceptibility of a canonical ensemble of quantum oscillators to the singular random metric. If the covariance of the metric is $\vert {\bf x}-{\bf x}^{\prime}\vert^{-4\alpha}$ $0< \alpha<\frac{1}{2}$ then the expansion of…
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…
The tunneling through an opaque barrier with a strong oscillating component is investigated. It is shown, that in the strong perturbations regime (in contrast to the weak one), higher perturbations rate does not necessarily improve the…
In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how…
Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain…
Some aspects of asymptotic freedom are discussed in the context of a simple two-particle non-relativisitic confining potential model. In this model asymptotic freedom follows from the similarity of the free-particle and bound state radial…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…
When a non-hermitian hamiltonian has a certain symmetry, such as the PT pseudo-hermiticity, it is still possible that the hamiltonian has a real spectrum. In this note, by adding an imaginary potential proportional to ip_1p_2 to the…
We study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal…
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even…